Deck 2: Methods for Describing Sets of Data

Question 1

The box plot shown below was constructed for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local soda bottling company.

We see that one soda can received 12.15 ounces of soda on the plot above. Based on the box plot presented, how would you classify this observation?

A) it has a lot of soda
B) suspect outlier
C) highly suspect outlier
D) expected observation

Answer 1

suspect outlier

Question 2

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) $400
C) $600
D) $465

Answer 2

D

Question 3

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

Answer 3

23 teams

Question 4

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

Question 5

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 $\begin{array}{lc}\text { Leaf Digit Unit }=0.01 & \text { Minimum } 1.9900 \\199 \text { represents } 1.99 & \text { Median } 3.1050 \\&\text { Maximum } 4.0000\end{array}$
$$\begin{array} { l l l } & \text { Stem } & \text { Leaves } \\1 & 19 & 9 \\5 & 20 & 0668 \\6 & 21 & 0 \\11 & 22 & 05567 \\15 & 23 & 0113 \\20 & 24 & 00005 \\33 & 25 & 0000000000067 \\46 & 26 & 0000005577789 \\61 & 27 & 000000134455578 \\79 & 28 & 000000000144667799 \\88 & 29 & 002356777 \\116 & 30 & 0000000000000000000011344559 \\( 19 ) & 31 & 0000000000112235666 \\117 & 32 & 0000000000000000345568 \\95 & 33 & 000000000025557 \\80 & 34 & 0000000000000000333444566677889 \\49 & 35 & 000003355566677899 \\31 & 36 & 000005 \\25 & 37 & 022235588899 \\13 & 38 & 00002579 \\5 & 39 & 7 \\4 & 40 & 0000 \\& & \\252 \text { cases included }\end{array}$$

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

Question 6

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

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

Question 7

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 was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, what percentage of the player's serve speeds are less than 70 mph?

A) at most 11%
B) approximately 2.5%
C) approximately 5%
D) at most 12.5%
E) at most 25%

Question 8

The total points scored by a basketball team for each game during its last season have been summarized in the table below. Which statement following the table must be true?

A) The range is at least 41 but at most 120.
B) The range is at least 81 but at most 100.
C) The range is 79.
D) The range is at least 41 but at most 79.

Question 9

A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $100 and a standard deviation of $14. Three solar homes reported monthly utility bills of $51, $48, and $56. Which of the following statements is true?

A) The utility bills for homes using solar power are about the same as those for homes using only gas and electricity.
B) Homes using solar power may have lower utility bills than homes using only gas and electricity.
C) Homes using solar power may actually have higher utility bills than homes using only gas and electricity.
D) Homes using solar power always have lower utility bills than homes using only gas and electricity.

Question 10

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

Question 11

The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming the distribution of commuting times is known to be moundshaped and symmetric, what percentage of these commuting times are between 50 and 110 minutes?

A) approximately 95%
B) approximately 68%
C) approximately 97.5%
D) approximately 81.5%

Question 12

A sample of professional golfers was taken and their driving distance (measured as the average distance as their drive off the tee) and driving accuracy (measured as the percentage of fairways that their drives landed in) were recorded. A scatterplot of the variables is shown below.
What relationship do these two variables exhibit?

A) They exhibit a positive linear relationship
B) They exhibit a curvillinear relationship
C) They exhibit a negative linear relationship
D) They exhibit no relationship

Question 13

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 percentage
C) a class frequency
D) a class

Question 14

Which number on the screen below is the sample standard deviation of the data?

A) 2.82
B) 5.8
C) 408
D) 2.67

Question 15

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 10
C) Approximately 25
D) Approximately 125

Question 16

Calculate the variance of a sample for which $n = 5 , \sum x ^ { 2 } = 1320 , \quad \sum x = 80 .$

A) 8.00
B) 326.00
C) $3.16$
D) 10.00

Question 17

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) 26.6%
C) 76%
D) 73.4%

Question 18

The box plot shown below was constructed for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local soda bottling company.

We see that one soda can received 12.30 ounces of soda on the plot above. Based on the box plot
Presented, how would you classify this observation?

A) it has a lot of soda
B) highly suspect outlier
C) expected observation
D) suspect outlier

Question 19

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 96 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) 86 mph
B) 96 mph
C) 101 mph
D) 91 mph

Question 20

Calculate the standard deviation of a sample for which

A) 46.00
B) 6.19
C) 164.00
D) 6.78

Question 21

The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score?

