MATH 120/20 CHAPTER 2 DRAFT
Pareto Chart
A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.
relative frequency distribution
lists each category of data together with the relative frequency
Frequency Distribution
A frequency distribution lists each category of data and the number of occurrences for each category of data.
histogram
A histogram is constructed by drawing rectangles for each class of data. The height of each rectangle is the frequency or relative frequency of the class. The width of each rectangle is the same, and the rectangles touch each other.
_________ are the categories by which data are grouped.
Classes
Determine whether the following statement is true or false. The shape of the distribution shown is best classified as skewed left.
False (actually skewed right)
Use the data summarized in Table 3 to construct a frequency bar graph and relative frequency bar graph.
Figure 1(a) shows the frequency bar graph, and Figure 1(b) shows the relative frequency bar graph.
A random sample of 100 adults aged 18 years or older were given a list of ice cream flavors and were asked to list which flavors they liked. The responses are given below. Chocolate. 45 Strawberry. 42 Vanilla. 23 Mocha. 19
Frequency Bar Graph
it is a good idea to...
It is a good idea to add up the relative frequencies to be sure they sum to 1. In fraction form, the sum should be exactly 1. In decimal form, the sum may differ slightly from 1 due to rounding.
Consider the information in the "Why we can't loseweight" chart shown to the right, which is in the magazine style of graph. Could the information provided be organized into a pie chart? Why or why not?
No. The percentages add up to more than 100%.
For jewelry prices in a jewelry store, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right.
Skewed right
In a relative frequency distribution, what should the relative frequencies add up to?
The relative frequencies add up to 1
relative frequency
The relative frequency is the proportion (or percent) of observations within a category and is found using the formula Relative frequency= Frequency/sum of all frequencies
In any frequency distribution, it is a good idea to...
add up the frequency column to make sure that it equals the number of observations. In Example 1, the frequency column totals to 30 as it should because there are 30 body parts (observations).
pie chart
is a circle divided into sectors. Each sector represents a category of data. The area of each sector is proportional to the frequency of the category.
A bar graph
is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. Rectangles of equal width are drawn for each category. The height of each rectangle represents the category's frequency or relative frequency.
The _________________ is the difference between consecutive lower class limits.
The class width is the difference between consecutive lower class limits.
The data to the right represent the number of customers waiting for a table at 6:00 P.M. for 40 consecutive Saturdays at Bobak's Restaurant. Complete parts (a) through (h) below.
(a) Are these data discrete or continuous? Explain. The data are discrete because there are a finite or countable number of values. Part 2 (b) Construct a frequency distribution of the data. Number of Customers Frequency 1-3 1 4-6 4 7-9 9 10-12 19 13-15 7 Part 3 (c) Construct a relative frequency distribution of the data. Number of Customers Relative Frequency 1-3 0.025 4-6 0.1 7-9 0.225 10-12 0.475 13-15 0.175 Part 4 (d) What percentage of the Saturdays had 10 or more customers waiting for a table at 6:00 P.M.? 65% Part 5 (e) What percentage of the Saturdays had 6 or fewer customers waiting for a table at 6:00 P.M.? 12.5% Part 6 (f) Construct a frequency histogram of the data. Choose the correct histogram below. (g) Construct a relative frequency histogram of the data. Choose the correct histogram below. (h) Describe the shape of the distribution. Choose the correct answer below. The distribution is skewed left because the left tail is longer than the right tail.
A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtains the data in the accompanying table. Complete parts (a) through (h) below.
(a) Are these data discrete or continuous? Explain. The given data are discrete because they can only have whole number values. Part 2 (b) Construct a frequency distribution of the data. Televisions Frequency 0 1 1 14 2 14 3 8 4 2 5 1 Part 3 (c) Construct a relative frequency distribution of the data. Televisions Relative Frequency 0. 0.025 1 0.35 2 0.35 3 0.2 4 0.05 5 0.025 Part 4 (d) What percentage of households in the survey have three televisions? 20% Part 5 (e) What percentage of households in the survey have four or more televisions? 7.5% Part 6 (f) Construct a frequency histogram of the data. Choose the correct graph below. (h) Describe the shape of the distribution. The distribution is skewed right.
