Question

analyzing mean absolute deviations
robins scores: 99, 108, 102, 107, 119. mean = 107; mad = 5.2
evelyns scores: 125, 137, 138, 145, 145. mean = 138; mad = 5.6
which statement about the mads is true?
since evelyns mad is
less than robins mad,
evelyns scores varied
more than robins.
since evelyns mad is
less than robins mad,
evelyns scores varied
less than robins.
since evelyns mad is
greater than robins
mad, evelyns scores
varied more than
robins.
since evelyns mad is
greater than robins
mad, evelyns scores
varied less than robins.

Explanation:

Step1: Understand the concept of MAD

The Mean Absolute Deviation (MAD) measures the average distance between each data point and the mean. A larger MAD indicates more variability in the data set.

Step2: Compare the MADs

Robin's MAD is \(5.2\) and Evelyn's MAD is \(5.6\). Since \(5.6>5.2\) (Evelyn's MAD > Robin's MAD).

Answer:

Since Evelyn’s MAD is greater than Robin’s MAD, Evelyn’s scores varied more than Robin’s.