3.5Using Boxplots for Displaying Summaries

1Interpret Boxplots

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the side -by-side boxplots below to answer the question. The boxplots summarize the number of sentenced prisoners by state in the Midwest and West.

1)Pick the statement that best describes the shape of the distribution for the states in the West.

A)The data appears to be roughly symmetrical with a possible outlier.

B)The data appears to be right - skewed with a possible outlier.

C)The data appears to be left - skewed with large variability.

Answer:B

2)Based on the boxplot for the Midwest, which of the following is true?

A) 25% of the states sentenced less than 1,435 prisoners.

B)25% of the states sentenced more than 29,928 prisoners.

C)50% of the states sentenced less than 4,322 prisoners.

D)50% of the states sentenced more than 29,928 prisoners.

Answer:B

3)Using the boxplot for the Midwest, determine which of the following statements about the distribution cannot be justified.

A) The range is 32,467.

B)About 75% of the West states had 3,887 or more prisoners.

C)The distribution is skewed to the right.

D)There are fewer states with 3887.5 to 6887 prisoners than states with 6887 to 15,706 prisoners.

Answer:D

4)Pick the statement that best describes the shape of the distribution for the states in the Midwest.

A) The data appears to be roughly symmetrical with a possible outlier.

B)The data appears to be right - skewed with a possible outlier.

C)The data appears to be left - skewed with large variability.

D)The data appears to be right - skewed with large variability.

Answer: D

5) Based on the boxplot for the West, which of the following is true?

A)25% of the states sentenced more than 15,706 prisoners.

B)25% of the states sentenced less than 3,888 prisoners.

C)50% of the states sentenced less than 15,706 prisoners.

D)50% of the states sentenced less than 22,662 prisoners.

Answer:A

6)Using the boxplot for the West, determine which of the following statements about the distribution cannot be justified.

A)The range is 32,467.

B)About 75% of the West states had 3,887 or more prisoners.

C)The distribution is skewed to the right.

D)There are fewer states with 3887.5 to 6887 prisoners than states with 6887 to 15,706 prisoners.

E)The interquartile range is about 11,819.

Answer:D

The following boxplot contains information about the length of time (in minutes) it took women participants to finish the marathon race at the 2012 London Olympics.

7)What can be said about the shape of the distribution of womenʹ s running times for the marathon?

A)The distribution is symmetric.

C)The distribution is left - skewed.

Answer:D

B)The distribution is unimodal.

D)The distribution is right- skewed.

8)The fastest 25% of women participants ran the marathon how quickly?

A)Less than 150 minutes.

C)More than 155 minutes.

Answer:A

B)Less than 155 minutes.

D) More than 160 minutes.

The following boxplot contains information about the length of time (in minutes) it took men participants to finish the marathon race at the 2012 London Olympics.

9)What can be said about the shape of the distribution of menʹ s running times for the marathon?

A)The distribution is symmetric.

C)The distribution is left - skewed.

Answer:D

B)The distribution is unimodal.

D)The distribution is right- skewed.

10)The slowest 25% of men participants ran the marathon how quickly?

A)Less than 136 minutes.

C)More than 139 minutes.

Answer:D

Solve the problem.

B)Less than 139 minutes.

D) More than 143 minutes.

11)The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG - 13, PG, and G. List ratings according to their media runtimes, from shortest to longest.

12)The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG - 13, PG, and G. List ratings according to their media runtimes, from longest to shortest.

A)R, PG- 13, PG, GB)G, PG, PG - 13, RC)G, PG, R, PG - 13D)PG - 13, R, PG, G

Answer:D

13)What feature of a distribution can NOT be determined from a boxplot?

Answer:B

14)What feature of a distribution can NOT be determined from a boxplot?

Answer:D

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

15)The boxplots below represent criticsʹ movie ratings (from 0 to 100) for movies that have been rated by the Motion Picture Association of America as R, PG - 13, PG, and G. List the movie ratings according to their median criticsʹ rating, from worst to best.

Answer:Worst to best: PG, PG - 13, R, G.

16)Approximately what value corresponds to the first quartile of the following boxplot?

Answer:Quartile 1 (Q1) is represented by the line that creates the left edge of the box. The value is greater than 20, but less than 30, so an appropriate estimate for Q1 would be 25.

17)What is one feature of a distribution that can NOT be determined from a boxplot?

Answer:There are 2 answers here: modality and the number of observations in the original data.

The following boxplot contains information about the length of time (in minutes) it took men participants to finish the marathon race at the 2012 London Olympics.

18)What do the dots on the right side of the boxplot represent? What does this mean in terms of marathon times?

Answer:The dots on the right side of the boxplot represent high outliers. This means that the men whose times are represented by the dots ran the marathon much slower than the rest of the participants.

19) The fastest 25% of men participants ran the marathon how quickly?

Answer:Faster than 136 minutes. (Note: Values may vary based on approximations, but should be between 135 and 137 minutes.)

2Construct Boxplots

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) Calculate the five- number summary for the following dataset.

2)Calculate the five- number summary for the following dataset.

Obtain the five -number summary for the given data.

Solve the problem.

4)Which boxplot represents the same data as the histogram shown below?

5)Which boxplot represents the same data as the histogram shown below?

6)Calculate the five- number summary for the following dataset. 51 53 62 34 36 39 43 63 73 79

7)Calculate the five- number summary for the following dataset.

41.19, 83.51, 19.98, 114.60, 63.08, 83.88

A)19.98, 41.19, 73.295, 83.88, 114.6

C)41.19, 73.295, 83.88, 114.6

Answer:A

B)19.98, 41.19, 75, 115, 83.88

D)19, 41, 63, 84, 115

8)The five - number summary of the ages of passengers on a cruise ship is listed below.

Consider the following two statements regarding outliers for this data and determine which, if any, are correct.

(i) There is at least one passenger whose age is a low outlier.

(ii) There is at least one passenger whose age is a high outlier.

A)Only statement (i) is correct.

C)Both statements (i) and (ii) are correct.

Answer:B

B)Only statement (ii) is correct.

D) Neither statement (i) or (ii) is correct.

9)The five - number summary of the ages of a group of 100 adults is listed below.

Consider the following two statements regarding outliers for this data and determine which, if any, are correct.

(i) There is at least one adult whose age is a low outlier.

(ii) There is at least one adult whose age is a high outlier.

A)Only statement (i) is correct.

C)Both statements (i) and (ii) are correct.

Answer:B

B)Only statement (ii) is correct.

D) Neither statement (i) or (ii) is correct.

10)Ten households were asked how many pets they currently own. The results are shown below.

1024321164

What is the IQR for this set of data?

Answer:C

11)Ten parents were asked the ages of their oldest child. The results are shown below.

291210622191614228

What is the IQR for this set of data?

Answer:B

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

12)The five - number summary of the length of phone calls of 100 people is listed below.

Consider the following two statements regarding outliers for this data and determine which, if any, are correct. Explain your reasoning.

(i) There is at least one person made a phone call that is a low outlier.

(ii) There is at least one person made a phone call that is a high outlier.

Answer:Only statement (ii) is correct - there is at least one cell phone which has a battery life that is a high outlier. In order to determine which values may be outliers, use the 1.5IQR Rule as follows:

13)Ten parents were asked the ages of their youngest child. The results are shown below.

62512206217222310

What is the IQR for this set of data?

Answer:When the values are arranged in order (2, 6, 6, 10, 12, 17, 20, 22, 23, 25), we find that Q3 = 22 and Q1 = 6. Therefore, IQR = Q3 - Q1 = 22 - 6 = 16.