The following data represent the number of potholes on 35 randomly selected 1-mile stretches of highway around a particular city. Complete parts (a) through (d) to the right. number of potholes 1 3. 3. 1. 4. 7. 5 1. 3. 6. 1. 2. 2. 1 2. 7. 1. 6. 2. 7. 1 6. 4. 4. 1. 1. 5. 3 6. 2. 3. 2. 7 1 3
(a) Construct a frequency distribution of the data. Potholes Frequency 1. 1010 2. 66 3. 66 4. 33 5. 22 6 44 7. 44 Part 2 (b) Construct a relative frequency distribution of the data. Potholes Relative Frequency 1 0.286 2 0.171 3 0.171 4 0.086 5 0.057 6. 0.114 7. 0.114 Part 3 (c) Using the results from part (b), what percentage of the stretches of highway have 3potholes? 17.1% Part 4 (d) Using the results from part (b), what percentage of the stretches of highway have 5 or more potholes? 28.5%
The data below represent the per capita (average) disposable income (income aftertaxes) for 25 randomly selected cities in a recent year. Complete parts (a) and (b). 30,254. 30,521. 30,729. 32,113 32,993. 33,642. 33,911. 34,218 34,696. 34,970 35,277. 35,584. 35,822. 35,934. 36,918 37,289. 37,799. 38,413. 38,730. 38,930 39,826. 40,189. 41,135. 41,444. 52,512
(a) Construct a frequency distribution with the first class having a lower class limit of 30,000 and a class width of 6000. Class Frequency 30,000−35,999 14 36,000−41,999 10 42,000−47,999. 0 48,000−53,999 1 Part 2 (b) Construct a relative frequency distribution with the first class having a lower class limit of 30,000 and a class width of 6000. Class Relative Frequency 30,000−35,999 0.56 36,000−41,999 0.4 42,000−47,999 0 48,000−53,999 0.04
The accompanying table shows the median household income (in dollars) for 25 randomly selected regions. Complete parts (a) through (g) below.
(a) Construct a frequency distribution. Use a first class having a lower class limit of 35,000 and a class width of 5000. Income Frequency 35,000-39,999 1 40,000-44,999. 2 45,000-49,999 4 50,000-54,999 8 55,000-59,999 4 60,000-64,999 3 65,000-69,999 2 70,000-74,999 1 (b) Construct a relative frequency distribution. Use a first class having a lower class limit of 35,000 and a class width of 5000. Income Relative Frequency 35,000-39,999 0.04 40,000-44,999 0.08 45,000-49,999 0.16 50,000-54,999 0.32 55,000-59,999 0.16 60,000-64,999 0.12 65,000-69,999 0.08 70,000-74,999 0.04 (c) Construct a frequency histogram. Choose the correct graph below. bell-shaped (d) Construct a relative frequency histogram. Choose the correct graph below. bell-shaped (e) Describe the shape of the distribution. The distribution is bell-shaped. (f) Repeat parts (a)-(e) using a class width of 10,000. Construct a frequency distribution. Income Frequency 35,000-44,999 3 45,000-54,999 12 55,000-64,999 7 65,000-74,999 3 Construct a relative frequency disribution. Income Relative Frequency 35,000-44,999 0.12 45,000-54,999 0.48 55,000-64,999 0.28 65,000-74,999 0.12 Construct a frequency histogram of the data. Choose the correct frequency histogram below. Describe the shape of the distribution. The distribution is bell-shaped. (g) Does one frequency distribution provide a better summary of the data than the other? Explain. The shape is not as clear in the distribution with fewer classes, so more classes should be used.
The data below represent the per capita (average) disposable income (income after taxes) for 25 randomly selected cities in a recent year. Complete parts (a) and (b). 30,265. 30,525. 30,803. 32,151. 32,917 33,624. 34,048. 34,195. 34,781. 34,835 35,118. 35,696. 35,897. 35,905. 36,819 37,319. 37,854. 38,387. 38,780. 38,853. 39,842. 40,299. 41,132. 41,315. 52,431
(a) Construct a frequency histogram of the data with a first class having a lower class limit of 30,000 and a class width of 6000. Choose the correct graph below. (b) Construct a relative frequency histogram of the data with a first class having a lower class limit of 30,000 and a class width of 6000. Choose the correct graph below.
