Alta - Ch. 2 - Descriptive Statistics

A data set is summarized in the frequency table below. The data set contains a total of 40 data values. What is the missing frequency?

$6$6​ The total number of data values is the sum of all the frequencies. We are told the data set contains a total of 40 data values. The seven given values add to 4+6+7+3+5+4+5=34, so the missing frequency is 40−34=6.

Porter is keeping track of the total number of books he has read over time. The line graph below shows the data. How many books did Porter read from month 2 to 5? Do not include the unit in your answer.

$7$7​ We can see that at month 2 the value is 4 and at month 5 the value is 11, so the difference is 7.

Marc is keeping track of the total number of movies he has watched over time. The line graph below shows the data where the number of movies corresponds to the number of movies that had been watched at the beginning of the week shown on the horizontal axis. How many movies did Marc watch between the beginning of week 1 and the beginning of week 5? Do not include the unit in your answer

$7$7​ We can see that at week 1 the value is 2 and at week 5 the value is 9, so the difference is 7.

The following data set provides bitcoin transactions throughout 2016 and 2017. What is the cumulative relative frequency for transactions between 300,000 and 349,999 in May 2017? Give your answer as a percentage rounded to the nearest whole number, but do not include the percent sign.

$73$73​ Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in the table.

A group of students were surveyed about the number of times they went to a movie theater last year. Their responses are summarized in the relative frequency table below. What is the missing relative frequency?

1$0.24$0.24​ The relative frequency of a data value is the proportion of times that data value appears in the data set. So the relative frequencies should sum to 1.00, or 100%. Number of MoviesRelative Frequency0−10.082−30.204−50.306−7□8−90.1010 or more0.08 The given relative frequencies sum to 0.08+0.20+0.30+0.10+0.08=0.76, so the missing relative frequency is 1.00−0.76=0.24.

A group of students were surveyed about the number of times they went to a movie theater last year. Their responses are summarized in the relative frequency table below. What is the cumulative relative frequency of students that went to 5 or fewer movies?

1$0.55$0.55​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. The Cumulative Relative Frequency of students that went to 5 or fewer movies is the sum of the first three Relative Frequencies: 0.05+0.23+0.27=0.55.

The values and relative frequencies for a set of data are shown below. Complete the cumulative relative frequency table.

1$0.73$0.73​ 2$1.00$1.00​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find the values in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. Data ValueRelative FrequencyCumulative Relative Frequency10.240.2420.320.5630.170.7340.271.00 The cumulative relative frequencies are: 0.240.24+0.32=0.560.24+0.32+0.17=0.730.24+0.32+0.17+0.27=1.00.

The ages of the students in an art class at the community center are listed below. 9,11,14,14,16,21,24,26,32,33,37,38,38,52,53,55 Complete the frequency table.

1$1$1​ 2$4$4​ 3$0$0​ The data is already ordered from least to greatest: 9,11,14,14,16,21,24,26,32,33,37,38,38,52,53,55 In the data range 0−9, there is 1 value: 9. In the data range 10−19, there are 4 data values: 11,14,14,16. In the data range 20−29, there are 3 data values: 21,24,26. In the data range 30−39, there are 5 data values: 32,33,37,38,38. In the data range 40−49, there are 0 data values. In the data range 50−59, there are 3 data values: 52,53,55.

The following data set provides bitcoin transactions throughout 2016 and 2017. What is the ratio of days of transactions between 200,000 and 249,999 conducted in May 2017 as compared to April 2017?

1:8 In May 2017, one day had a transaction between 200,000 and 249,999. In April 2017, eight days had transactions between 200,000 and 249,999.

A data set is summarized in the frequency table below. Using the table, determine the number of values greater than or equal to 8. Give your answer as a single number. For example if you found the number of values was 33, you would enter 33.

27 $27$27​ The relevant values are highlighted in the table below. Summing the frequencies for these values, we find 4+6+8+4+5=27

Given the following histogram for a set of data, how many values in the data set are greater than 10.5 but less than 12.5?

5 Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So to find the number of values which are greater than 10.5 but less than 12.5, we look at the heights of the bars between those values and add them. 2+3=5

The following data set provides bitcoin transactions throughout 2016 and 2017. What is the ratio of days of transactions between 250,000 and 299,999 conducted in May 2017 as compared to April 2017?

5:13 In May 2017, five days had transactions between 250,000 and 299,999. In April 2017, thirteen days had transactions between 250,000 and 299,999.

A data set is summarized in the frequency table below. Using the table, determine the number of data values less than or equal to 5. Give your answer as a single number. For example if you found the number of values was 19, you would enter 19.

$16$16​ To find the number of data values less than or equal to 5, we add the frequencies for the values 3, 4, and 5. The relevant values are highlighted in the table below. Summing the frequencies for these values, we find 9+4+3=16

Given the frequency table, how many times does the data value 3 show up in the data set?

4 The frequency column in a frequency table shows how many times that data value shows up in the data set.

The bar graph below shows the number of men and women in different classes. What is the total number of women across all the classes shown? Do not include the units in your answer

To find the total number of women across all of the classes shown, you should find the height of the red bar from each group and add them. This comes out to 10+16+15=41.

Which of the following sets of data should not be displayed with a pie chart? Assume that only the two given categories will be included.

the percentage of people that own dogs and the percentage of people that own cats A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

A group of students were surveyed about the number of books they read last summer. Their responses are summarized in the relative frequency table below. What is the cumulative relative frequency of students that read 5 or fewer books?

$0.76$0.76​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. The Cumulative Relative Frequency of students that read 5 or fewer books is the sum of the first three Relative Frequencies: 0.08+0.36+0.32=0.76

Carrie is a salesperson who earns a commission on every unit she sells. The number of units Carrie sells per week for half of a year are given in the table below Use Excel to create a line graph for the data. How many times does the number of units sold increase from a number below 12 to a number above 12?

$5$5​ 1. Copy the weeks and the number of sales into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in these two columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on Line to create a line graph, and select the first option. Observe the graph and find the number of spikes in the graph where the number of units sold increased from below 12 to above 12. Since this happens 5 times, there are 5 times where the number of units sold increased from below 12 to above 12.

The cumulative relative frequency table for a set of data is shown below. What is the missing cumulative relative frequency?

0.6 The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. The missing Cumulative Relative Frequency is the sum of the first two Relative Frequencies: 0.35+0.25=0.60

The frequency table below shows the ages of the students in a psychology lecture hall. Complete the Relative Frequency column of the table. Do not round.

