Among 300 fatal car accidents, 135 were single-car crashes, 66 were two-car crashes, and 99 involved three or more cars. Calculate the relative frequency and percent of fatal car accidents by the number of cars involved.

Answer:

Single car crashes 0.45 (45%); Two car crashes 0.22 (22%); Three car crashes 0.33 (33%).

The EPA sends out a survey to learn about people’s water usage habits. Some of the questions included in the survey are given below.

Q1. How many times a week do you take a shower?
Q2. Do you leave the water running when you brush your teeth?

Q3. When you water your lawn, how long do you let the water run?

For each question, determine if it leads to categorical responses or quantitative responses.

Answer:

Q1 and Q3 lead to quantitative responses, while Q2 leads to categorical responses.

The percent of data which lie between the lower and upper quartiles is

A. 10%.

B. 25%.

C. 50%.

D. 75%.

Answer: C

A five-number summary for a data set is 35, 50, 60, 70, 90. About what percent of the observations are between 35 and 90?

A. 25%

B. 50%

C. 95%

D. 100%

Answer: D

A five-number summary given in Case Study 1.1 for the fastest ever driving speeds reported by 102 women was: 30, 80, 89, 95, 130.

What is the interquartile range of these data?

A. 6

B. 9

C. 15

D. 100

Answer: C

A five-number summary given in Case Study 1.1 for the fastest ever driving speeds reported by 102 women was: 30, 80, 89, 95, 130.

Fill in the blank in the following sentence: Approximately 25% of the women reported a fastest ever driving speed of at least _____ mph.

A. 25

B. 80

C. 89

D. 95

Answer: C

A five-number summary given in Case Study 1.1 for the fastest ever driving speeds reported by 102 women was: 30, 80, 89, 95, 130.

Fill in the blank in the following sentence: Approximately 25% of the women reported a fastest ever driving speed of at most _____ mph.

A. 30

B. 80

C. 89

D. 95

Answer: B

In a survey, students are asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 9, 14, 20, 60.

Which interval describes the number of hours spent studying in a typical week for about 50% of the students sampled?

A. 2to9

B. 9to14

C. 9 to 20

D. 14 to 20

Answer: C

In a survey, students are asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 9, 14, 20, 60.

Fill in the blank in the following sentence. About 75% of the students spent at least ____ hours studying in a typical week.

A. 9

B. 14

C. 20

D. 45

Answer: A

Which of the following provides the most information about the shape of a data set?

A.Boxplot

B. Pie chart

C. Five number summary

D. Stem-and-leaf plot

Answer: D

According to a national sleep foundation survey, around 31 million Americans are sleep deprived. They also say women need more sleep than men and are being short-changed. Below are the five number summaries for the number of hours of sleep at night based on a survey of American men and women.

Men: 5.5, 6, 6.5, 7.5, 9 Women: 4.5, 5, 6, 7, 8

Write a sentence to compare men versus women in terms of the median amount of sleep at night

Answer:

The survey shows that the median about of sleep at night for women is 6 hours, about a half an hour less than that for men (which was 6.5 hours).

According to a national sleep foundation survey, around 31 million Americans are sleep deprived. They also say women need more sleep than men and are being short-changed. Below are the five number summaries for the number of hours of sleep at night based on a survey of American men and women.

Men: 5.5, 6, 6.5, 7.5, 9 Women: 4.5, 5, 6, 7, 8

Write a sentence to compare men versus women in terms of the interquartile range for the amount of sleep at night.

Answer:

Based on the survey, about 50% of the men get between 6 and 7.5 hours of sleep at night, while the interquartile range for women is from 5 to 7 hours of sleep.

According to a national sleep foundation survey, around 31 million Americans are sleep deprived. They also say women need more sleep than men and are being short-changed. Below are the five number summaries for the number of hours of sleep at night based on a survey of American men and women.

Men: 5.5, 6, 6.5, 7.5, 9 Women: 4.5, 5, 6, 7, 8

What percent of women sleep at least 6 hours at night? What percent of men do so?

Answer:

Based on the survey, about 50% of the women get at least 6 hours of sleep at night, while 75% of men do so.

A list of 5 pulse rates is: 70, 64, 80, 74, 92. What is the median for this list?

A. 74

B. 76

C. 77

D. 80

Answer: A

Which one of the following statements is most correct about a skewed dataset?

A. The mean and median will usually be different.

B. The mean and median will usually be the same.

C. The mean will always be higher than the median.

D. Whether the mean and median are the same depends on whether the data set is skewed to the right or to the left.

Answer: A

Listed below is a stem-and-leaf plot of the times it took 13 students to drink a 12 ounce beverage. Values for stems represent seconds and values for leaves represent tenths of a second.

3| 1234

3| 5

4| 0

5| 6

6| 11379

7|

8| 2

What was the median time to drink the beverage?