On the basis of a population survey, there were 91.3 million males and 98.9 million females 25 years old or older in a certain country. The educational attainment of the males and females is shown in the accompanying table. Complete parts (a) through (d) below.
(a) Construct a relative frequency distribution for males. Express each relative frequency as a decimal. Educational Attainment Relative Frequency (males) Not a high school graduate (A) 0.1468 High school graduate (B) 0.3242 Some college, but no degree (C) 0.1566 Associate's degree (D) 0.0953 Bachelor's degree (E) 0.1928 Advanced degree (F) 0.0843 Part 2 (b) Construct a relative frequency distribution for females. Express each relative frequency as a decimal. Educational Attainment. Relative Frequency(females) Not a high school graduate (A) 0.1405 High school graduate (B) 0.3185 Some college, but no degree (C). 0.1668 Associate's degree (D). 0.0971 Bachelor's degree (E) 0.1871 Advanced degree (F) 0.0900 Part 3 (c) Construct a side-by-side relative frequency bar graph, with male numbers represented by the left bars and female numbers represented by the right bars in each category. Choose the correct graph below. (d) Compare each gender's educational attainment. Choose the correct answer below. Each gender's educational attainment is about the same.
To predict future enrollment in a school district, fifty households within the district were sampled, and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table. Complete parts (a) through (c) below. Number of Children under 5 Number of Households 0 15 1 12 2 16 3 4 4 3
(a) Construct a relative frequency distribution of the data. Number of Children under 5 Relative Frequency 0 0.3 1 0.24 2 0.32 3 0.08 4 0.06 Part 2 (b) What percentage of households has two children under the age of 5? 32% Part 3 (c) What percentage of households has one or two children under the age of 5? 56%
Over the course of a decade, a certain police department issued 158.2 thousand speeding tickets. The ages of the males and females who received tickets are shown below. Use this information to answer parts a through c. Age Groups Males(in thousands) Females(in thousands) 16 - 25 28.2 22.4 26 - 35 19.3 17.3 36 - 45 15.4 14.1 46 - 55 8 8.2 > 56 12.4. 12.9
(a) Construct a relative frequency distribution of the males who received tickets. (Round answers to three decimal places.) Age Group Relative Frequency 16-25 0.339 26-35 0.232 36-45 0.185 46-55 0.096 >56 0.149 Part 2 (b) Construct a relative frequency distribution of the females who received tickets. (Round answers to three decimal places.) Age Group. Relative Frequency 16-25 0.299 26-35 0.231 36-45 0.188 46-55 0.109 >56 0.172 Part 3 (c) Construct a side-by-side relative frequency bar graph. Choose the correct graph below where in each age grouping, the left bar represents males and the right bar represents females.
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) through (e). O B. AB. A. AB A O O O. O. A O. AB O O. A. A B O A A. B. A. A A A. O A O O A A B. A B. O. B. A. O. A O. O. B. O. A. O. A. O. O. O
(a) Construct a relative frequency distribution. Blood Type Relative Frequency A 0.380.38 AB 0.060.06 B 0.140.14 O 0.42 (b) According to the data, which blood type is most common? O Part 3 (c) According to the data, which blood type is least common? ABAB Part 4 (d) Use the results of the sample to conjecture the percentage of the population that has type O blood. Is this an example of descriptive or inferential statistics? Select the correct choice below and fill in the answer box to complete your choice. (Type a whole number.) 4242%; inferential (e) Contact a local hospital and ask them the percentage of the population that is blood type O. Why might the results differ? The results might differ because there is always a chance that the sample surveyed is unlike the population.
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) and (b). O B. AB. O. AB A O. O O O A O AB. O. O. A A B. O A. A B. A. O. A. A. O. A. O O. O A B A. B. O. B. A A A O O B O A O A O O O
(a) Draw a frequency bar graph. (b) Draw a relative frequency bar graph.
Part 1 The following frequency histogram represents the IQ scores of a random sample ofseventh-grade students. IQs are measured to the nearest whole number. The frequency of each class is labeled above each rectangle. Use the histogram to answers parts (a) through (g).