A) 70.5
B) cannot be determined
C) 78
D) 99

Question 22

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 was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric.
What percentage of the player's serves were between 115 mph and 145 mph?

A) at most 13.5%
B) approximately 16%
C) at most 2.5%
D) at most 34%

Question 23

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

Question 24

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?

A) 75% of the students sampled had textbook costs that exceeded $500.
B) 75% of the students sampled had textbook costs equal to $500.
C) 25% of the students sampled had textbook costs that exceeded $500.
D) The average of the 500 textbook costs was $500.

Question 25

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. $$\begin{array} { r | l l l l l l l l l } \text { Stem } & & & & & \\\hline 3 & 1 & 6 & & & & & & \\4 & 0 & 3 & 4 & 7 & 8 & 9 & 9 & 9 \\5 & 0 & 1 & 1 & 2 & 3 & 4 & 5 & \\6 & 1 & 2 & 5 & 6 & 6 & & & \\7 & 1 & 4 & & & & & \\8 & & & & & & & \\9 & 5 & & & & & &\end{array}$$ What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)?

A) 1%
B) 5%
C) 4%
D) 20%

Question 26

By law, a box of cereal labeled as containing 24 ounces must contain at least 24 ounces of cereal. The machine filling the boxes produces a distribution of fill weights that is mound-shaped and symmetric, with a mean equal to the setting on the machine and with a standard deviation equal to 0.02 ounce. To ensure that most of the boxes contain at least 24 ounces, the machine is set so that the mean fill per box is 24.06 ounces. What percentage of the boxes do, in fact, contain at least 24 ounces?

Question 27

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

Question 28

A recent survey was conducted to compare the cost of solar energy to the cost of gas or
electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $124.00 and a standard deviation of $15.00. Assuming the distribution is mound-shaped and symmetric, would you expect to see a 3-bedroom house using gas or electric energy with a monthly utility bill of $236.50? Explain.

Question 29

The output below displays the mean and median for the state high school dropout rates in
year 1 and in year 5. $$\begin{array} { l r r } & \text { Year 1 } & \text { Year 5 } \\\text { N } & 51 & 51 \\\text { MEAN } & 28.22 & 26.56 \\\text { MEDIAN } & 27.53 & 25.18\end{array}$$ Use the information to determine the shape of the distributions of the high school dropout rates in year 1 and year 5.

Question 30

The table shows the number of each type of book found at an online auction site during arecent search.

$$\begin{array} { | l | c | } \hline \text { Type of Book } & \text { Number } \\\hline \text { Children's } & 51,033 \\\hline \text { Fiction } & 141,114 \\\hline \text { Nonfiction } & 253,074 \\\hline \text { Educational } & 67,252 \\\hline\end{array}$$ a. Construct a relative frequency table for the book data.
b. Construct a pie chart for the book data.

Question 31

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

Question 32

Which of the following is a measure of the variability of a distribution?

A) skewness
B) range
C) sample size
D) median

Question 33

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 standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z-score for this student's textbook expenditure.

A) -2
B) -3
C) +2
D) +3

Question 34

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

Question 35

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 55 miles per hour?

A) 0.64
B) 0.50
C) 0.14
D) 7

Question 36

Explain how using a scale break on the vertical axis of a histogram can be misleading.

Question 37

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 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds?

Speeds: 50 mph, 80 mph, and 105 mph

A) 50 is the only outlier.
B) 50, 80, and 105 are all outliers.
C) 50 and 80 are both outliers, 105 is not.
D) None of the three speeds are outliers.

Question 38

The z-score for a value x is -2.5. State whether the value of x lies above or below the mean and by how many standard deviations.

Question 39

The temperature fluctuated between a low of 73°F and a high of 89°F. Which of the following could be calculated using just this information?

A) variance
B) median
C) standard deviation
D) range

Question 40

The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes?

A) at least 75%
B) at least 89%
C) at least 0%
D) at least 95%

Question 41

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.

$$\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}$$

Question 42

Explain how it can be misleading to draw the bars in a histogram so that the width of each bar is proportional to its height rather than have all bars the same width.

Question 43

A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 310 and a standard deviation of 50 on a standardized test. Find and interpret the z-score of a student who scored 490 on the standardized test.

