Question

annette sold pumpkins as a community fundraiser. she used the plot below to compare the number of pumpkins sold on each thursday in october and the number sold on each friday in october.
pumpkin sales in october
fridays
thursdays
0 10 20 30 40 50 60
number sold
which statement about the data variability is true?
a. the interquartile range is the same for sales on thursdays as it is for sales on fridays.
b. the interquartile range is greater for sales on fridays than it is for sales on thursdays.

Explanation:

Step1: Recall IQR definition

The interquartile range (IQR) is the length of the box in a box - plot, calculated as \(IQR = Q_3 - Q_1\), where \(Q_3\) is the third quartile and \(Q_1\) is the first quartile.

Step2: Analyze box - plots

For the box - plot of Thursdays: Let's assume the left end of the box ( \(Q_1\)) is around 10 and the right end of the box ( \(Q_3\)) is around 30. So \(IQR_{Thursdays}=30 - 10 = 20\).
For the box - plot of Fridays: Let's assume the left end of the box ( \(Q_1\)) is around 20 and the right end of the box ( \(Q_3\)) is around 40. So \(IQR_{Fridays}=40 - 20 = 20\).
So the interquartile range is the same for sales on Thursdays as it is for sales on Fridays.

Answer:

A. The interquartile range is the same for sales on Thursdays as it is for sales on Fridays.