Question

use the side - by - side boxplots shown to complete parts (a) through (e).
(b) what is the third quartile of variable y?
the third quartile of variable y is 50. (round to the nearest integer as needed.)
(c) which variable has more dispersion? why?
a. variable y—the interquartile range of variable y is larger than that of variable x.
b. variable x—the interquartile range of variable x is larger than that of variable y.
c. variable x—the range of variable y is smaller than that of variable x.
d. variable y—the range of variable x is smaller than that of variable y.
e. both dispersions are equal.

Explanation:

Step1: Understand interquartile range (IQR)

IQR is a measure of dispersion. It is calculated as \(IQR = Q_{3}-Q_{1}\), where \(Q_{3}\) is the third quartile and \(Q_{1}\) is the first quartile. A larger IQR indicates more dispersion.

Step2: Analyze box - plots

In a box - plot, the length of the box represents the IQR. Variable \(y\)'s box (which represents the IQR) is longer than variable \(x\)'s box.

Answer:

A. Variable y—the interquartile range of variable y is larger than that of variable x.