1$0.075$0.075​ 2$0.225$0.225​ Add the frequencies to find total number of data values in the set of data. 9+18+27+30+21+15=120 Dividing each frequency by this total gives the relative frequency. AgeFrequency RelativeFrequency 1799120=0.075181818120=0.15192727120=0.225203030120=0.25212121120=0.175221515120=0.125

For which of the following sets of data is a pie chart appropriate? Assume that only the two given categories will be included.

the percentage of students with known food allergies and the percentage of students without known food allergies A pie chart is only appropriate when the data categories account for the entirety of the sample. A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

Given the frequency table below, what is the relative frequency of the data value 7?

$0.15$0.15​ Add the frequencies to find total number of data values in the set of data. 7+6+4+3=20 Dividing each frequency by this total gives the relative frequency. The data value 7 occurs with frequency 3, so the relative frequency for the value 7 is3/20=0.15

The following data set provides bitcoin transactions throughout 2016 and 2017. What is the relative frequency for transactions between 350,000 and 399,999 in May 2017? Give your answer as a decimal to the nearest hundreth.

$0.27$0.27​ To find the relative frequency of all data values, divide each frequency by the total number of data values in the sample-in this case, 26. An additional column is added to the right side of the frequency table for the data. This is called a relative frequency table.

A clothing designer would like to determine which dress color in a particular design is the most popular. The colors that the dress comes in and the number of sales of this dress in each color are given in the table below.

$5$5​ 1. Copy the dress colors and the number of times each color was purchased into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in these two columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on Line to create a line graph. In this case, click on Line with Markers to be able to see the markers where each of the data values lie. Notice that the marker over the blue label is at 30. There are five markers that are higher than the marker for the blue dresses. Therefore, there are five colors that have more sales than the blue dress.

Carrie is a salesperson who earns a commission on every unit she sells. The number of units Carrie sells per week for half of a year are given in the table below.

$5$5​ 1. Copy the weeks and the number of sales into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in these two columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on Line to create a line graph, and select the first option. Observe the graph and find the number of spikes in the graph where the number of units sold increased from below 12 to above 12. Since this happens 5 times, there are 5 times where the number of units sold increased from below 12 to above 12.

James is a computer technician who thinks that he is seeing an unusual number of viruses on the computers he is fixing. He compiles the number of viruses found on the last 20 computers in the following table.

$8$8​ 1. Copy the data into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in these two columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on Column to create a bar graph. Notice that eight of the bars have a height that is below 2. Therefore, eight of the computers had fewer than two viruses.

An insurance company hires an analytics company to collect data on various factors affecting the health of its customers and potential customers. One question they sought to answer was how many hours a week adults are exercising. The company they hired used their own database of email addresses to send out a survey to a random sample. The responses from 31 of the surveys are included below. Create a dot plot of the dataset using Excel. Choose the correct dot plot below.

To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 enter "=COUNTIF($A$2:$A2,A2)". 3. Copy and paste B2 to each cell below B2 that is adjacent to thedata in column A. This counts the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. The dot plot should look like the following image.

David conducted a survey in which he collected data on the percentage of students that have science majors and the percentage of students that have humanities majors. Which of the following could sufficiently display the data if only the two given categories are to be included?

bar graph The two given categories of data could potentially have overlap. In addition to this, it is likely that there are individuals that do not belong to either category. In this sense, the percentages will not account for 100% of the individuals sampled and a pie chart will not sufficiently display the data. A bar graph should be used.

The cumulative relative frequency table for a set of data is shown below. What is the missing cumulative relative frequency?

$0.6$0.6​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. The missing Cumulative Relative Frequency is the sum of the first three Relative Frequencies: 0.1+0.2+0.3=0.6

A data set is summarized in the frequency table below. Using the table, determine the total number of values in the data set that are less than or equal to 7.

$19$19​ The relevant values are highlighted in the table below. Summing the frequencies for these values, we find 8+4+3+2+2=19

The relative frequencies for a set of data are shown in the table below. If there are a total of 20 data values, with what frequency does the data value 3 occur?

$9$9​ Dividing each frequency by the total number of data values gives the relative frequency. So multiplying the relative frequency by the total number of data values gives the frequency. The data value 3 occurs with relative frequency 0.45 in a data set of 20 values, so the frequency of the data value 3 is 0.45(20)=9 . The data value 3 occurs 9 times.

Given the frequency table below, what is the relative frequency of the data value 8?

$\frac{6}{30}$630​​ Add the frequencies to find total number of data values in the set of data. 2+7+9+6+6=30 Dividing each frequency by this total gives the relative frequency. The data value 8 occurs with frequency 6, so the relative frequency for the value 8 is6/30=0.2

The bar graph below shows the number of men and women in different groups. What is the total number of men across all the groups shown? Do not include the units in your answer.

Correct answers:$29$29​ To find the total number of men across all of the groups shown, you should find the height of the blue bar from each group and add them. This comes out to 13+16=29.

Several executives were asked how many suits they own. The results are tabulated in the following frequency table. Which histogram accurately summarizes the data?

Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So for example, to find the first bar, which has values greater than 7.5 but less than 8.5, we note that the frequency for 8 is 6, so the height of that bar is 6.

The students in a gym class measured the length of their longest jump (in feet). The results were tallied and are reported in the following histogram. How many students jumped greater than 8.5 but less than 11.5 feet?

Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So to find the number of values which are greater than 8.5 but less than 11.5, we look at the heights of the bars between those values and add them. 3+3+1=7

The sales department from Real Madrid wants to find the relationship between memorabilia sales and number of goals during games. The first part of the research is to determine the frequency of goals per game. The frequency table below shows the number of goals Real Madrid scored in each of their soccer games in April and May of 2015. Given the frequency table below, which of the following is the corresponding relative frequency table?

Value0123479Frequency 0.071 0.214 0.143 0.286 0.143 0.071 0.071 By adding the frequencies, we see that there are a total of 14 games in the set of data. Dividing each frequency by this total gives the relative frequency. So, the relative frequency for the value 0 is 114=0.071 The relative frequency for the value 1 is 314=0.214 Continuing in this manner you find that the second answer choice has the correct relative frequency table.

A university is hosting a summer camp for various age groups. The table below gives the relative frequency distribution for the various age groups who have registered for the camp. It is known that 50 individuals have registered for the camp. How many individuals are between the ages of 9 and 11 years old?

We are told the total number of individuals who have currently registered for the camp, and, from the table, we know that 40% of these individuals are between the ages of 9 and 11 years old. To determine the frequency of registered 9 to 11 years old, we find the product of the total number of registered individuals and the relative frequency of 9 to 11 year-olds. (50)(0.40)=20 Thus, 20 individuals between the ages of 9 to 11 year-olds have registered for the summer camp.

Given the frequency table below, what is the relative frequency of the data value 1?

$\frac{6}{25}$625​​ Add the frequencies to find total number of data values in the set of data. 6+5+5+2+7=25 Dividing each frequency by this total gives the relative frequency. The data value 1 occurs with frequency 6, so the relative frequency for the value 1 is625=0.24

According to the information above, which of the following is an appropriate analysis of the snowfall amounts?