Question 44

Complete the frequency table for the data shown below.
$\begin{array}{lllll}\text { green } & \text { blue } & \text { brown } & \text { orange } & \text { blue } \\\text { brown } & \text { orange } & \text { blue } & \text { red } & \text { green } \\\text { blue } & \text { brown } & \text { green } & \text { red } & \text { brown } \\\text { blue } & \text { brown } & \text { blue } & \text { blue } & \text { red }\end{array}$

$\begin{array}{l|l}\text { Color } & \text { Frequency } \\\hline \text { Green } & \\\hline \text { Blue } & \\\hline \text { Brown } & \\\hline \text { Orange } & \\\hline &\end{array}$

Question 45

The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). Three hundred parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television.
The upper quartile for the distribution was given as 20 hours. Interpret this value.

Question 46

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.
$\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\\ 11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29 \end{array}$

a. Complete the class frequency table for the data.
$$\begin{array} { | c | c | } \hline \text { Total Medals } & \text { Frequency } \\\hline 1 - 5 & \\\hline 6 - 10 & \\\hline 11 - 15 & \\\hline 16 - 20 & \\\hline 21 - 25 & \\\hline 26 - 30 & \\\hline\end{array}$$
b. Using the classes from the frequency table, construct a histogram for the data.

Question 47

The following data represent the scores of 50 students on a statistics exam. $$\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array}$$
a. Find the lower quartile, the upper quartile, and the median of the scores.
b. Find the interquartile range of the data and use it to identify potential outliers.
c. In a box plot for the data, which scores, if any, would be outside the outer fences?
Which scores, if any, would be outside the inner fences but inside the outer fences?

Question 48

The total points scored by a basketball team for each game during its last season have been
summarized in the table below.
$$\begin{array} { | c | c | } \hline \text { Score } & \text { Frequency } \\\hline 41 - 60 & 3 \\\hline 61 - 80 & 8 \\\hline 81 - 100 & 12 \\\hline 101 - 120 & 7 \\\hline\end{array}$$
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 49

In a summary of recent real estate sales, the median home price is given as $325,000. What percentile corresponds to a home price of $325,000?

Question 50

Suppose that 50 and 75 are two elements of a population data set and their z-scores are -3 and 2, respectively. Find the mean and standard deviation.

Question 51

The table shows the number of each type of car sold in June.
$$\begin{array} { | l | c | } \hline \text { Car } & \text { Number } \\\hline \text { compact } & 7,204 \\\hline \text { sedan } & 9,089 \\\hline \text { small SUV } & 20,418 \\\hline \text { large SUV } & 13,691 \\\hline \text { minivan } & 15,837 \\\hline \text { truck } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array}$$ 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 52

A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 93 jobs and a standard deviation of 8. On what percentage of days do the number of jobs submitted exceed 101?

Question 53

The data below show the types of medals won by athletes representing the United States in the Winter Olympics.

$$\begin{array} { l l l l l l l } \text { gold } & \text { gold } & \text { silver } & \text { gold } & \text { bronze } & \text { silver } & \text { silver } \\\text { bronze } & \text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { silver } & \text { gold } \\\text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { bronze } & \text { gold } & \text { silver } \\\text { gold } & \text { gold } & \text { bronze } & \text { bronze } & & &\end{array}$$ 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.

Question 54

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?
$$\begin{array} { l | c | c } \begin{array} { l } \text { Employee } \\\text { Theft }\end{array} & \begin{array} { c } \text { Percentage } \\\text { in year 1 }\end{array} & \begin{array} { c } \text { Percentage } \\\text { in year 2 }\end{array} \\\hline \text { Yes } & 34 & 23 \\\text { No } & 51 & 68 \\\text { Don't know } & 15 & 9 \\\text { Totals } & 100 & 100\end{array}$$

Question 55

The scores for a statistics test are as follows: $\begin{array} { l l l l l l l l l l } 87 & 76 & 92 & 77 & 92 & 96 & 88 & 85 & 66 & 89 \end{array}$
$\begin{array} { l l l l l l l l l l } 79 & 96 & 50 & 98 & 83 & 88 & 82 & 51 & 10 & 69 \end{array}$
Create a stem-and-leaf display for the data.

