Deck 2: Methods for Describing Sets of Data

Question 1

The bar graph shows the political affiliation of 1000 registered U.S. voters. What percentage of the voters belonged to one of the traditional two parties (Democratic or Republican)?

A) 75%
B) 40%
C) 35%
D) 25%

Answer 1

A

Question 2

The data below show the types of medals won by athletes representing the United States in the Winter Olympics. a. Construct a frequency table for the data. b. Construct a relative frequency table for the data. c. Construct a frequency bar graph for the data.

Answer 2

Question 3

If 25% of your statistics class is sophomores, then in a pie chart representing classifications of the students in your statistics class the slice assigned to sophomores is 90°.

Answer 3

True

Question 4

The pie chart shows the classifications of students in a statistics class. What percentage of the class consists of freshman, sophomores, and juniors?

A) 86%
B) 14%
C) 44%
D) 54%

Question 5

Either vertical or horizontal bars can be used when constructing a bar graph.

Question 6

The table shows the number of each type of book found at an online auction site during a recent search. a. Construct a relative frequency table for the book data. b. Construct a pie chart for the book data.

Question 7

The slices of a pie chart must be arranged from largest to smallest in a clockwise direction.

Question 8

The table shows the number of each type of car sold in June. a. Construct a relative frequency table for the car sales. b. Construct a Pareto diagram for the car sales using the class percentages as the heights of the bars.

Question 9

Complete the frequency table for the data shown below.

Question 10

The bars in a bar graph can be arranged by height in ascending order from left to right.

Question 11

260 randomly sampled college students were asked, among other things, to state their year in school (freshman, sophomore, junior, or senior). The responses are shown in the bar graph below. How many of the students who responded would be classified as upperclassmen (e.g., juniors or seniors)?

A) Approximately 100
B) Approximately 125
C) Approximately 10
D) Approximately 25

Question 12

A frequency table displays the proportion of observations falling into each class.

Question 13

A sample of 100 e-mail users were asked whether their primary e-mail account was a free account, an institutional (school or work) account, or an account that they pay for personally. Identify the classes for the resulting data.

Question 14

One of the questions posed to a sample of 286 incoming freshmen at a large public university was, "Do you have any tattoos?" Their responses are shown below in the pie chart. Please note that the values shown represent the number of responses in each category. Based on the responses shown in the pie chart, what percentage of the freshmen responded with "Yes?"

A) 76
B) 76%
C) 26.6%
D) 73.4%

Question 15

What characteristic of a Pareto diagram distinguishes it from other bar graphs?

Question 16

What number is missing from the table? $$\begin{array} { | c | c | c | } \hline \begin{array} { c } \text { Grades } \\\text { on Test }\end{array} & \text { Frequency } & \begin{array} { c } \text { Relative } \\\text { Frequency }\end{array} \\\hline \text { A } & 6 & .24 \\\hline \text { B } & 7 & \\\hline \text { C } & 9 & .36 \\\hline \text { D } & 2 & .08 \\\hline \text { F } & 1 & .04 \\\hline\end{array}$$

A) .28
B) .07
C) .72
D) .70

Question 17

What class percentage corresponds to a class relative frequency of .37?

A) 37%
B) .37%
C) .63%
D) 63%

Question 18

In an eye color study, 25 out of 50 people in the sample had brown eyes. In this situation, what does the number .50 represent?

A) a class relative frequency
B) a class
C) a class frequency
D) a class percentage

Question 19

What number is missing from the table? $$\begin{array} { | l | c | c | } \hline \begin{array} { c } \text { Year in } \\\text { College }\end{array} & \text { Frequency } & \begin{array} { c } \text { Relative } \\\text { Frequency }\end{array} \\\hline \text { Freshman } & 600 & .30 \\\hline \text { Sophomore } & 560 & .28 \\\hline \text { Junior } & & .22 \\\hline \text { Senior } & 400 & .20 \\\hline\end{array}$$

A) 440
B) 220
C) 480
D) 520

Question 20

The manager of a store conducted a customer survey to determine why customers shopped at the store. The results are shown in the figure. What proportion of customers responded that merchandise was the reason they shopped at the store?

Question 21

Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 300 students and recorded how long it took each of them to find a parking spot. Which of the following types of graphs should not be used to display information concerning the students parking times?

A) pie chart
B) stem-and-leaf display
C) histogram
D) box plot

Question 22

The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics.

Question 23

All class intervals in a histogram have the same width.

Question 24

A dot plot of the speeds of a sample of 50 cars passing a policeman with a radar gun is shown below. What proportion of the motorists were driving above the posted speed limit of 60 miles per hour?

A) 0.18
B) 0.22
C) 0.04
D) 2

Question 25

Class relative frequencies must be used, rather than class frequencies or class percentages, when constructing a Pareto diagram.

Question 26

A histogram can be constructed using either class frequencies or class relative frequencies as the heights of the bars.

