Question

The table lists the heights (in centimeters) of preschool girls and boys on a playground. Heights of Preschool Boys (centimeters) Heights of Preschool Girls (centimeters) 105.1 104.8 101.3 87 86.7 95 93.8 92.1 92.4 100 85.2 90.3 99.6 98.6 97.5 101.7 102.9 89.4 107 92.1 Based on the table, which of the following is true? A. The difference of the medians is about one-half the interquartile range of either data set. B. The difference of the medians is about one-fourth the interquartile range of either data set. C. The medians cannot be compared based on their interquartile ranges because the interquartile ranges are 1 centimeter apart. D. The medians cannot be compared based on their interquartile ranges because the interquartile ranges are 3 centimeters apart. Reset Next Comparing Data Distributions: Mastery Test © 2018 Edmentum. All rights reserved.

Answer 1

Answer:

B. The difference of the medians is about one-fourth the interquartile range of either data set

Step-by-step explanation:

Given the heights of preschool boys in cms

105.1 104.8 101.3 87 86.7 95 93.8 92.1 92.4 100

Arrange them in ascending order

86.7 87 92.1 92.4 93.8 95 100 101.3 104.8 105.1

Median = 93.8: Q1 = 87:Q3=101.3

IQR = Q3-Q1 = 4.3

Given the heights of preschool girls in cms

 85.2 90.3 99.6 98.6 97.5 101.7 102.9 89.4 107 92

Arrange them in ascending order

 85.2 89.4 90.3 92 97.5 98.6 99.6 101.7 102.9 107

Median = 97.5: Q1 = 89.4:Q3=101.7

IQR = 4.2

Differnce in the medians = 3.7

Diff in IQR = 0.1

B. The difference of the medians is about one-fourth the interquartile range of either data set because

0.4 = 4(0.1)