QUESTIONS
Question 1
You are told that a data set has a median of 35 and a mean of 42. Which of the following is a logical conclusion?
Question 2
Based on the z scores found above, in which city would a home priced at 200,000 be closer to the mean price, compared to the distribution of prices in the city?
Question 3
In a recent national survey, the mean price for a 2000 sq ft home in Florida is $240,000 with a standard deviation of $16,000. The mean price for the same sized home in Ohio is $170,000 with a standard deviation of $12,000.
In which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?
Find the z-score corresponding to each state.
Question 4
Which of the following frequency tables show a skewed data set? Select all answers that apply.
Question 5
The following data set represents the ages of all 6 of Nancy’s grandchildren.
11,8,5,6,3,9
Given that the variance of this data set is 7, what is the standard deviation of their ages?
- Round the final answer to one decimal place.
Question 6
The following data set represents the ages of all 6 of Nancy’s grandchildren.
11,8,5,6,3,9
Find the variance of their ages.
- If necessary, round the final answer to one decimal place.
Question 7
The following data set represents the ages of all 6 of Nancy’s grandchildren.
11,8,5,6,3,9
To determine the “spread” of the data, would you employ calculations for the sample standard deviation, or population standard deviation for this data set?
Question 8
A group of five friends are long-distance runners who will be running in an upcoming marathon. To prepare for the marathon, each of the friends recorded the number of miles they ran each week for 12 weeks. The results of the friends’ training are shown in the data set provided below. Which of the friends was the most consistent with the number of miles run each week during the training? Hint: You should not need to compute the standard deviation for each friend.
| Ashton | Caleb | Jordan | Kyle | Noah |
| 24 | 35 | 22 | 15 | 13 |
| 34 | 36 | 39 | 26 | 29 |
| 25 | 34 | 26 | 24 | 18 |
| 31 | 35 | 41 | 25 | 31 |
| 19 | 37 | 38 | 27 | 15 |
| 33 | 35 | 37 | 24 | 19 |
| 27 | 34 | 40 | 25 | 27 |
| 29 | 36 | 27 | 26 | 32 |
| 36 | 35 | 21 | 32 | 15 |
| 16 | 33 | 42 | 24 | 17 |
| 18 | 36 | 33 | 21 | 28 |
| 26 | 35 | 35 | 27 | 21 |
Question 9
A food processing plant fills snack-sized bags of crackers. The mean number of crackers in each bag is 22 and the standard deviation is 2. The factory supervisor selects one bag that contains 24 crackers.
Which of the following statements is true?
Question 10
Given the following box-and-whisker plot, decide if the data is skewed or symmetric.
Question 11
A data set of the population densities of 15 U.S. states has a mean of 154 and a median of 94. Which of the following is a logical conclusion?
Question 12
Which of the following histograms shows a skewed data set?
Select all correct answers.
Question 13
Which of the following box-and-whisker plots shows a skewed data set? Select all answers that apply.
Question 14
You are told that a data set has a median of 64 and a mean of 52. Which of the following is a logical conclusion?
Question 15
A data set lists the number of questions each student asked the teacher during a math class. For this data set, the minimum is 4, the first quartile is 6, the median is 7, the third quartile is 9, and the maximum is 16. Construct a box-and-whisker plot that shows the number of questions asked.
Question 16
A data set lists the number of times a machine breaks each month in a clothing factory over the past year. For this data set, the minimum is 4, the median is 14, the third quartile is 17, the interquartile range is 6, and the maximum is 18. Construct a box-and-whisker plot that shows the number of times the machine breaks.
Question 17
Based on the box-and-whisker plot you constructed above, what is the interquartile range of the data?
Question 18
A data set lists the number of red lights Stan encounters as he drives to work each day. For this data set, the minimum is 0, the first quartile is 2, the median is 3, the third quartile is 5, and the maximum is 6.
Construct a box-and-whisker plot that shows the number of red lights. Drag the dots to create the box plot. Note: It is helpful to set the median first.
Question 19
Given the following box-and-whisker plot, what is the third quartile of the data?
Question 20
Based on the box-and-whisker plot you constructed above, what is the interquartile range of the data?
Question 21
A data set lists the number of times students buy snacks each month at the school vending machine. For this data set, the minimum is 1, the first quartile is 3, the median is 5, the third quartile is 7, and the maximum is 17. Construct a box-and-whisker plot that shows the number of purchased snack.
Question 22
Given the following list of data, what is the five-number summary?
8, 9, 10, 10, 10, 11, 11, 13, 13, 13, 19, 19, 20, 20, 20
Question 23
Given the following list of data, what is the five-number summary?
2, 5, 7, 7, 9, 9, 9, 10, 10, 11, 12
Question 24
The data below are the monthly average high temperatures for New York City. What is the five-number summary?