From the data, there was fluctuating snowfall during the five days. The y-values represent the snowfall amounts each day. As you move from left to right along the x-axis, the y-values fluctuate up and down. For example, at day 1, there was 2 inches of snowfall. At day 2, there was 6 inches of snowfall, but by day 3, the snowfall amount dropped to 2 inches.

A travel agency is conducting research on how many times families went on vacation during the last year. The following table shows the number of times sampled families went on vacation.

Remember that the height of each bar in a bar graph equals the number of values that fall in that bar category. So for example, to find the first bar, which represents no vacations, we note that the frequency for no vacations is 3 in the table, so the height of that bar is 3. Therefore, 3 families did not go on vacation during the last year

The ages of the students in a creative writing seminar are listed below. 17,22,20,18,19,20,17,17,22,18,20,18,17,18,21,18,18,19,19,19,20,19,21,21 Complete the frequency table.

The frequency of a data value is the number of times it appears in the data set. Count the number of time each age appears in the list. 17,22,20,18,19,20,17,17,22,18,20,18,17,18,21,18,18,19,19,19,20,19,21,21 The age 17 appears 4 times. The age 18 appears 6 times. The age 19 appears 5 times. The age 20 appears 4 times. The age 21 appears 3 times. The age 22 appears 2 times.

A set of data is summarized by the stem and leaf plot below. Stem12Leaf26688899900112455567

There are 1$$ values in the data set which are greater than or equal to 10 and less than or equal to 19. There are 2$$ values in the data set which are greater than or equal to 20 and less than or equal to 29. Correct answers:1$9$9​2$11$11​ Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 9 entries in the leaf column of the first row (with stem 1), so there are 9 values in the data set which are greater than or equal to 10 and less than or equal to 19.

Jason polled a large sample of students to find the percentage of in-state students and the percentage of out-of-state students. Which data display(s) could sufficiently display the data if only the two given categories are to be included?

either a pie chart or a bar graph Each person surveyed must fit in exactly one of given data categories. This implies that the percentages must account for 100% of the individuals in the sample. Therefore, either a bar graph or a pie chart will sufficiently display the data.

Which of the following sets of data should not be displayed with a pie chart? Assume that only the two given categories will be included.

the percentage of people who have a full-time job and the percentage of people who have a part-time job A pie chart is not appropriate if the given data has percentages that sum to more than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient. In the case above, it is possible that a single individual could have both a full-time job and a part-time job, which would make the percentages sum to more than 100%.

Gail is a car salesperson, who keeps track of her sales over time. The line graph below shows the data for the number of cars she sells per week. At what week were her sales 8? Do not include the unit in your answer.

$5$5​ By looking horizontally from the y-axis value 8, we can see that the corresponding value of time is 5.

A small accounting firm serving individuals and small businesses is preparing for tax season. One of the initiatives for this year is a Premium Program for clients with an income of $150,000 or more a year. To prepare an objective goal setting in the new program, the managers at the firm used the data for the first 10 weeks from last year's season. In the table, the data represents the amount of clients per week with an income of $150,000 or more. Given the cumulative relative frequency table below, what number is missing from the fourth row of the right column?

0.80 Cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the corresponding row and all previous rows.

The values and relative frequencies for a set of data are shown below. Complete the cumulative relative frequency table.

1$0.19$0.19​ 2$0.83$0.83​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find the values in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. The cumulative relative frequencies are: 0.190.19+0.35=0.540.19+0.35+0.29=0.830.19+0.35+0.29+0.17=1.00.

A group of students were surveyed about the number of books they read last summer. Their responses are summarized in the relative frequency table below. What is the cumulative relative frequency of students that read 7 or fewer books?

1$0.83$0.83​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. Number of BooksRelative FrequencyCumulative Relative Frequency0−10.070.072−30.340.414−50.270.686−70.150.838−90.110.9410 or more0.061.00 The Cumulative Relative Frequency of students that read 7 or fewer books is the sum of the first four Relative Frequencies: 0.07+0.34+0.27+0.15=0.83

The following data set provides bitcoin transactions throughout 2016 and 2017. What is the ratio of days of transactions between 300,000 and 349,999 conducted in May 2017 as compared to April 2017?

13:9 In May 2017, 13 days had transactions between 300,000 and 349,000. In April 2017, 9 days had transactions between 300,000 and 349,000.

According to the data given in the previous question, what can the travel agency conclude about the sampled families?

According to the data, a majority of the sampled families went on vacation at least twice. 18 families went on vacation at least twice. Since 32 families were sampled by the travel agency, 18 families represent a majority of the families sampled. Therefore, according to this data, a majority of the sampled families went on vacation at least twice.

If the gym was going to expand only one part of their gym to provide more space, which area should they most likely expand?

According to the data, the gym should expand the runner's track. According to the data, if the gym could only expand one room, the gym should expand the track. 22 people chose running as their preferred work-out, which has the highest bar in the bar graph.

Students at Bruce's school are allowed to play more than one sport. So, Brent polled a large sample of students to find how many students were on each sports team at the high school - basketball, volleyball, baseball, and hockey. Which of the following could sufficiently display the data if only the four given categories are to be included?

Bar Graph As long as there is no overlap of data values (i.e. a data value does not fall into two different categories), you may use either a bar graph or a pie chart. But, in this case, students can play more than one sport, and so one data value (or student) could fall in two or more categories. So, it is better to use a bar graph. A pie chart with overlapping data values can be misleading.

Bar graph: a graph to summarize and organize categorical data consisting of rectangular bars that are separated from each other and the length (or height) of the bar for each category is proportional to the number or percent of individuals in each categoryA Bar graph may also be referred to as a Bar chart Categorical data: data separated into qualitative categories Pie chart: a type of graph where a circle is divided into sectors, or slices, which each show the proportion of that subcategory compared to the wholeA Pie chart may also be referred to as a Pie graph or a Circle graph Line graph: a bar graph with the tops of the bars represented by points joined by lines (with rest of the bar not shown) and are only appropriate for ordered (rather than qualitative) variables that show how a quantity changes over timeA Line graph may also be referred to as a Line chart or as a Time series graph

Bar graph: a graph to summarize and organize categorical data consisting of rectangular bars that are separated from each other and the length (or height) of the bar for each category is proportional to the number or percent of individuals in each categoryA Bar graph may also be referred to as a Bar chart Categorical data: data separated into qualitative categories Pie chart: a type of graph where a circle is divided into sectors, or slices, which each show the proportion of that subcategory compared to the wholeA Pie chart may also be referred to as a Pie graph or a Circle graph Line graph: a bar graph with the tops of the bars represented by points joined by lines (with rest of the bar not shown) and are only appropriate for ordered (rather than qualitative) variables that show how a quantity changes over timeA Line graph may also be referred to as a Line chart or as a Time series graph

According to the information above, which of the following is an appropriate analysis of the taxi's distance?