(a) How many students were sampled? 200 students Part 2 (b) Determine the class width. The class width is 10. Part 3 (c) Identify the classes and their frequencies. Choose the correct answer below. B) 60-69, 2; 70-79, 3; 80-89, 13; 90-99, 42; 100-109, 56; 110-119, 43; 120-129, 30; 130-139, 7; 140-149, 3; 150-159, 1 Part 4 (d) Which class has the highest frequency? 100-109 Part 5 (e) Which class has the lowest frequency? A. 150-159 Part 6 (f) What percent of students had an IQ of at least 130? 5.5% Part 7 (g) Did any students have an IQ of 161? No, because there are no bars, or frequencies, greater than an IQ of 160.
The data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. Find (a) the number of classes, (b) the class limits for the second class, and (c) the class width. Speed (km/hr) Number of Players 10-15.9 7 16-21.9 20 22-27.9 206 28-33.9 419
(a) There are 4 classes. Part 2 (b) The lower class limit for the second class is 16. Part 3 The upper class limit for the second class is 21.9 Part 4 (c) The class width is 6.
The following graph represents the results of a survey, in which a random sample of adults in a certain country was asked if a certain action was morally wrong in general. Complete parts (a) through (c) below.
(a) What percent of the respondents believe the action is morally acceptable? About 70% of the respondents (b) If there are 293 million adults in the country, how many believe that the action is morally wrong? About 6565 million adults Part 3 (c) If a polling organization claimed that the results of the survey indicate that 10% of adults in the country believe that the action is acceptable in certain situations, would you say this statement is descriptive or inferential? Why? The statement is inferential because it makes a prediction.
The following Pareto chart shows the position played by the most valuable player (MVP) in a certain baseball league for the last 81 years. Use the chart to answer parts (a) through (d).
(a) Which position had the most MVPs? The position with the most MVPs was outfield (OF). Part 2 (b) How many MVPs played short stop (SS)? 77 MVPs played short stop. Part 3 (c) How many more MVPs played outfield (OF) than short stop? 2525 more MVPs played outfield than short stop. Part 4 (d) There are three outfield positions (left field, center field, right field). Given this, how might the graph be misleading? The chart seems to show that one position has many more MVPs because three positions are combined into one. They should be separated.
Suppose you are considering investing in a Roth IRA. You collect the data in Table 12, which represent the five-year rate of return (in percent, adjusted for sales charges) for a simple random sample of 40 large-blend mutual funds. Construct a frequency and relative frequency distribution of the data. Five-Year Rate of Return of Mutual Funds 10.94 14.60 12.80 16.00 11.93 15.68 9.03 13.40 10.53 13.98 13.86 12.36 13.54 9.94 13.93 13.63 14.12 14.88 14.77 13.13 8.28 19.43 12.98 13.16 12.26 14.20 14.80 13.26 13.67
Approach To construct a frequency distribution, first create classes of equal width. Table 12 has 40 observations that range from 8.28 to 19.43 so we decide to create the classes such that the lower class limit of the first class is 8 (a little smaller than the smallest data value) and the class width is There is nothing magical about the choice of 1 as a class width. We could have selected a class width of 2 or 3 or any other class width (although some class widths are better than others). Choose a class width that you think will summarize the data nicely. The second class has a lower class limit of 8+1=9. The classes cannot overlap, so the upper class limit of the first class is 8.99. Continuing in this fashion, we obtain the following classes: 8−8.99 9−9.99 ⋅⋅⋅ 19−19.99 This gives us twelve classes. Tally the number of observations in each class, count the tallies, and create the frequency distribution. Divide the frequency of each class by the number of observations, to obtain the relative frequency. Solution Tally the data in Table 12 as shown in the second column of Table 13. The third column shows the frequency of each class. From the frequency distribution, we conclude that a five-year rate of return between 13% and 13.99% occurs with the most frequency. The fourth column shows the relative frequency of each class. So 32.5% of the large-blend mutual funds had a five-year rate of return between 13% and 13.99%. One mutual fund had a five-year rate of return between 19% and 19.99%. We might consider this mutual fund worthy of our investment. This type of information would be more difficult to obtain from the raw data.
Construct a frequency and relative frequency histogram of the five-year rate of return data discussed in Example 3.
