Question

use the same scales to construct modified boxplots for the pulse rates of men and women from the accompanying data sets. identify any outliers. click the icon to view the data sets. determine the boxplot that best represents the mens pulse rate data. choose the correct graph. mens pulse rates: 60 58 68 70 59 90 85 75 77 75 87 54 104 66 66 56 80 62 74 78 50 62 67 62 64 47 68 58 70 58 68 77 68 60 70 70 74 63 51 57 womens pulse rates: 78 66 67 73 79 78 99 70 65 78 70 54 77 78 78 92 96 61 100 99 76 66 82 60 74 80 73 88 89 73 80 74 78 105 62 74 70 87 75 81

Explanation:

Step1: Organize data in ascending - order

First, arrange the men's pulse - rate data in ascending order: 47, 50, 51, 54, 56, 57, 58, 58, 58, 59, 60, 60, 62, 62, 62, 64, 66, 66, 67, 68, 68, 68, 68, 70, 70, 70, 74, 74, 75, 75, 77, 77, 80, 85, 87, 90, 104

Step2: Calculate quartiles

The median (Q2) of the data set with \(n = 36\) values is the average of the 18th and 19th ordered values. So, \(Q2=\frac{66 + 67}{2}=66.5\). The lower half of the data has \(n_1 = 18\) values. The median of the lower half (Q1) is the average of the 9th and 10th ordered values in the lower - half data set, \(Q1=\frac{58+59}{2}=58.5\). The upper half of the data also has \(n_2 = 18\) values. The median of the upper half (Q3) is the average of the 9th and 10th ordered values in the upper - half data set, \(Q3=\frac{74 + 75}{2}=74.5\)

Step3: Identify outliers

The inter - quartile range \(IQR=Q3 - Q1=74.5−58.5 = 16\). The lower fence for outliers is \(Q1-1.5\times IQR=58.5-1.5\times16=58.5 - 24 = 34.5\). The upper fence for outliers is \(Q3 + 1.5\times IQR=74.5+1.5\times16=74.5 + 24 = 98.5\). The value 104 is an outlier.

Step4: Match with box - plot

A modified box - plot will have a box from Q1 to Q3 with a line at the median. The whiskers will extend to the non - outlier minimum and maximum values, and the outlier (104) will be represented as a separate point.

Answer:

C.