From the data, the taxi was farthest, in miles, from the depot after 5 hours. At hour 5, along the x-axis, the taxi was 10 miles from the taxi depot. 10 is the largest y-value plotted on the line graph, which is the farthest distance (in miles) the taxi traveled from the depot.

The Terman Study of the Gifted followed children who scored above a certain level on an I.Q. test into adulthood. The study collected information on the same participants, including the average height of the group, approximately every five years. Which of the following could best display how the average height of participants changes over time?

Line graph Line graphs are best used to show comparison of a changing quantity over time. The x-axis on the line graph could represent the year of the study, while the y-axis could show the average height of participants that year. A bar graph could display the data, with each bar as a different year, but would not be as effective in showing the increase or decrease over time as a line graph. A pie chart would not have been appropriate, since there is not a "whole" to which you can compare each category.

A chess club meets every month and the members each tally how many times they won a game of chess during the past month. The following table shows the number of wins for each member of the club. Create the corresponding bar graph to represent this data below. Drag the dots on the top of the bar graph to create the chart.

Remember that the height of each bar in a bar graph equals the number of values that fall in that bar category. So for example, to find the first bar, which represents the number of wins for Joe, we note that the frequency for wins by Joe is 0 in the table, so the height of that bar is 0. Therefore, Joe won 0 games of chess during the past month. joe-0 aaron-6 karen-7 michelle-7 barbara-12

Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table? Value- Frequency 2-0.23 3-0.33 4-0.23 5-0.21

ValueFrequency20.2330.5640.7951 Remember that a cumulative frequency table adds the relative frequencies for the previous entries in the table. For example, the entry for the value 4 is 0.23+0.33+0.23=0.79 This cumulative frequency table could be used by a Hotel to see the percentage of customers that rate the hotel at each star level. For example, at the 4 star, 79% of people voting have the hotel at 4 stars or less. This could show the Hotel if improvements are needed.

Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table? Value Frequency 4-0.35 5-0.2 6-0.05 7-0.4

ValueFrequency40.3550.5560.671 Remember that a cumulative frequency table adds the relative frequencies for the previous entries in the table. For example, the entry for the value 6 is 0.35+0.2+0.05=0.6

Deborah polled a large sample of individuals to find the percentage of people who jog more than three times a week and the percentage of people who lift weights more than three times per week. Which of the following could sufficiently display the data if only the two given categories are to be included?

bar graph The two given categories of data could potentially have overlap. In addition to this, it is likely that there are individuals that do not belong to either category. In this sense, the percentages will not account for 100% of the individuals sampled and a pie chart will not sufficiently display the data. A bar graph should be used.

Karen polled a large sample of individuals to find the percentage of people who own cell phones and the percentage of people who own tablets. Which of the following could sufficiently display the data if only the two given categories are to be included?

bar graph The two given categories of data could potentially have overlap. In addition to this, it is likely that there are individuals that do not belong to either category. In this sense, the percentages will not account for 100% of the individuals sampled and a pie chart will not sufficiently display the data. A bar graph should be used.

Virginia polled a large sample of individuals to find the percentage of students with known food allergies and the percentage of students without known food allergies. Which of the following could sufficiently display the data if only the two given categories are to be included?

either a pie chart or a bar graph Each person surveyed must fit in exactly one of given data categories. This implies that the percentages must account for 100% of the individuals in the sample. Therefore, either a bar graph or a pie chart will sufficiently display the data.

Which of the following sets of data should not be displayed with a pie chart? Assume that only the two given categories will be included

the percentage of people that own dogs and the percentage of people that own cats A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient. Your answer: the percentage of people that support a new speed limit law and the percentage of people who oppose the new speed limit law

For which of the following sets of data is a pie chart appropriate? Assume that only the two given categories will be included.

the percentage of people that support a new speed limit law and the percentage of people who oppose the new speed limit law A pie chart is only appropriate when the data categories account for the entirety of the sample. A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

A group of students were surveyed about the number of pets they have. Their responses are summarized in the relative frequency table below. What is the missing relative frequency?

$0.35$0.35​ The relative frequency of a data value is the proportion of times that data value appears in the data set. So the relative frequencies should sum to 1.00, or 100%. Number of PetsRelative Frequency00.301□20.153 or more0.20 The given relative frequencies sum to 0.30+0.15+0.20=0.65, so the missing relative frequency is 1.00−0.65=0.35.

The cumulative relative frequency table for a set of data is shown below. What is the missing cumulative relative frequency?

$0.42$0.42​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. The missing Cumulative Relative Frequency is the sum of the first two Relative Frequencies: 0.18+0.24=0.42

A group of students were surveyed about the number of times they went to a movie theater last year. Their responses are summarized in the relative frequency table below. What is the cumulative relative frequency of students that went to 7 or fewer movies?

$0.82$0.82​ The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. The Cumulative Relative Frequency of students that went to 7 or fewer movies is the sum of the first four Relative Frequencies: 0.08+0.20+0.30+0.24=0.82

Several people were asked to report the number of hours of sleep they average per night. The results are shown in the histogram below. How many of those people average greater than 4.5 but less than 6.5 hours of sleep per night?

$11\text{ people}$11 people​ Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So to find the number of values which are greater than 4.5 but less than 6.5, we look at the heights of the bars between those values and add them. 7+4=11

The students in a first-grade class were all asked to time how long (in seconds) they could hold their breath. The results were tallied and are presented in the following histogram. How many of those students held their breath greater than 12.5 but less than 15.5 seconds?

$13\text{ students }$13 students ​ Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So to find the number of values which are greater than 12.5 but less than 15.5, we look at the heights of the bars between those values and add them. 2+5+6=13

The sales department from Real Madrid wants to find the relationship between memorabilia sales and number of goals during games. The first part of the research is to determine the frequency of goals per game. The frequency table below shows the number of goals Real Madrid scored in each of their soccer games in April and May of 2015. Determine the total number of data values (games) represented in the table.

$14$14​ The sum of the numbers in the Frequency column represent the total number of data values in the set. 1+3+2+4+2+1+1=14 So, there are 14 total data values in this set.

Alice is keeping track of the total number of books she has read over time. The line graph below shows the data. How many books did Alice read from month 2 to 3? Do not include the unit in your answer.

$2$2​ We can see that at month 2 the value is 4 and at month 3 the value is 6, so the difference is 2.

A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6. Give your answer as a single number. For example if you found the number of values was 14, you would enter 14.

$20$20​ The relevant values are highlighted in the table below. Summing the frequencies for these values, we find 5+3+2+3+4+3=20

The students in a gym class were timed to see how long (in minutes) it took them to run one mile. The results are displayed in the following histogram. How many students took greater than 6.5 but less than 9.5 minutes to run a mile?

