how does the mean absolute deviation (mad) of the data in set 2 compare to the mean absolute deviation of…

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?\nset 1: 16, 15, 10, 12\nset 2: 16, 62, 15, 10, 12\nthe mad of set 2 is 10 less than the mad of set 1.\nthe mad of set 2 is 13.35 more than the mad of set 1.\nthe mad of set 2 is 10 more than the mad of set 1.\nthe mad of set 2 is 13.35 less than the mad of set 1.

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?\nset 1: 16, 15, 10, 12\nset 2: 16, 62, 15, 10, 12\nthe mad of set 2 is 10 less than the mad of set 1.\nthe mad of set 2 is 13.35 more than the mad of set 1.\nthe mad of set 2 is 10 more than the mad of set 1.\nthe mad of set 2 is 13.35 less than the mad of set 1.

Answer

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)