STATS CHAP 2
After constructing any relative frequency distribution, what should be the sum of the relative frequencies?
1 or 100%
(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?
12 classes
A group of 12 randomly selected students were asked how many traffic tickets they have received since they started driving.
DOT PLOT GRAPH--> DOT PLOT---> COMPUTE
What is wrong with the following class limits for organizing weight data for a sample of 200 adult men in the United States? 140-150 pounds 150-160 pounds 160-170 pounds 170-180 pounds 180-190 pounds 190-200 pounds 200-210 pounds 210-220 pounds 220-230 pounds
The classes are overlapping.
Which of the statements below is true concerning bar graphs?
The height of each bar represents the category's frequency or relative frequency.
True or false? A histogram and a relative frequency histogram, constructed from the same data, always have the same basic shape. Choose the correct answer below.
True. A relative frequency histogram will have a different scale on the y-axis but the same shape as a regular histogram.
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?
6 classes
(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?
3 classes
Suppose that you have data which indicates that 90% of adults in a nearby town have cell phones. Of those who have cell phones, 30% use Carrier A, 30% use Carrier B, 10% use Carrier C, 20% use Carrier D, 5% use Carrier E, and 5% use other carriers. Which of the following is not a reasonable graph to display this information?
Histogram
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.
LOWER, UPPER
The _________________ is the difference between consecutive lower class limits.
CLASS WIDTH
______are the categories by which data are grouped.
CLASSES
The following stem-and-leaf plot shows the daily high temperature in a town on April 1st for twenty-four random years. Would you expect the mean to be higher or lower than the median? Explain.
The mean should be higher than the median, since the distribution is skewed right.
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.
For IQ scores of students, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right.
bell shaped
The numbers used to separate the classes of a frequency distribution, but without the gaps created by class limits, are called ____________________.
class boundaries
A ____________________ is found by adding the lower and upper class limit and then dividing the sum by 2.
class midpoint
The ____________________ is the difference between two consecutive lower class limits or two consecutive upper class limits.
class width
The ____________________ for a class is the sum of the frequencies for that class and all previous classes.
cumulative class frequency
A(n) ____________________ is a bar graph in which 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.
histogram
The following stem-and-leaf plot shows the daily high temperature in a town on April 1st for twenty-four random years. Which measures of center and spread are most appropriate for this data?
median and interquartile range
A frequency distribution lists _______ of occurrences of each category of data.
number
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
A relative frequency distribution lists the _________ of occurrences of each category of data.
proportion
The data below represent the per capita (average) disposable income (income after taxes) for 25 randomly selected cities in a recent year.
skewed right
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) and (b).(a) Draw a frequency bar graph.(b) Draw a relative frequency graph.
(a) Graph B (b) Graph A
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.
(d) Using the results from part (b), what percentage of the stretches of highway have 5 or more potholes? ADD 5 POT+ 6+7 THEN MULTIPLY BY 100
Suppose that you have data which indicates that 90% of adults in a nearby town have cell phones. Of those who have cell phones, 30% use Carrier A, 30% use Carrier B, 10% use Carrier C, 20% use Carrier D, 5% use Carrier E, and 5% use other carriers. Would a bar graph or pie chart be better if the goal is to compare Carrier B and Carrier C? Explain.
A bar graph would be better since you are trying to compare two parts, not a part to the whole. The angles might be difficult to judge on a pie chart, making it hard to directly compare two sectors.
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) through (e). (a) Construct a relative frequency distribution. (b) According to the data, which blood type is most common? (c) According to the data, which blood type is least common? (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. (e) Contact a local hospital and ask them the percentage of the population that is blood type O. Why might the results differ?
A. ---- B. O C. AB D. 44 INFERENTIAL E. The results might differ because there is always a chance that the sample surveyed is unlike the population.
The following frequency histogram represents the IQ scores of a random sample of seventh-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? (b) Determine the class width. c) Identify the classes and their frequencies. Choose the correct answer below. (d) Which class has the highest frequency? (e) Which class has the lowest frequency? (f) What percent of students had an IQ of at least 120? (g) Did any students have an IQ of 162?
A. 200 students b. class width is 10 c. 60-69, 2; 70-79, 2; 80-89, 13;90-99, 46; 100-109, 49; 110-119, 43;120-129, 33;130-139, 8; 140-149, 3; 150-159, d. 100-109 e. 150-159 f. take 120 all the way through add them divide by 200 multiply by 100 g. No, because there are no bars, or frequencies, greater than an IQ of 160.
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) and (b). (a) Draw a frequency bar graph. (b) Draw a relative frequency bar graph.
A. A B. D
On the basis of a population survey, there were 90.9 million males and 96.8 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. (b) Construct a relative frequency distribution for females. Express each relative frequency as a decimal. (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.
A. ADD AND DIVIDE B. ADD AND DIVIDE C. GRAPH--> CHART---> COLUM D. Each gender's educational attainment is about the same.