$21\text{ students }$21 students ​ Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So to find the number of values which are greater than 6.5 but less than 9.5, we look at the heights of the bars between those values and add them. 6+8+7=21

The speed (in mph) of randomly selected bicyclists were measured as they were approaching a hill. The results are presented in the following histogram. How many of those bicyclists were traveling greater than 8.5 but less than 11.5 mph as they were approaching the hill?

$22\text{ bicyclists }$22 bicyclists ​ Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So to find the number of values which are greater than 8.5 but less than 11.5 , we look at the heights of the bars between those values and add them. 4+5+13=22

The relative frequencies for a set of data are shown in the table below. If there are a total of 25 data values, with what frequency does the data value 2 occur?

$4$4​ Dividing each frequency by the total number of data values gives the relative frequency. So multiplying the relative frequency by the total number of data values gives the frequency. The data value 2 occurs with relative frequency 0.16 in a data set of 25 values, so the frequency of the data value 2 is 0.16(25)=4 . The data value 2 occurs 4 times.

A data set is summarized in the frequency table below. The data set contains a total of 50 data values. What is the missing frequency?

$4$4​ The total number of data values is the sum of all the frequencies. We are told the data set contains a total of 50 data values. The nine given values add to 5+6+5+6+5+8+4+4+3=46, so the missing frequency is 50−46=4.

A data set is summarized in the frequency table below. The data set contains a total of 40 data values. What is the missing frequency?

$5$5​ The total number of data values is the sum of all the frequencies. We are told the data set contains a total of 40 data values. The seven given values add to 2+4+9+6+8+2+4=35, so the missing frequency is 40−35=5.

Consider a country whose annual budget results in the following budget deficits (in millions of dollars) each year. Create a line graph of the data using Excel. For how many of the years was the deficit greater than or equal to $320 million?

$9$9​ 1. Copy the years and deficits into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in these two columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on Line to create a line graph. In this case, click on Line with Markers to be able to see the markers where each of the data values lie. Notice that nine of the markers are at or above 320. Therefore, nine of the years had a deficit of at least $320 million.

Vance is a road and driving safety expert who is working with a data collection firm to analyze how much people drive to and from work. Vance randomly selected 26 employees who work at an office that agreed to let Vance poll their employees. The data are included below. Create the dot plot of the dataset using Excel. Find the median and the mode using the dot plot.

$\text{Median}=0.50,\ \text{Mode}=0.25$Median=0.50, Mode=0.25​ To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 enter "=COUNTIF($A$2:$A2,A2)". 3. Select cell B2 and pull down the bottom right square until the column is aligned with the column to the left. This gives you the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. To find the median, count an equal number of dots from the left side and from the right side to identify the dot in the middle. If there are two middle dots, then average their value. The mode(s) is/are the location(s) on the horizontal axis of the tallest column of dots. For the given dataset, there are two middle dots, both above 0.50. Therefore, the median is 0.50. The tallest column of dots is above 0.25, where there are 10 dots. Therefore, the mode is 0.25.

A census that was recently conducted asked each household how many children under the age of 18 live in the household. A subset of the data including the answers from 20 households is included below. Create a dot plot of the dataset using Excel. Then, find the median and the mode using the dot plot.

$\text{Median}=1,\ \text{Mode}=1$Median=1, Mode=1​ To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 enter "=COUNTIF($A$2:$A2,A2)". 3. Select cell B2 and pull down the bottom right square until the column is aligned with the column to the left. This gives you the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. To find the median, count an equal number of dots from the left side and from the right side to identify the dot in the middle. Since there are two middle dots, find the average of their value. The mode(s) is/are the location(s) on the horizontal axis of the tallest column of dots. For the given dataset, there are two middle dots, both above 1. Therefore, the median is 1. The tallest column of dots is above 1, where there are 8 dots. Therefore, the mode is 1.

A researcher at a sleep study institute is conducting a study on whether adults sleep a different number of hours on the weekends than they do on weeknights. The researcher asked a random sample of adults via an email survey how many hours they sleep a night on a typical Saturday. A subset of the data consisting of 21 responses is provided below. Create the dot plot of the dataset using Excel. Then use the dot plot to find the median and the mode.

$\text{Median}=6,\ \text{Mode}=5$Median=6, Mode=5​ To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 enter "=COUNTIF($A$2:$A2,A2)". 3. Select cell B2 and pull down the bottom right square until the column is aligned with the column to the left. This gives you the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. To find the median, count an equal number of dots from the left side and from the right side to identify the dot in the middle. The mode(s) is/are the value(s) on the horizontal axis with the tallest column of dots. For the given dataset, there is one middle dot above 6. Therefore, the median is 6. The tallest column of dots is above 5, where there are 5 dots. Therefore, the mode is 5.

A manager at a local fast food restaurant is attempting to schedule staff for the upcoming month. To ensure proper staffing to serve customers in a timely manner, the manager reviews the number of transactions that occurred at various times of the day during the previous month. The table below summarizes the transactions. If 8000 transactions occurred during the previous month, determine the frequency of transactions that occurred between the hours of 12:30 PM and 3:30 PM.

1$3200$3200​ We know that the total number of transactions for the previous month was 8000, and we know that 40% of these transactions occurred between 12:30 PM and 3:30 PM. To find the product of the total number of transactions and the relative frequency of transactions that occurred between 12:30 PM and 3:30 PM. (8000)(0.40)=3200 So, 3200 transactions occurred between the hours of 12:30 PM and 3:30 PM.

The following frequency table shows the number of goals scored by members of a soccer team in a given season. Fill in the blanks to complete the corresponding relative frequency table.

1$\frac{3}{50}$350​​ 2$\frac{9}{50}$950​​ 3$\frac{7}{50}$750​​ The relative frequency for each row is the frequency for that row, divided by the sum of the frequency column. For this example the sum of the frequency column is 50. A relative frequency is the ratio (fraction or proportion) of the number of times a data value occurs (frequency) in the set of the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of data values in the sample. Relative frequencies can be written as fractions, percents, or decimals.

A veterinarian is comparing the lengths in inches and weights in pounds of 20 cats that were brought in for their checkups. The data are given in the table below. Use Excel to create a graph with a line representing the lengths of the cats and bars representing the weights of the cats

1. Copy the cat names, lengths, and weights into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in the first three columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on either Column, for a bar graph, or Line, for a line graph. In this case, start from a bar graph by pressing the column option and then the first option from the menu that pops up. 4. Click on one of the bars that represent the cat weights. These are the bars that will be changed to be represented by a line. 5. Notice that there is now a new set of options in Excel labeled Chart Tools. Click on the tab labeled Design and select the option Change Chart Type. 6. In the Change Chart Type menu, select the format that you would like this piece of data to take. Since the number is currently represented by a bar, select the first option under Line. 7. Press OK to complete the chart with the data displayed in two different ways.