Question 56

The data below represent the numbers of absences and the final grades of 15 randomly
selected students from a statistics class. Construct a scattergram for the data. Do you detect
a trend? $$\begin{array} { c c c } \text { Student } & \text { Number of Absences } & \text { Final Grade as a Percent } \\1 & 5 & 79 \\2 & 6 & 78 \\3 & 2 & 86 \\4 & 12 & 56 \\5 & 9 & 75 \\6 & 5 & 90 \\7 & 8 & 78 \\8 & 15 & 48 \\9 & 0 & 92 \\10 & 1 & 78 \\11 & 9 & 81 \\12 & 3 & 86 \\13 & 10 & 75 \\14 & 3 & 89 \\15 & 11 & 65\end{array}$$

Question 57

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 and standard deviation of the test scores are 76 and 4, respectively, and the distribution of scores is mound-shaped and symmetric. If a firm wanted to give the best 2.5% of the trainees a big promotion, what test score would be used to identify the trainees in question?

Question 58

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.
$$\begin{array} { c c c c c c c c c } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}$$

Question 59

Explain how it can be misleading to report only the mean of a distribution without any measure of the variability.

Question 60

Use a graphing calculator or software to construct a box plot for the following data set.

Question 61

The calculator screens summarize a data set.
a. Identify the smallest measurement in the data set.
b. Identify the largest measurement in the data set.
c. Calculate the range of the data set.

Question 62

The scores of nine members of a women's golf team in two rounds of tournament play are listed below.
$$\begin{array} { l | c | c | c | c | c | c | c | c | c } \text { Player } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Round 1 } & 85 & 90 & 87 & 78 & 92 & 85 & 79 & 93 & 86 \\\text { Round 2 } & 90 & 87 & 85 & 84 & 86 & 78 & 77 & 91 & 82\end{array}$$ Construct a scattergram for the data.

Question 63

For a given data set, which is typically greater, the range or the standard deviation?

Question 64

The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. $$\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array}$$ Find the z-scores for the highest and lowest exam scores.

Question 65

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:

$\begin{array}{lllr}\text { Company A } & \$ 71 & \text { Company F } & \$ 25.9 \\\text { Company B } & 63.7 & \text { Company G } & 24.6 \\\text { Company C } & 54.5 & \text { Company H } & 23.1 \\\text { Company D } & 54.1 & \text { Company I } & 23.6 \\\text { Company E } & 28.5 & \text { Company J } & 19.8\end{array}$
Calculate the mean and median for the data.

Question 66

Given the sample variance of a distribution, explain how to find the standard deviation.

Question 67

Explain how stretching the vertical axis of a histogram can be misleading.

Question 68

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 69

Calculate the mean of a sample for which $\sum x = 196 \text { and } n = 8$

Question 70

The mean x of a data set is 18, and the sample standard deviation s is 2. Explain what the interval (12, 24) represents.

Question 71

A radio station claims that the amount of advertising each hour has an a mean of 17 minutes and a standard deviation of 2.5 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 11.75 minutes. Based on your observation, what would you infer about the radio station's claim?

Question 72

For a given data set, the lower quartile is 45, the median is 50, and the upper quartile is 57.
The minimum value in the data set is 32, and the maximum is 81.
a. Find the interquartile range.
b. Find the inner fences.
c. Find the outer fences.
d. Is either of the minimum or maximum values considered an outlier? Explain.

Question 73

What is the primary advantage of a time series plot?

Question 74

A retail store's customer satisfaction rating is at the 88th percentile. What percentage of retail stores has higher customer satisfaction ratings than this store?

Question 75

The ages of five randomly chosen professors are 58, 61, 62, 69, and 44. Calculate the sample variance of these ages.

Question 76

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.
$$\begin{array} { | c | c | } \hline \text { Score } & \text { Frequency } \\\hline 41 - 60 & 3 \\\hline 61 - 80 & 8 \\\hline 81 - 100 & 12 \\\hline 101 - 120 & 7 \\\hline\end{array}$$

Question 77

The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. $$\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array}$$ What percentage of the scores lies within one standard deviation of the mean? two standard deviations of the mean? three standard deviations of the mean? Based on these percentages, do you believe that the distribution of scores is mound-shaped and symmetric? Explain.

Question 78

The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. $$\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array}$$ Use the z-score method to identify potential outliers among the scores.

Question 79

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 80

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 190 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 190 times collected.