A. 3.5 seconds.

B. 4.0 seconds.

C. 5.6 seconds.

D. 6.9 seconds.

Answer: C

Listed below is a stem-and-leaf plot of the times it took 13 students to drink a 12 ounce beverage. Values for stems represent seconds and values for leaves represent tenths of a second.

3| 1234

3| 5

4| 0

5| 6

6| 11379

7|

8| 2

The lower quartile is

A. 3.1 seconds.

B. 3.35 seconds.

C. 3.4 seconds.

D. 3.5 seconds.

Answer: B

Listed below is a stem-and-leaf plot of the times it took 13 students to drink a 12 ounce beverage. Values for stems represent seconds and values for leaves represent tenths of a second.

3| 1234

3| 5

4| 0

5| 6

6| 11379

7|

8| 2

The upper quartile is

A. 6.9 seconds.

B. 6.5 seconds.

C. 6.1 seconds.

D. 5.6 seconds.

Answer: B

Which of the following would indicate that a dataset is skewed to the right?

A. The interquartile range is larger than the range.

B. The range is larger than the interquartile range.

C. The mean is much larger than the median.

D. The mean is much smaller than the median.

Answer: C

An outlier is a data value that

A. is larger than 1 million.

B. equals the minimum value in a set of data.

C. equals the maximum value in a set of data.

D. is not consistent with the bulk of the data.

Answer: D

Which statistic is not resistant to an outlier in the data?

A. Lower quartile

B. Upper quartile

C. Median

D. Mean

Answer: D

Which one of these statistics is unaffected by outliers?

A. Interquartile range

B. Mean

C. Standard deviation

D. Range

Answer: A

Which one of the following statistics would be affected by an outlier?

A. Median

B. Standard deviation

C. Lower quartile

D. Upper quartile

Answer: B

Which of the following could account for an outlier in a dataset?

A. Natural variability in the measurement of interest.

B. Recording the wrong category for an individual's value of a categorical variable.

C. A symmetric distribution for the measurement of interest.

D. Measuring more than one variable for each individual.

Answer: A

Determine whether the following statement is true or false and explain your answer: Outliers cause complications in all statistical analyses.

False, outliers do affect some statistics such as means and standard deviations. However, there are appropriate measures of location and spread if outliers are present and cannot be discarded, namely, the median and the interquartile range.

Determine whether the following statement is true or false and explain your answer: Since outliers cause complications in statistical analyses, they should be discarded before computing summaries such as the mean and the standard deviation.

False. Although outliers do affect summaries such as the mean and standard deviation, they should never be discarded without justification.

What is a reasonable action if an outlier is a legitimate data value and represents natural variability for the group and variable measured?

The value should not be discarded; in fact, it may be one of the more interesting values in the data set.

What is a reasonable action if an outlier was a mistake made in measuring the object?

The value should be corrected if possible or discarded if not possible to correct it.

What is a reasonable action if an outlier is the value for the only young subject in a sample where all of the other values were for older subjects?

The value should be discarded and the results summarized and reported for the older subjects only.

Which choice lists two statistics that give information only about the location of a dataset and not the spread?

A. IQR and standard deviation

B. Mean and standard deviation

C. Median and range

D. Mean and median

Answer: D

Which of the following measures is not a measure of spread?

A. Variance

B. Standard deviation

C. Interquartile range

D. Median

Answer: D

Which one of the following summary statistics is not a measure of the variation (spread) in a data set?

A. Median

B. Standard deviation

C. Range

D. Interquartile range

Answer: A

The head circumference (in centimeters) of 15 college-age males was obtained, resulting in the following measurements: 55, 56, 56, 56.5, 57, 57, 57, 57.5, 58, 58, 58, 58.5, 59, 59, 63. If the last measurement (63 cm's) were incorrectly recorded as 73, which one of the following statistics would change?

A. Q1 (1st quartile)

B. Standard deviation

C. Median

D. Q3 (3rd quartile)

Answer: B

Which of the following is true about the relationship between the standard deviation s and the range for a large bell-shaped data set?

A. The range is approximately 1/2 of a standard deviation.

B. The range is approximately 2 standard deviations.

C. The range is approximately 6 standard deviations.

D. The range is approximately 1/6 of a standard deviation

Answer: C

By inspection, determine which of the following sets of numbers has the smallest standard deviation.

A. 2,3,4,5

B. 4,4,4,5

C. 0,0,5,5

D. 5,5,5,5

Answer: D

The mean hours of sleep that students get per night is 7 hours, the standard deviation of hours of sleep is 1.7 hours, and the distribution is approximately normal. Complete the following sentence. For about 95% of students, nightly amount of sleep is between ______.