Given the data above, after tallying up the wins during the chess club meeting, which member of the club was most likely the winner?

According to the data, the member, Barbara, was most likely the winner. According to the data, Barbara won 12 games of chess during the past month. Since she has the highest bar in the bar graph, Barbara was most likely the winner when the scores were tallied during the chess club meeting.

Jane is a hiring manager who is looking at the various resumes that were submitted for a job opening at her company. The applicants specified their years of education as well as their years of experience.

Applicant 6 1. Copy the applicant names, years of education, and years of experience into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in the first three columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on either Column, for a bar graph, or Line, for a line graph. For this problem, we will start from a bar graph, so press the Column option and then the first option from the menu that pops up. 4. Click on one of the bars that represent the years of education. These are the bars that will be changed to be represented by a line. 5. Notice that there is now a new set of options in Excel labeled Chart Tools. Click on the tab labeled Design and select the option Change Chart Type. 6. In the Change Chart Type menu, select the format that you would like this piece of data to take. Since the number is currently represented by a bar, select the first option under Line. 7. Press OK to complete the chart with the data displayed in two different ways. Look at all the bars where the number of years of education line is at least 16. Notice that the largest bar belongs to Applicant 6, who has 18 years of education and 3 years of experience. Therefore, the applicant with the most experience and at least 16 years of education is Applicant 6.

Jane is a hiring manager who is looking at the various resumes that were submitted for a job opening at her company. The applicants specified their years of education as well as their years of experience. Use a line graph to represent the years of education and a bar graph to represent the years of experience. Which applicant has the most years of experience, given that he or she has at least 16 years of education?

Applicant 6 1. Copy the applicant names, years of education, and years of experience into an Excel spreadsheet. 2. Highlight all of the cells with data values, along with the titles in the first three columns. Click the Insert tab in Excel to bring up options for various types of graphs. 3. Under Insert, click on either Column, for a bar graph, or Line, for a line graph. For this problem, we will start from a bar graph, so press the Column option and then the first option from the menu that pops up. 4. Click on one of the bars that represent the years of education. These are the bars that will be changed to be represented by a line. 5. Notice that there is now a new set of options in Excel labeled Chart Tools. Click on the tab labeled Design and select the option Change Chart Type. 6. In the Change Chart Type menu, select the format that you would like this piece of data to take. Since the number is currently represented by a bar, select the first option under Line. 7. Press OK to complete the chart with the data displayed in two different ways. Look at all the bars where the number of years of education line is at least 16. Notice that the largest bar belongs to Applicant 6, who has 18 years of education and 3 years of experience. Therefore, the applicant with the most experience and at least 16 years of education is Applicant 6.

Josslyn is a car salesperson who keeps track of her sales over time. The line graph below shows how many cars she sells per week. A line graph titled Cars Sold Over Time has a horizontal x-axis labeled Weeks from 0 to 6 in increments of 1 and a vertical y-axis labeled Cars Sold from 0 to 16 in increments of 2. The graph consists of seven plotted points connected by line segments from left to right. The coordinates of the plotted points are at left-parenthesis 0 comma 5 right-parenthesis, left-parenthesis 1 comma 14 right-parenthesis, left-parenthesis 2 comma 16 right-parenthesis, left-parenthesis 3 comma 7 right-parenthesis, left-parenthesis 4 comma 10 right-parenthesis, left-parenthesis 5 comma 12 right-parenthesis, and left-parenthesis 6 comma 8 right-parenthesis. What was the change in cars sold from week 2 to 6? Do not include the unit in your answer.

Correct answers:$-8$−8​ We can see that at week 2 the value is 16 and at week 6 the value is 8. Therefore, the difference is 8−16=−8.

A gym is conducting research on their customer's preferred work-out routine during the week. The following table shows the preferred work-outs for the selected gym customers. Create the corresponding bar graph to represent this data below. Drag the dots on the top of the bar graph to create the chart.

Remember that the height of each bar in a bar graph equals the number of values that fall in that bar category. So for example, to find the first bar, which represents running, we note that the frequency for running is 22 in the table, so the height of that bar is 22. Therefore, 22 people chose running as their preferred exercise.

The following frequency table gives the number of students of each age at a Montessori school. Which histogram accurately summarizes the data?

Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So for example, to find the first bar, which has values greater than 3.5 but less than 4.5, we note that the frequency for 4 is 7, so the height of that bar is 7.

The weights (in pounds) of babies born in the pediatric wing of a hospital on a certain day are displayed in the following histogram. How many of those babies weighed greater than 8.5 but less than 10.5 pounds?

Remember that the height of each bar in a histogram equals the number of values that are in the range for that bar. So to find the number of values which are greater than 8.5 but less than 10.5, we look at the heights of the bars between those values and add them. 6+6=12

The following data set provides bitcoin transactions throughout 2016 and 2017. Caluculate the average number of transactions conducted during April 2017 and May 2017. Which of the following statements are true? Select all that apply.

The average number of transactions in April 2017 was between 250,000 and 299,999. The average number of transactions in May 2017 was between 300,000 and 349,999. The difference in the number of average transactions conducted during April and May was about 46,000. The May average was 324227.1154. The April average was 278557.7667. The difference between the two is 45,669.35 or about 46,000.

A company has released a new product, which is being sold through a major online retailer. The company making the product is tracking its reviews carefully, and a sample of the review scores from 23 of the customers is included below. Create the dot plot of the dataset using Excel, and then interpret the plot

The dot plot shows a left-skewed distribution with a mode of 5 and a median of 5, indicating that most though not all reviews give the product a score of 5 out of 5. To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 write "=COUNTIF($A$2:$A2,A2)". 3. Copy and paste B2 to each cell below B2 that is adjacent to the data in column A. This counts the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. To find the median, count an equal number of dots from the left side and from the right side to identify the dot in the middle. If there are two middle dots, then average their value. The mode(s) is/are the location(s) on the horizontal axis of the tallest column of dots. For the given data set, the middle dot is above 5. Therefore, the median is 5. The tallest column of dots is above 5, where there are 13 dots. Therefore, the mode is 5. Here, the left tail of the distribution is longer than the right tail, so the distribution is left-skewed, indicating that most though not all reviews give the product a score of 5 out of 5.

A researcher wants to know how many screens people who work in technology interact with or look at daily, including televisions, phones, tablets, and computer monitors. The question was asked via an email survey to a random sampling of people. The data are included below. Create the dot plot of the dataset using Excel, and then interpret the plot. Choose the correct answer below.