40, 40, 48, 61, 72, 78, 84, 84, 76, 65, 54, 42
Question 25
Given the following list of data, what is the five-number summary?
4, 4, 4, 5, 5, 7, 8, 9, 10, 10, 10, 10, 11, 12, 13
Question 26
Given the following list of data, what is the five-number summary?
10, 10, 10, 14, 14, 16, 17, 17, 18, 18, 19, 19, 19, 20, 21
Question 27
The average high temperatures in January for New York City, between 1986 and 1998, are recorded in the Country Studies/Area Handbook Series, sponsored by the U.S. Department of the Army. The data below are a sample of four of these temperatures.
54, 42, 40, 40
What is the standard deviation of this data set?
- Round the final answer to one decimal place.
Question 28
The average high temperatures in January for New York City, between 1986 and 1998, are recorded in the Country Studies/Area Handbook Series, sponsored by the U.S. Department of the Army. The data below are a sample of four of these temperatures.
54,42,40,40
What is the variance of this data set?
- Round the final answer to one decimal place.
Question 29
The average high temperatures in January for New York City, between 1986 and 1998, are recorded in the Country Studies/Area Handbook Series, sponsored by the U.S. Department of the Army. The data below are a sample of four of these temperatures.
54,42,40,40
To determine the “spread” of the data, would you employ calculations for the sample standard deviation, or population standard deviation for this data set?
Question 30
The following data values represent the daily amount spent by a family each day during a 7-day summer vacation.
Find the standard deviation of this data set:
$96, $125, $80, $110, $75, $100, $121
- Round the final answer to one decimal place.
Question 31
The following data values represent the daily amount spent by a family each day during a 7-day summer vacation.
Find the variance of this dataset:
$96, $125, $80, $110, $75, $100, $121
- Round the final answer to one decimal place.
Question 32
The following data values represent the daily amount spent by a family each day during a 7-day summer vacation.
$96, $125, $80, $110, $75, $100, $121
To determine the “spread” of the data, would you employ calculations for the sample standard deviation, or population standard deviation for this data set?
Question 33
The following frequency table summarizes a set of data. What is the five-number summary?
| Value | Frequency |
| 3 | 1 |
| 5 | 2 |
| 6 | 2 |
| 7 | 1 |
| 8 | 3 |
| 10 | 3 |
| 11 | 1 |
| 12 | 2 |
Question 34
The following frequency table summarizes a set of data. What is the five-number summary?
| Value | Frequency |
| 9 | 3 |
| 10 | 3 |
| 11 | 1 |
| 13 | 3 |
| 14 | 1 |
| 15 | 5 |
| 16 | 1 |
| 17 | 1 |
| 18 | 1 |
Question 35
According to U.S. climate data, the monthly average high temperatures, in degrees Fahrenheit, for the city of Chicago are listed below.
32,34,43,55,65,75,81,79,73,61,47,36
Find the five-number summary for this data.
Question 36
Given the following frequency table of data, what is the potential outlier?
| Value | Frequency |
| 11 | 1 |
| 12 | 2 |
| 13 | 12 |
| 14 | 6 |
| 15 | 7 |
| 16 | 2 |
| 17 | 0 |
| 18 | 0 |
| 19 | 0 |
| 20 | 0 |
| 21 | 0 |
| 22 | 0 |
| 23 | 1 |
Question 37
Given the following frequency table of data, what is the potential outlier?
| Value | Frequency |
| 8 | 1 |
| 9 | 0 |
| 10 | 0 |
| 11 | 0 |
| 12 | 0 |
| 13 | 0 |
| 14 | 0 |
| 15 | 0 |
| 16 | 1 |
| 17 | 4 |
| 18 | 10 |
| 19 | 4 |
| 20 | 6 |
Question 38
In the Alaskan temperature data set, what is the outlier, if any?
5,12,14,19,19,21,25,29,33
Question 39
The data set below contains the average low temperature in April for 9 Alaskan cities. What is the interquartile range of this data set?
5,12,14,19,19,21,25,29,33
Question 40
A data set lists the number of strikes scored per team during a bowling league championship. For this data set, the minimum is 2, the first quartile is 3, the median is 5, the third quartile is 7, and the maximum is 14. Construct a box-and-whisker plot that shows the number of strikes score
Question 41
A data set lists the number of points deducted on the quiz scores of 25 students taking a finance course. For this data set, the minimum is 3, the first quartile is 11, the median is 13, the third quartile is 14, and the maximum is 17. Construct a box-and-whisker plot that shows the points deducted.
Question 42
A data set lists the number of extra credit points awarded on midterm scores of 15 students taking a statistics course. For this data set, the minimum is 3, the median is 15, the third quartile is 16, the interquartile range is 4, and the maximum is 19. Construct a box-and-whisker plot that shows the extra credit points awarded.