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). (a) Construct a relative frequency distribution of the data. (b) What proportion of the tickets were for New York? (c) Construct a frequency bar graph. Choose the correct answer below. (d) Construct a relative frequency bar graph. Choose the correct answer below. (e) Construct a pie chart. Choose the correct answer below. (f) A local news broadcast reported that 14.6% of tickets purchased from the airline are for flights to San Diego. What is wrong with this statement?
A. ADD UP VALUES TO GET TOTAL AND DIVIDE B. 0.235 C. B D. A E. B F. No level of confidence is provided along with the estimate.
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? (b) If there are 24 million adults in the country, how many believe that the action is morally wrong? (c) If a polling organization claimed that the results of the survey indicate that 7% of adults in the country believe that the action is acceptable in certain situations, would you say this statement is descriptive or inferential? Why?
A. About 70% of the respondents B. 20/100=0.2 x 241=48.1 C. The statement is inferential because it makes a prediction.
The pie chart below depicts the beverage size customers choose while at a fast food restaurant. Complete parts (a) through (c). (a) What is the most popular size? What percentage of customers choose this size? (b) What is the least popular size? What percentage of customers choose this size? (c) What percent of customers choose a large-sized beverage?
A. Small; 44% B. Medium; 11% C. 32%
The following Pareto chart shows the position played by the most valuable player (MVP) in a certain baseball league for the last 83 years. Use the chart to answer parts (a) through (d). a) Which position had the most MVPs? (b) How many MVPs played pitcher (P)? (c) How many more MVPs played outfield (OF) than pitcher? (d) There are three outfield positions (left field, center field, right field). Given this, how might the graph be misleading?
A. The position with the most MVPs was outfield (OF). B. 7 C. 25 D. The chart seems to show that one position has many more MVPs because three positions are combined into one. They should be separated.
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? If it makes sense, draw a pie chart. Choose the correct answer below. (b) Would it make sense to draw a pie chart for the highest elevation? If it makes sense, draw a pie chart. Choose the correct answer below.
A. YES, A B. NO, NO
What is an advantage to using a stem-and-leaf plot instead of a histogram to display data?
A stem-and-leaf plot allows for retrieval of the original data from the plot while the histogram does not.
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 Which of the following graphs would be most appropriate for visually displaying the results?
Frequency Bar Graph
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown.Draw a pie chart.
GRAPH D
Which information can you obtain from a stem-and-leaf plot but not from a histogram?
Minimum and maximum data values
Consider the information in the "Why we can't lose weight" 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%.
Suppose a newspaper surveys 250 adults in a nearby town and inquires about their cell phone carrier. The accompanying table summarizes the results. Does this table describe a relative frequency distribution? Why or why not?
No. The sum of the relative frequencies is 95%, not 100%.
Determine the level of measurement of the variable. LETTER GRADES IN A MATH COURSE
ORDINAL
Suppose you want to know if more technical service calls are made to homes with cable television or with satellite dish television. Should you use frequencies or relative frequencies to make the comparison? Why?
Relative frequencies should be used since there is likely a difference in the number of users of cable and satellite television. If you make comparisons using frequencies, the results can be very misleading for different population sizes.
This histogram shows the heights of 20 students in a statistics class. Explain why it is not appropriate to find summary statistics for this distribution.
Since there appear to be two modes, this data probably represents men and women and should be split into those two groups before finding any summary statistics.
Which two graphs allow the reader to retrieve the original list of data?
Stem-and-leaf plots and dotplots
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.
Determine whether the quantitative variable is discrete or continuous. POPULATION IN A CITY
The variable is discrete because it is countable.
Determine whether the variable is qualitative or quantitative. ADDRESS
The variable is qualitative because it is an attribute characteristic.
Determine whether the variable is qualitative or quantitative. NAMER OF ORIGIN
The variable is qualitative because it is an attribute characteristic.
Over the course of a decade, a certain police department issued 157.8 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.(a) Construct a relative frequency distribution of the males who received tickets.(b) Construct a relative frequency distribution of the females who received tickets.(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)Age Group Relative Frequency16-25 0.31526-35 0.2336-45 0.18946-55 0.114>56 0.152 (b) 75.716-25 0.29426-35 0.22736-45 0.19746-55 0.108>55 0.175( c) Graph B
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) through (e).(a) Construct a relative frequency distribution(b) According to the data, which blood type is most common?(c) According to the data, which blood type is the least common?(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.(e) Contact a local hospital and ask them the percentage of the population that is blood type O. Why might the results differ?
a)Blood Type Frequency A 19/50 = 0.38AB 3/50 = 0.06B 7/50 = 0.14O 21/50 = 0.42 (b) O (c) AB (d) 42% inferential (e) The results might differ because there is always a chance that the sample surveyed is unlike the population.
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. a) There are______ classes b) The lower class limit for the second class is _____ The upper class limit for the first class is ______ c) The class width is_______
a. 5 b. 10 c. 14.9 d. 5
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. Click the icon to view the table of television counts. a) Are these data discrete or continuous? Explain.
a. The given data are discrete because they can only have whole number values.
In a relative frequency distribution, what should the relative frequencies add up to?
add up to 1