Approach To draw the frequency histogram, use the frequency distribution in Table 13. First, label the lower class limits of each class on the horizontal axis. Then, for each class, draw a rectangle whose width is the class width and whose height is the frequency. For the relative frequency histogram, the height of the rectangle is the relative frequency. Solution Figures 7(a) and (b) show the frequency and relative frequency histograms, respectively.
A physical therapist wants to determine types of rehabilitation required by her patients. To do so, she obtains a simple random sample of of her patients and records the body part requiring rehabilitation. See Table 1. Construct a frequency distribution of location of injury.
Approach: To construct a frequency distribution, create a list of the body parts (categories) and tally each occurrence. Then, add up the number of tallies (observations) to determine the frequency. Solution: Table 2 shows that the back is the most common body part requiring rehabilitation, with a total frequency of 12.
Why shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency distribution?
Classes shouldn't overlap so there is no confusion as to which class an observation belongs.
Guidelines for Determining the Lower Class Limit of the First Class and Class Width
Choosing the Lower Class Limit of the First Class Choose the smallest observation in the data set or a convenient number slightly smaller than the smallest observation in the data set. For example, in Table 12, the smallest observation in 8.28. A convenient lower class limit of the first class is 8. Determining the Class Width Decide on the number of classes. Generally, there should be between 5 and 20 classes. The smaller the data set, the fewer the classes. For example, we might think ten classes would be a good choice for the data in Table 12. Determine the class width by computing Class width≈largest data value − smallest data valuenumber of classes Round the value to a convenient number. For example, using the data in Table 12, we obtain class width ≈19.43−8.2810=1.115. Round this down to 1 because this is an easy number to work with. Rounding up may result in fewer classes than were originally intended, while rounding down may result in more class than originally intended.
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. O. B AB A AB O O O O O A O AB. O O A A AB A A. A B A A A A O. A. O. O A A. B A B O AB A A A O O AB O A A A O O O
Construct a frequency distribution. Blood Type. Frequency A 21 AB 6 B 4 O 19
An Internet media and market research firm measured the amount of time an individual spends viewing a specific Webpage. The data in the accompanying table represent the amount of time, inseconds, a random sample of 40 surfers spent viewing a Webpage. Create the graphical summary. Write a sentence that describes the data.
Create the graphical summary. Choose the correct graph below. Part 2 Write a sentence that describes the data. Choose the correct answer below. The distribution is skewed right.
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. O B AB. A. AB. A. O O. O. O. A. O. AB. O O A A. B. O. A. A. B. A. A A A O. A O. O. O. A B A. B. O. B. A. A. A. O. O AB. O. A. O. A. O O O
Draw a pie chart.
A frequency distribution lists the ____________ of occurrences of each category of data, while a relative frequency distribution lists the _______________ of occurrences of each category of data.
Number, Proportion
The frequency data in Table 4 represent the educational attainment (level of education) in 1990 and 2016 of adults 25 years and older who are U.S. residents. The data are in thousands. So 39,344represents 39,344,000. Educational Attainment. 1990. 2016. Not a high school graduate. 39,344. 23,453 High school diploma. 47,643. 62,002 Some college, no degree. 29,780. 36,003 Associate's degree 9,792. 21,657 Bachelor's degree 20,833. 44,778 Graduate or professional degree 11,478. 27,122 Totals. 158,870. 215,015
PART A - Draw a side-by-side relative frequency bar graph of the data. Approach: First, determine the relative frequencies of each category for each year. To construct side-by-side bar graphs, draw two bars for each category of data—one for 1990, the other for 2016. Solution: Table 5 shows the relative frequency of each category (by the year). The side-by-side bar graph is shown in Figure 3. TABLE 5 Educational Relative Relative Attainment. Frequency Frequency In 1990 In 2016 Not a high school graduate 0.2476 0.1091 High school diploma 0.2999 0.2884 Some college, no degree. 0.1874 0.1674 Associate's degree 0.0616 0.1007 Bachelor's degree 0.1311 0.2083 Graduate or professional degree. 0.0722 0.1261 PART B The side-by-side bar graph illustrates that the proportion of Americans 25 years and older who had some college but no degree was higher in 1990. This information is not clear from the frequency table (Table 4) because the total population sizes are different. The increase in the number of Americans who did not complete a degree is due partly to the increases in the size of the population. In addition, the number of individuals with a Bachelor's degree more than doubled (20,833 to 44,778). However, from the side-by-side bar graph, we see that the proportion of Americans 25 years and older who had a Bachelor's degree did not double. It is also clear that adult Americans have more education in 2016 than in 1990 with a much higher percentage of the population having at least a bachelor's degree (20.33% in 1990 versus 33.44% in 2016).