Question 43
Based on the box-and-whisker plot you constructed above, what is the range of the data?
Question 44
A data set lists the number of “gutter balls” bowled by each player in a bowling tournament. For this data set, the minimum is 0, the first quartile is 1, the median is 2, the third quartile is 3, and the maximum is 7.
Construct a box-and-whisker plot that shows the number of “gutter balls”. Drag the dots to create the box plot. Note: It is helpful to set the median first.
Question 45
The monthly average high temperatures for New York City have the following five number summary: the minimum is 40, the median is 63, the third quartile is 77, the interquartile range is 32, and the maximum is 84.
Which of these shows the correct box-and-whisker plot for the data?
Question 46
Given the following box-and-whisker plot, which statements are true? Select all that apply.
Question 47
Several executives were asked how many suits they own. The results are tabulated in the following frequency table.
Which histogram accurately summarizes the data?
| Value | Frequency |
| 8 | 6 |
| 9 | 5 |
| 10 | 3 |
| 11 | 5 |
| 12 | 3 |
| 13 | 2 |
Question 48
According to the histogram, how many rockets soared greater than 18.5 but less than 20.5 hundred feet in the air?
Question 49
Given the following frequency distribution table for a set of data about the heights of model rockets (in hundreds of feet) for all participants at a science fair, construct a histogram that accurately summarizes the data.
| Model Rocket Heights (in hundreds of feet) | Frequency |
| 10.5-12.5 | 3 |
| 12.5-14.5 | 7 |
| 14.5-16.5 | 9 |
| 16.5-18.5 | 12 |
| 18.5-20.5 | 8 |
| 20.5-22.5 | 4 |
Create the corresponding histogram to represent this data below. Drag the dots on the top of the histogram to create the chart.
Question 50
Given the following histogram for a set of data, how many values in the data set are greater than 10.5 but less than 12.5?
Question 51
Which of the data sets represented by the following histograms has the smallest standard deviation?
Question 52
Which of the data sets represented by the following histograms has the largest standard deviation?
Question 53
Suppose that you are conducting a survey of adults and recording the number of books each individual read in the past year. The mean number of books is 12, and the standard deviation is 4. Allen reads exclusively nonfiction books, and he read 20 in the past year.
Which of the following statements is true?
Question 54
Which of the data sets represented by the following histograms has the smallest standard deviation?
Question 55
Three high school basketball teams measured the heights of all of their basketball players:
The Derby Dragons have a mean height of 72.0 inches and a standard deviation of 1.2.
The Aviston Aces have a mean height of 70.8 inches and a standard deviation of 0.7.
The Ballwin Bears have a mean height of 73 inches and a standard deviation of 1.0.
On average, which team is a taller? Which team has players whose heights are more consistent?
Question 56
Which of the data sets represented by the following histograms has the largest standard deviation?
Question 57
A primary school is conducting a canned food drive. The mean number of canned goods donated by each student is 10 and the standard deviation is 3. Alberto participated in the food drive by donating 16 canned goods.
Which of the following statements is true?
Question 58
Using the following set of data (the same as in the previous problem), find the sample standard deviation:
6, 12, 11, 11.
Question 59
Find the sample variance of the following set of data:
6, 12, 11, 11.
Question 60
Using the following set of data (the same as in the previous problem), find the sample standard deviation:
11, 10, 10, 11, 6, 12.
Question 61
Find the sample variance of the following set of data:
11, 10, 10, 11, 6, 12.
Question 62
The speed (in mph) of randomly selected bicyclists were measured as they were approaching a hill. The results are presented in the following histogram.
How many of those bicyclists were traveling greater than 8.5 but less than 11.5 mph as they were approaching the hill?
Question 63
Several people were asked to report the number of hours of sleep they average per night. The results are shown in the histogram below. How many of those people average greater than 4.5 but less than 6.5 hours of sleep per night?
Question 64
A data set lists the number of times each student raised their hand during an algebra class. For this data set, the minimum is 1, the first quartile is 8, the median is 10, the interquartile range is 3, and the maximum is 13. Construct a box-and-whisker plot that shows the number of times students raised their hand.
Question 65
A data set lists the number of hours each student, from a chemistry class, studied for a final exam. For this data set, the minimum is 1, the median is 11, the third quartile is 12, the interquartile range is 4, and the maximum is 15. Construct a box-and-whisker plot that shows the number of hours studied.
Question 66
Given the following box-and-whisker plot, decide if the data is skewed or symmetric.
Question 67
Given the following histogram, decide if the data is skewed or symmetric.
Question 68
Which of the following histograms shows a skewed data set? Select all that apply.
Question 69
Given the following histogram, decide if the data is skewed or symmetric.
