Question

how does the mean absolute deviation (mad) of the data in set 2 compare to the mean absolute deviation of the data in set 1?
set 1: 16, 15, 10, 12
set 2: 16, 62, 15, 10, 12
the mad of set 2 is 10 less than the mad of set 1.
the mad of set 2 is 13.35 more than the mad of set 1.
the mad of set 2 is 10 more than the mad of set 1.
the mad of set 2 is 13.35 less than the mad of set 1.

Explanation:

Step1: Calculate mean of Set 1

Set 1: \(16, 15, 10, 12\)
Mean (\(\mu_1\)) = \(\frac{16 + 15 + 10 + 12}{4}\) = \(\frac{53}{4} = 13.25\)

Step2: Calculate MAD of Set 1

Absolute deviations: \(|16 - 13.25| = 2.75\), \(|15 - 13.25| = 1.75\), \(|10 - 13.25| = 3.25\), \(|12 - 13.25| = 1.25\)
MAD (\(M_1\)) = \(\frac{2.75 + 1.75 + 3.25 + 1.25}{4}\) = \(\frac{9}{4} = 2.25\)

Step3: Calculate mean of Set 2

Set 2: \(16, 62, 15, 10, 12\)
Mean (\(\mu_2\)) = \(\frac{16 + 62 + 15 + 10 + 12}{5}\) = \(\frac{115}{5} = 23\)

Step4: Calculate MAD of Set 2

Absolute deviations: \(|16 - 23| = 7\), \(|62 - 23| = 39\), \(|15 - 23| = 8\), \(|10 - 23| = 13\), \(|12 - 23| = 11\)
MAD (\(M_2\)) = \(\frac{7 + 39 + 8 + 13 + 11}{5}\) = \(\frac{78}{5} = 15.6\)

Step5: Compare \(M_2\) and \(M_1\)

Difference: \(15.6 - 2.25 = 13.35\)
So, \(M_2\) is \(13.35\) more than \(M_1\).

Answer:

The MAD of set 2 is 13.35 more than the MAD of set 1. (Third option)