The dot plot shows a right-skewed distribution with a median of 6 and a mode of 8, indicating that while most people interact with or look at around 6 to 8 screens, some users interact with many more screens. To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 write "=COUNTIF($A$2:$A2,A2)". 3. Copy and paste B2 to each cell below B2 that is adjacent to the data in column A. This counts the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. To find the median, count an equal number of dots from the left side and from the right side to identify the dot in the middle. If there are two middle dots, then average their value. The mode(s) is/are the location(s) on the horizontal axis of the tallest column of dots. For the given dataset, there are two middle dots, both above 6. Therefore, the median is 6. The tallest column of dots is above 8, where there are 5 dots. Therefore, the mode is 8. The right tail of the distribution is longer than the left tail, so the distribution is right-skewed. This indicates that while most people interact with or look at around 6 to 8 screens, some users interact with many more screens.

A study was sponsored by an organization dedicated to the health and well-being of domesticated canines and felines. For the study, a large pet store chain distributed surveys to a random sampling of customers. One of the questions asked people how many cats and dogs they had. The results of a sample of 32 answers are included below. Create the dot plot of the dataset using Excel, and then interpret the plot. Choose the correct answer below.

The dot plot shows an approximately symmetric distribution with a median of 2 and a mode of 2, indicating that most customers of the pet store cluster around having 2 cats or dogs. To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 write "=COUNTIF($A$2:$A2,A2)". 3. Copy and paste B2 to each cell below B2 that is adjacent to the data in column A. This counts the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. To find the median, count an equal number of dots from the left side and from the right side to identify the dot in the middle. If there are two middle dots, then average their value. The mode(s) is/are the location(s) on the horizontal axis of the tallest column of dots. For the given dataset, the middle dot is above 2. Therefore, the median is 2. The tallest column of dots is above 2, where there are 14 dots. Therefore, the mode is 2. The right tail of the distribution is the same length as the left tail, so the distribution is approximately symmetric. This indicates that most customers of the pet store cluster around having 2 cats or dogs.

A principal is trying to determine how many students attend detention each school night. She records the number of students attending detention after school for 22 school days. The data are provided below. Create the dot plot of the dataset using Excel, and then interpret the plot.

The dot plot shows an approximately uniform distribution, where values 0 through 6 have frequencies from 2 to 5. So, the number of students attending detention each day is a mix of relatively few students, relatively many students, and days that are somewhere in the middle. To construct a dot plot with Excel follow these steps: 1. Open Excel and put the data in column A starting at A1. 2. In cell B2 write "=COUNTIF($A$2:$A2,A2)". 3. Copy and paste B2 to each cell below B2 that is adjacent to the data in column A. This counts the occurrence of each value in the dataset. 4. Create a scatter plot with the count on the vertical axis and the values on the horizontal axis. To find the median, count an equal number of dots from the left side and from the right side to identify the dot in the middle. If there are two middle dots, then average their value. The mode(s) is/are the location(s) on the horizontal axis of the tallest column of dots. For the given dataset, there are two middle dots. One is above 2 and the other is above 3. Therefore, the median is their average, 2.5. The tallest column of dots is above 1, where there are 5 dots. Therefore, the mode is 1. There does not appear to be any clustering around the median or mode, so the distribution cannot be said to be skewed. The dot plot is relatively flat, suggesting that the distribution is uniform.

A set of data is summarized by the stem and leaf plot below.

The value 30 appears 1$$ time(s) in the data set. The value 39 appears 2$$ time(s) in the data set. The value 45 appears 3$$ time(s) in the data set. Correct answers:1$3$3​2$2$2​3$2$2​ To find the number of times 30 appears in the data set, note that the stem (the part of the number before the last digit) is 3, and the leaf is 0. In the row for the stem 3, the leaf 0 occurs 3 times, so 30 appears 3 times in the data set.

A set of data is summarized by the stem and leaf plot below.

The value 33 appears 1$$ time(s) in the data set. The value 27 appears 2$$ time(s) in the data set. The value 36 appears 3$$ time(s) in the data set. Correct answers:1$3$3​2$6$6​3$1$1​ To find the number of times 33 appears in the data set, note that the stem (the part of the number before the last digit) is 3, and the leaf is 3. In the row for the stem 3, the leaf 3 occurs 3 times, so 33 appears 3 times in the data set.Similarly for the other answers.

A set of data is summarized by the stem and leaf plot below.

The value 39 appears 1$$ time(s) in the data set. The value 42 appears 2$$ time(s) in the data set. The value 22 appears 3$$ time(s) in the data set. Correct answers:1$4$4​2$1$1​3$1$1​ To find the number of times 42 appears in the data set, note that the stem (the part of the number before the last digit) is 4, and the leaf is 2. In the row for the stem 4, the leaf 2 occurs 1 time, so 42 appears 1 time in the data set.

A set of data is summarized by the stem and leaf plot below.

The value 56 appears 1$$ time(s) in the data set. The value 42 appears 2$$ time(s) in the data set. The value 18 appears 3$$ time(s) in the data set. Correct answers:1$2$2​2$2$2​3$1$1​ To find the number of times 42 appears in the data set, note that the stem (the part of the number before the last digit) is 4, and the leaf is 2. In the row for the stem 4, the leaf 2 occurs 2 times, so 42 appears 2 times in the data set.

The data listed below represents the amount of snow, recorded for five days, in inches. Create the corresponding line graph to represent this data below.

The x-axis represents the day and the y-axis represents the amount of snowfall. According to the data, there should be points at (1,2) (2,6) (3,2) (4,9) (5,6) where the x variable represents the day and the y variable represents the amount of snowfall (in inches) on a particular day. For instance, on day 2, there was 6 inches of snowfall.

The data listed below represents the distance from a city taxi depot (to the nearest mile) by the number of hours since a taxi left the depot to pick up passengers. Create the corresponding line graph to represent this data below.

The x-axis represents the time in hours and the y-axis represents the number of miles. According to the data, there should be points at (0,0) (1,3) (4,6) (5,10) (6,5) (7,3) (10,2) where the x variable represents the number of hours since the taxi left the depot and the y variable represents the number of miles the taxi is from the depot. For instance, when it was 4 hours since the taxi left the depot, the taxi was 6 miles from the depot.

Given the frequency table below, which of the following is the corresponding relative frequency table? Value-Frequency 1-6 2-8 3-3 4-8

ValueFrequency10.2420.3230.1240.32 By adding the frequencies, we see that there are a total of 25 values in the set of data. Dividing each frequency by this total gives the relative frequency. So, for example, the relative frequency for the value 1 is 6/25=0.24 This relative frequency table could be used by HR to have employees rate how satisfied they are with their end of year reviews on a scale of least 1 - most 4. Then, finding the relative frequency to compare satisfaction percentages.