A. 5.3 and 8.7 hrs

B. 5and9hrs

C. 3.6 and 10.4 hrs

D. 1.9 and 12.1 hrs

Answer: C

For a large sample of blood pressure values, the mean is 120 and the standard deviation is 10. Assuming a bell- shaped curve, which interval is likely to be about the interval that contains 95% of the blood pressures in the sample?

A. 110 to 130

B. 100 to 140

C. 90 to 150

D. 50 to 190

Answer: B

For a large sample of blood pressure values, the mean is 120 and the standard deviation is 10. Assuming a bell- shaped curve, which interval is likely to be about the interval from the minimum to maximum blood pressures in the sample?

A.120 to 150

B. 110 to 130

C. 90 to 150

D. 50 to 190

Answer: C

78. Which of the following would indicate that a dataset is not bell-shaped?

A. The range is equal to 5 standard deviations.

B. The range is larger than the interquartile range.

C. The mean is much smaller than the median.

D. There are no outliers.

Answer: C

1. The possible values for a standardized score (z-score) A. can be any number: positive, negative, or 0. B. must be within the range from -3 to 3 C. must be non-negative. D. must be strictly positive.

Answer: A

Which of the following best describes the standardized (z) score for an observation?

A. It is the number of standard deviations the observation falls from the mean.

B. It is the most common score for that type of observation.

C. It is one standard deviation more than the observation.

D. It is the center of the list of scores from which the observation was taken.

Answer: A

Scores on an achievement test averaged 70 with a standard deviation of 10. Serena's score was 85. What was her standardized score (also called a z-score)?
A. -1.5
B. 1.5

C. 15

D. 85

Answer: B

Suppose that amount spent by students on textbooks this semester has approximately a bell- shaped distribution. The mean amount spent was $300 and the standard deviation is $100.

Which choice best completes the following sentence? About 68% of students spent between ____.

A. $300 and $400

B. $200 and $400

C. $100 and $500

D. $266 and $334

Answer: B

Suppose that amount spent by students on textbooks this semester has approximately a bell- shaped distribution. The mean amount spent was $300 and the standard deviation is $100.

What amount spent on textbooks has a standardized score equal to 0.5?

A. $150

B. $250

C. $300.50

D. $350

Answer: D

Suppose that amount spent by students on textbooks this semester has approximately a bell- shaped distribution. The mean amount spent was $300 and the standard deviation is $100.

What percent of students spent more than $350?

A. 50%

B. 0.5%

C. 69.15%

D. 30.85%

Answer: D

Suppose that amount spent by students on textbooks this semester has approximately a bell- shaped distribution. The mean amount spent was $300 and the standard deviation is $100.

A student spent $500 on textbooks. What percentile does their value correspond to?

A. 97.5th percentile

B. 95th percentile

C. 5th percentile

D. 2.5th percentile

Answer: A

Explain the difference between the population standard deviation

The population standard deviation is a measure of spread in the population and is a parameter (fixed value,

usually unknown). The sample standard deviation is an estimate of the population standard deviation and is a statistic.

For each of the following numerical summaries, decide whether it is a resistant statistic or not: mean, median, standard deviation, range, interquartile range.

Resistant statistics would include the median and the interquartile range. Non-resistant statistics would include the mean, the standard deviation, and the range.

Suppose that the average height for college men is 66 inches. If the height distribution is bell-shaped, and 95% of the men have heights between 60 inches and 72 inches, what is the standard deviation of heights for this population?

3 inches

The average rainfall during the month of November in San Francisco, California, is 2.62 inches. The standard deviation is 2.79 inches.

What is the standardized score (z-score) for 5.18 inches, the rainfall in San Francisco during November 2001?

.918

The average rainfall during the month of November in San Francisco, California, is 2.62 inches. The standard deviation is 2.79 inches.

What is the standardized score (z-score) for 11.78 inches, the rainfall in San Francisco during November 1885?

3.28

The average rainfall during the month of November in San Francisco, California, is 2.62 inches. The standard deviation is 2.79 inches.

What is the standardized score (z-score) for 1 inch of rain in November?

-.581

Suppose that the average number of years to graduate at a university is 4 years, with a standard deviation of 0.5 years. Assume a bell-shaped distribution for years to graduate.

From the Empirical Rule, what is a range of values that 68% of the students should graduate between?

3.5 to 4.5 years

Suppose that the average number of years to graduate at a university is 4 years, with a standard deviation of 0.5 years. Assume a bell-shaped distribution for years to graduate.

From the Empirical Rule, what is a range of values that 95% of the students should graduate between?

3 to 5 years

Suppose that the average number of years to graduate at a university is 4 years, with a standard deviation of 0.5 years. Assume a bell-shaped distribution for years to graduate.

From the Empirical Rule, what is a range of values that 99.7% of the students should graduate between?

2.5 to 5.5 years