Question 70
Given the following box-and-whisker plot, decide if the data is skewed or symmetric.
Question 71
Given the following frequency table, decide if the data is skewed or symmetrical.
| Value | Frequency |
| 4 | 1 |
| 5 | 10 |
| 6 | 8 |
| 7 | 28 |
| 8 | 50 |
| 9 | 69 |
| 10 | 72 |
| 11 | 62 |
| 12 | 52 |
| 13 | 23 |
| 14 | 16 |
| 15 | 6 |
| 16 | 3 |
Question 72
Which of the following frequency tables shows a skewed data set? Select all answers that apply.
A.
| Value | Frequency |
| 7 | 4 |
| 8 | 8 |
| 9 | 12 |
| 10 | 16 |
| 11 | 15 |
| 12 | 13 |
| 13 | 10 |
| 14 | 5 |
B.
| Value | Frequency |
| 5 | 3 |
| 6 | 3 |
| 7 | 8 |
| 8 | 12 |
| 9 | 15 |
| 10 | 19 |
| 11 | 19 |
| 12 | 10 |
| 13 | 4 |
| 14 | 3 |
| 15 | 3 |
| 16 | 1 |
| Value | Frequency |
| 12 | 1 |
| 13 | 2 |
| 14 | 3 |
| 15 | 13 |
| 16 | 10 |
| 17 | 26 |
| 18 | 25 |
| 19 | 15 |
| 20 | 5 |
D.
| Value | Frequency |
| 0 | 9 |
| 1 | 15 |
| 2 | 18 |
| 3 | 23 |
| 4 | 21 |
| 5 | 9 |
| 6 | 3 |
| 7 | 2 |
Question 73
Suppose there is an estate sale featuring many items sold at different prices. The mean selling price of the items is 75 dollars, and the standard deviation is 20. A piece of costume jewelry is priced at 15 dollars.
Which of the following statements is true?
Question 74
Which of the data sets represented by the following histograms has the smallest standard deviation?
Question 75
Based on the z-scores calculated above for Martin and Lawrence, whose salary is higher, when compared to their companies?
Question 76
Martin and Lawrence want to know whose salary is higher, when compared to the distribution of salaries at their jobs. The table shows their salaries, as well as the mean salary and standard deviation for each of the companies at which they work.
| Name | Annual Salary | Company Mean Salary |
Company Standard Deviation |
| Martin | $44,000 | $40,000 | $6,400 |
| Lawrence | $46,000 | $41,500 | $7,200 |
Find the z-scores corresponding to each man’s salary. Round to three decimal places, if necessary.
Question 77
Which of the two flights is more late, compared to its usual performance?
Question 78
An airline has two flights each day from City A to City B. A random sample of 10 morning flights left the gate an average of 15 minutes late with a standard deviation of 5 minutes. A random sample of 10 evening flights left the gate an average of 20 minutes late with a standard deviation of 3 minutes.
Suppose both the morning and evening flights are 30 minutes late. To determine which flight is more late than usual, first find the z-scores. Round to one decimal place if necessary.
Question 79
Based on the z-scores calculated above for Stephan’s electric bills in IL and FL, in which state is his electric bill higher, when compared to their respective distributions?
Question 80
When Stephan moved from Illinois to Florida, his average monthly electric bill increased from $83 to $102. He is curious to know whether his IL or FL electric bill is relatively more or less expensive, when compared to the distribution of electric bills for each state. In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20. In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00.
Compute the z-scores for Stephan’s IL and FL electric bills. Round to three decimal places if necessary.
ANSWERS
Question 1
You are told that a data set has a median of 35 and a mean of 42. Which of the following is a logical conclusion?
Answer:
The data are skewed to the right.
Question 2
Based on the z scores found above, in which city would a home priced at 200,000 be closer to the mean price, compared to the distribution of prices in the city?
Answer:
Neither
Question 3
In a recent national survey, the mean price for a 2000 sq ft home in Florida is $240,000 with a standard deviation of $16,000. The mean price for the same sized home in Ohio is $170,000 with a standard deviation of $12,000.
In which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?
Find the z-score corresponding to each state.
Answers:
z-score =
1 = -2.5
2 = 2.5
Question 4
Which of the following frequency tables show a skewed data set? Select all answers that apply.
Answer:
| Value | Frequency |
| 0 | 2 |
| 1 | 11 |
| 2 | 30 |
| 3 | 22 |
| 4 | 15 |
| 5 | 12 |
| 6 | 6 |
| 7 | 1 |
| 8 | 1 |
| Value | Frequency |
| 13 | 1 |
| 14 | 6 |
| 15 | 9 |
| 16 | 15 |
| 17 | 27 |
| 18 | 28 |
| 19 | 10 |
| 20 | 4 |
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