Question 27

The payroll amounts for all teams in an international hockey league are shown below using a graphical technique from chapter 2 of the text. How many of the hockey team payrolls exceeded $20 million (Note: Assume that no payroll was exactly $20 million)?

A) 8 teams
B) 23 teams
C) 10 teams
D) 18 teams

Question 28

The bars in a histogram should be arranged by height in descending order from left to right.

Question 29

A data set contains the observations 5, 3, 6, 1, 4. Find $\sum x^ { 2 } .$

A) 87
B) 361
C) 38
D) 19

Question 30

The scores for a statistics test are as follows: Create a stem-and-leaf display for the data.

Question 31

The total points scored by a basketball team for each game during its last season have been summarized in the table below. a. Explain why you cannot use the information in the table to construct a stem-and-leaf display for the data. b. Construct a histogram for the scores.

Question 32

For large data sets, a stem-and-leaf display is a better choice than a histogram.

Question 33

252 randomly sampled college students were asked, among other things, to estimate their college grade point average (GPA). The responses are shown in the stem-and-leaf plot shown below. Notice that a GPA of 3.65 would be indicated with a stem of 36 and a leaf of 5 in the plot. How many of the students who responded had GPA's that exceeded 3.55? Stem and Leaf Plot of GPA 252 cases included

A) 31
B) 49
C) 39
D) 19

Question 34

An annual survey sent to retail store managers contained the question "Did your store suffer any losses due to employee theft?" The responses are summarized in the table for two years. Compare the responses for the two years using side-by-side bar charts. What inferences can be made from the charts?

Question 35

A data set contains the observations 2, 6, 4, 7, 3. Find $\sum { x }$ .

A) 22
B) 19
C) 1008
D) 5

Question 36

A data set contains the observations 8, 1, 6, 7, 2. Find $\left( \sum { x } \right) ^ { 2 }$

A) 576
B) 154
C) 48
D) 24

Question 37

Fill in the blank. One advantage of the __________ is that the actual data values are retained in the graphical summarization of the data.

A) stem-and-leaf plot
B) histogram
C) pie chart 2.3 Summation Notation
1 Use Summation Notation

Question 38

Which of the graphical techniques below can be used to summarize qualitative data?

A) bar graph
B) dot plot
C) stem-and-leaf plot
D) box plot

Question 39

A Pareto diagram is a pie chart where the slices are arranged from largest to smallest in a counterclockwise direction.

Question 40

A survey was conducted to determine how people feel about the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. $\begin{array}{r|llllllll}\text { Stem } & \text { Leaf } & & & & & \\\hline 3 & 3 & 6 & & & & & & \\4 & 0 & 3 & 4 & 7 & 8 & 9 & 9 & 9 \\5 & 0 & 1 & 1 & 2 & 3 & 4 & 5 \\6 & 1 & 2 & 5 & 6 & 6 & & & \\7 & 5 & 8 & & & & & & \\8 & & & & & & & & \\9 & 3 & & & & & & &\end{array}$
What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)?

A) 4%
B) 1%
C) 12%
D) 3%

Question 41

The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5. $$\begin{array} { l r r } & \text { Year 1 } & \text { Year 5 } \\\text { N } & 51 & 51 \\\text { MEAN } & 28.26 & 26.26 \\\text { MEDIAN } & 27.41 & 25.28\end{array}$$ Interpret the year 5 median dropout rate of 25.28.

A) Half of the 51 states had a dropout rate below 25.28%.
B) Most of the 51 states had a dropout rate close to 25.28%.
C) The most frequently observed dropout rate of the 51 states was 25.28%.
D) Half of the 51 states had a dropout rate of 25.28%.

Question 42

The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the mean, median, and mode of the numbers of medals won by these countries.

Question 43

Which expression represents the sum of the squares of the observations in a data set?

Question 44

A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: $$\begin{array} { l l l l l } 72 & 77 & 70 & 80 & 90 \\78 & 65 & 93 & 69 & 94 \\73 & 96 & 80 & 66 & 85 \\67 & 72 & 85 & 74 & 77 \\64 & 91 & 79 & 68 & 86\end{array}$$ Find the median of the observations.

A) 77
B) 74
C) 78
D) 77.5

Question 45

Calculate the mean of a sample for which

Question 46

Question 47

A data set contains the observations 8, 3, 2, 6, 7. Find $\sum ( x - 5 )$

A) 1
B) 51
C) 31
D) 21

Question 48

In a distribution that is skewed to the right, what is the relationship of the mean, median, and mode?

A) mean > median > mode
B) median > mean > mode
C) mode > median > mode
D) mode > mean > median

Question 49

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample mean for the data.

A) $450
B) $465
C) $600
D) $400

Question 50

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the mean is correct?

A) The average of the textbook costs sampled was $500
B) The most frequently occurring textbook cost in the sample was $500
C) 50% of the students sampled had textbook costs equal to $500
D) 50% of the students sampled had textbook costs that were less than $500

Question 51

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 95 miles per hour. Suppose that the statistician indicated that the serve speed distribution was skewed to the left. Which of the following values is most likely the value of the median serve speed?

