Question

there are two dot plots (for jonon and eduardo) with number lines from 0 to 30. below the plots, there are multiple - choice options: a. the difference of the medians is half the interquartile range of either data set. b. the difference of the medians is one - fourth the interquartile range of either data set. c. their medians cannot be compared based on their interquartile ranges because the interquartile ranges are 9... d. their medians cannot be compared based on their interquartile ranges because the interquartile ranges are 6...

Explanation:

Step1: Count data points for Jannon

Jannon's data: 8,8,10,12,12,14,21,21,26,26,30 → 11 points
Median (6th value): 14
Q1 (3rd value):10, Q3 (9th value):26 → IQR=26-10=16

Step2: Count data points for Eduardo

Eduardo's data: 7,10,10,15,19,20,20,20,22,25,25 →11 points
Median (6th value):20
Q1 (3rd value):10, Q3 (9th value):25 → IQR=25-10=15

Step3: Calculate median difference

Median difference:20-14=6

Step4: Compare difference with IQRs

6 is not half (8/7.5) or 1/4 (4/3.75) of IQRs.

Answer:

A. The difference of the medians is half the interquartile range of either data set.
B. The difference of the medians is one-fourth the interquartile range of either data set.
C. Their medians cannot be compared based on their interquartile ranges because the interquartile ranges are 9
D. Their medians cannot be compared based on their interquartile ranges because the interquartile ranges are 6

(Note: Assuming a typo in C/D, but based on calculation, 6≠half/1/4 of IQRs, so comparison via IQR ratio fails.)