A set of data is summarized by the stem and leaf plot below. Stem1234Leaf1356671123348900002367788811122334567777

There are $$8 values in the data set which are greater than or equal to 20 and less than or equal to 29. There are $$6 values in the data set which are greater than or equal to 10 and less than or equal to 19. There are $$14 values in the data set which are greater than or equal to 40 and less than or equal to 49.There are 1$$ values in the data set which are greater than or equal to 20 and less than or equal to 29. There are 2$$ values in the data set which are greater than or equal to 10 and less than or equal to 19. There are 3$$ values in the data set which are greater than or equal to 40 and less than or equal to 49. Correct answers:1$8$8​2$6$6​3$14$14​ Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 6 entries in the leaf column of the first row (with stem 1), so there are 6 values in the data set which are greater than or equal to 10 and less than or equal to 19. 8, 6, 14

A set of data is summarized by the stem and leaf plot below.

There are 1$$ values in the data set which are greater than or equal to 10 and less than or equal to 19. There are 2$$ values in the data set which are greater than or equal to 30 and less than or equal to 39.There are 3$$ values in the data set which are greater than or equal to 40 and less than or equal to 49. Correct answers:1$14$14​2$9$9​3$7$7​ Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 14 entries in the leaf column of the first row (with stem 1), so there are 14 values in the data set which are greater than or equal to 10 and less than or equal to 19.

A set of data is summarized by the stem and leaf plot below.

There are 1$$ values in the data set which are greater than or equal to 20 and less than or equal to 29. There are 2$$ values in the data set which are greater than or equal to 10 and less than or equal to 19. Correct answers:1$8$8​2$12$12​ Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 12 entries in the leaf column of the first row (with stem 1), so there are 12 values in the data set which are greater than or equal to 10 and less than or equal to 19.

A set of data is summarized by the stem and leaf plot below.

There are 1$$ values in the data set which are greater than or equal to 20 and less than or equal to 29. There are 2$$ values in the data set which are greater than or equal to 30 and less than or equal to 39. There are 3$$ values in the data set which are greater than or equal to 10 and less than or equal to 19. Correct answers:1$8$8​2$11$11​3$11$11​ Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 11 entries in the leaf column of the first row (with stem 1), so there are 11 values in the data set which are greater than or equal to 10 and less than or equal to 19.

A set of data is summarized by the stem and leaf plot below. Stem12Leaf11223344667789126899

There are 1$$ values in the data set which are greater than or equal to 20 and less than or equal to 29. There are 2$$values in the data set which are greater than or equal to 10 and less than or equal to 19. Correct answers:1$6$6​2$14$14​ Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 14 entries in the leaf column of the first row (with stem 1), so there are 14 values in the data set which are greater than or equal to 10 and less than or equal to 19.

A set of data is summarized by the stem and leaf plot below. Stem12345Leaf33456789924671489912446666678800122344577777888999

There are 1$$ values in the data set which are greater than or equal to 30 and less than or equal to 39. There are 2$$ values in the data set which are greater than or equal to 10 and less than or equal to 19. Correct answers:1$5$5​2$9$9​ Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 9 entries in the leaf column of the first row (with stem 1), so there are 9 values in the data set which are greater than or equal to 10 and less than or equal to 19.

Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table?

ValueFrequency40.2850.5260.5670.7681 Remember that a cumulative frequency table adds the relative frequencies for the previous entries in the table. For example, the entry for the value 6 is 0.28+0.24+0.04=0.56 This cumulative frequency table could be used by an internet provider to see the percentage of customers that rate the service from a least 4 - most 8. For example, at the 6, 56% of people voting have the service at a 6 or less. This could show the internet provider that upgrades may be needed.

Bruce polled a large sample of individuals to find the percentage of students on a school sports team and the percentage of people on an intramural sports team. Which of the following could sufficiently display the data if only the two given categories are to be included?

bar graph The two given categories of data could potentially have overlap. In addition to this, it is likely that there are individuals that do not belong to either category. In this sense, the percentages will not account for 100% of the individuals sampled and a pie chart will not sufficiently display the data. A bar graph should be used.

Stephanie polled a large sample of individuals to find the percentage of people who like horror films and the percentage of people who like romantic dramas. Which of the following could sufficiently display the data if only the two given categories are to be included?

bar graph The two given categories of data could potentially have overlap. In addition to this, it is likely that there are individuals that do not belong to either category. In this sense, the percentages will not account for 100% of the individuals sampled and a pie chart will not sufficiently display the data. A bar graph should be used.

All students are classified as either full-time or part-time. Kenneth conducted a survey in which he collected data on the percentage of students that are full-time and the percentage of students that are part-time. Which of the following could sufficiently display the data if only the two given categories are to be included?

either a pie chart or a bar graph Each person surveyed must fit in exactly one of given data categories. This implies that the percentages must account for 100% of the individuals in the sample. Therefore, either a bar graph or a pie chart will sufficiently display the data.

Deborah conducted a survey in which she collected data on the percentage of workers with college degrees and the percentage of workers without college degrees. Which of the following could sufficiently display the data if only the two given categories are to be included?

either a pie chart or a bar graph Each person surveyed must fit in exactly one of given data categories. This implies that the percentages must account for 100% of the individuals in the sample. Therefore, either a bar graph or a pie chart will sufficiently display the data.

Howard polled a large sample of individuals to find the percentage of students that are males and the percentage of students that are females. Which of the following could sufficiently display the data if only the two given categories are to be included?

either a pie chart or a bar graph Each person surveyed must fit in exactly one of given data categories. This implies that the percentages must account for 100% of the individuals in the sample. Therefore, either a bar graph or a pie chart will sufficiently display the data.

For which of the following sets of data is a pie chart appropriate? Assume that only the two given categories will be included.

the percentage of adults with children and the percentage of adults without children A pie chart is only appropriate when the data categories account for the entirety of the sample. A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

For which of the following sets of data is a pie chart appropriate? Assume that only the two given categories will be included.

the percentage of city residents that are married and the percentage of city residents that are not married A pie chart is only appropriate when the data categories account for the entirety of the sample. A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

For which of the following sets of data is a pie chart appropriate? Assume that only the two given categories will be included.

the percentage of people that speak only one language and the percentage of people that speak multiple languages A pie chart is only appropriate when the data categories account for the entirety of the sample. A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

Which of the following sets of data should not be displayed with a pie chart? Assume that only the two given categories will be included.

the percentage of people who like horror films and the percentage of people who like romantic dramas A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

Which of the following sets of data should not be displayed with a pie chart? Assume that only the two given categories will be included.

the percentage of people who own cell phones and the percentage of people who own tablets A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.

Which of the following sets of data should not be displayed with a pie chart? Assume that only the two given categories will be included.

the percentage of students on a school sports team and the percentage of people on an intramural sports team A pie chart is not appropriate if the given data has percentages that sum to greater than 100%, resulting from overlap in categories, or less than 100%, resulting from omitting other categories. If an individual could be in each of the categories or neither of the categories, a pie chart will not be sufficient.