A) 102 mph
B) 88 mph
C) 81 mph
D) 95 mph

Question 52

Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean of the test scores is 74. Additional information indicated that the median of the test scores was 84. What type of distribution most likely describes the shape of the test scores?

A) skewed to the left
B) symmetric
C) skewed to the right
D) unable to determine with the information given

Question 53

A data set contains the observations 1, 6, 4, 5, 7. Find $\sum x ^ { 2 } - \frac { \left( \sum x \right) ^ { 2 } } { 5 }$

A) 21.2
B) 423.2
C) 101.6
D) 232.8

Question 54

The scores for a statistics test are as follows: $$\begin{array} { l l l l l l l l l l } 95 & 76 & 68 & 77 & 73 & 92 & 81 & 85 & 77 & 89 \\79 & 87 & 50 & 60 & 85 & 72 & 85 & 62 & 18 & 74\end{array}$$ Compute the mean score.

A) 74.25
B) 77.45
C) 65.20
D) 75

Question 55

A shoe retailer keeps track of all types of information about sales of newly released shoe styles. One newly released style was marketed to tall people. Listed below are the shoe sizes of 12 randomly selected customers who purchased the new style. Find the mode of the shoe sizes.

Question 56

The calculator screens summarize a data set. a. How many data items are in the set? b. What is the sum of the data? c. Identify the mean, median, and mode, if possible.

Question 57

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct?

A) The average of the textbook costs sampled was $425
B) The most frequently occurring textbook cost in the sample was $425
C) 50% of the students sampled had textbook costs equal to $425
D) 50% of the students sampled had textbook costs that were less than $425

Question 58

During one recent year, U.S. consumers redeemed 6.79 billion manufacturers' coupons and saved themselves $2.56 billion. Calculate and interpret the mean savings per coupon.

A) The average savings was $0.38 per coupon.
B) The average savings was 265.2 cents per coupon.
C) Half of all coupons were worth more than 265.2 cents in savings.
D) Half of all coupons were worth more than $0.38 in savings.

Question 59

Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: Calculate the mean and median for the data.

Question 60

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample median for the data.

A) $450
B) $465
C) $600
D) $400

Question 61

The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries.

Question 62

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample range for the data.

A) $99.37
B) $98.75
C) $450
D) $250

Question 63

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data.

A) $99.37
B) $98.75
C) $450
D) $250

Question 64

In symmetric distributions, the mean and the median will be approximately equal.

Question 65

The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5. Use the information to determine the shape of the distributions of the high school dropout rates in year 1 and year 5.

Question 66

The total points scored by a basketball team for each game during its last season have been summarized in the table below. Identify the modal class of the distribution of scores.

Question 67

The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places. 180, 100, 195, 130, 155

A) 38.1772
B) 243.3465
C) 174.0675
D) 137.11

Question 68

In a symmetric and mound shaped distribution, we expect the values of the mean, median, and mode to differ greatly from one another.

Question 69

Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 280 students and recorded how long it took each of them to find a parking spot. The times had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 280 times collected.

Question 70

In skewed distributions, the mean is the best measure of the center of the distribution since it is least affected by extreme observations.

Question 71

Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: $$\begin{array} { l r l r } \text { Company A } & \$ 71.4 & \text { Company F } & \$ 27.1 \\\text { Company B } & 60.1 & \text { Company G } & 25.1 \\\text { Company C } & 56.5 & \text { Company H } & 23.1 \\\text { Company D } & 55 & \text { Company I } & 22.9 \\\text { Company E } & 28.6 & \text { Company J } & 20.6\end{array}$$ Calculate the sample variance.

A) 372.307
B) 3759.244
C) 2070.113
D) 1854.860

Question 72

Calculate the range of the following data set: 9, 6, 9, 2, 8, 10, 6, 6, 9

A) 8
B) 10
C) 2
D) 12

Question 73

The mean and the median are useful measures of central tendency for both qualitative and quantitative data.

Question 74

In practice, the population mean μ is used to estimate the sample mean x.

Question 75

In general, the sample mean is a better estimator of the population mean for larger sample sizes.

Question 76

A shoe company reports the mode for the shoe sizes of men's shoes is 12. Interpret this result.

A) The most frequently occurring shoe size for men is size 12
B) Most men have shoe sizes between 11 and 13.
C) Half of the shoes sold to men are larger than a size 12
D) Half of all men's shoe sizes are size 12

Question 77

Which of the following is not a measure of central tendency?

A) range
B) median
C) mode
D) mean

Question 78

The calculator screens summarize a data set. a. Identify the mean and the median. b. Based only on the mean and the median, do you expect that the data set is skewed to the right, symmetric, or skewed to the left? Explain.

Question 79

The ages of five randomly chosen professors are 69, 52, 55, 62, and 49. Calculate the sample variance of these ages.

Question 80

The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?

A) median
B) mode
C) mean
D) range