Select the correct choices that complete the sentence below. The _________ class limit is the smallest value within the class and the ________ class limit is the largest value within the class.
The lower class limit is the smallest value within the class and the upper class limit is the largest value within the class.
Is the statement below true or false? There is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others.
The statement is true. Any correctly constructed frequency distribution is valid. However, some choices for the categories or classes give more information about the shape of the distribution.
Using the summarized data in Table 2, construct a relative frequency distribution.
The sum of all the values in the frequency column in Table 2 is 30. We now compute the relative frequency of each category. For example, the relative frequency of the category Back is 12/30=0.4. The relative frequencies are shown in column 3 of Table 3. From the distribution, the most common body part for rehabilitation is the back.
roblem The frequency data presented in Table 6 represent the educational attainment of U.S. residents 25 years and older in 2016. The data are in thousands so 23,453 represents 23,453,000. Construct a pie chart of the data. TABLE 6 Educational Attainment 2016 Not a high school graduate 23,453 High school diploma 62,002 Some college, no degree 36,003 Associate's degree 21,657 Bachelor's degree 44,778 Graduate or professional degree. 27,122 Total 215,015
We use the same approach for the remaining categories to obtain Table 7. To construct a pie chart by hand, we use a protractor to approximate the angles for each sector.
The following data represent the number of potholes on 35 randomly selected 1-mile stretches of highway around a particular city. Complete parts (a) and (b) below. number of potholes 1. 3. 3. 1. 4. 7. 5. 3. 6. 1. 2. 2. 1. 2. 1. 6. 2. 7. 1. 5. 4. 1. 1. 5. 3. 6. 2. 3 2. 7. 1. 3 1 7 4
(a) Construct a frequency histogram of the data. Choose the correct answer below. (b) Construct a relative frequency histogram of the data. Choose the correct answer below.
An airline offers discounted flights from Atlanta to five American cities. Below is a frequency distribution of the number of tickets purchased for each location based on a random sample of purchased tickets. Complete parts (a) through (f). Response. Frequency Las Vegas 1114 Orlando 835 New York 1370 Chicago 496 San Diego 672
(a) Construct a relative frequency distribution of the data. Response Relative Frequency Las Vegas 0.248 Orlando 0.186 New York 0.305 Chicago 0.111 San Diego 0.150 Part 2 (b) What proportion of the tickets were for New York? 0.305 (f) A local news broadcast reported that 15% of tickets purchased from the airline are for flights to San Diego. What is wrong with this statement? No level of confidence is provided along with the estimate.
Use the applet available below to complete parts (a) through (c). (a) How many classes are in the histogram for the Five-Year Rate of Return data when the "Starting point" is 8 and the "Bin width" is 2? (b) How many classes are in the histogram for the Five-Year Rate of Return data when the "Starting point" is 8 and the "Bin width" is 4? (c) How many classes are in the histogram for the Five-Year Rate of Return data when the "Starting point" is 8 and the "Bin width" is 1?
(a) There are 6 classes. Part 2 (b) There are 3 classes. Part 3 (c) There are 12 classes.
The pie chart below depicts the beverage size customers choose while at a fast food restaurant. Complete parts (a) through (c). A pie chart Medium 20%Large 15%XL 56%Small 9%
(a) What is the most popular size? What percentage of customers choose this size? XL; 56% Part 2 (b) What is the least popular size? What percentage of customers choose this size? Small; 9% Part 3 (c) What percent of customers choose a medium-sized beverage? 20%
The data in the accompanying table represent the land area and highest elevation for each of seven states of a country. Complete parts (a) and (b).
(a) Would it make sense to draw a pie chart for land area? Yes Part 2 If it makes sense, draw a pie chart. Choose the correct answer below. C. Part 3 (b) Would it make sense to draw a pie chart for the highest elevation? No Part 4 If it makes sense, draw a pie chart. Choose the correct answer below. It does not make sense to draw a pie chart for highest elevation
