Question

how does the mean absolute deviation (mad) of the data in set 1 compare to the mean absolute deviation of the data in set 2?

set 1: 12, 8, 10, 50
set 2: 13, 9, 8

the mad of set 1 is 13 less than the mad of set 2.
the mad of set 1 is 13 more than the mad of set 2.
the mad of set 1 is 2 more than the mad of set 2.
the mad of set 1 is 2 less than the mad of set 2.

Explanation:

Step1: Calculate mean of Set 1

Mean of Set 1: $\frac{12 + 8 + 10 + 50}{4}=\frac{80}{4} = 20$

Step2: Find absolute deviations for Set 1

$|12 - 20| = 8$, $|8 - 20| = 12$, $|10 - 20| = 10$, $|50 - 20| = 30$

Step3: Calculate MAD of Set 1

MAD of Set 1: $\frac{8 + 12 + 10 + 30}{4}=\frac{60}{4}=15$

Step4: Calculate mean of Set 2

Mean of Set 2: $\frac{13 + 9 + 8}{3}=\frac{30}{3}=10$

Step5: Find absolute deviations for Set 2

$|13 - 10| = 3$, $|9 - 10| = 1$, $|8 - 10| = 2$

Step6: Calculate MAD of Set 2

MAD of Set 2: $\frac{3 + 1 + 2}{3}=\frac{6}{3}=2$

Step7: Compare MADs

Difference: $15 - 2 = 13$ (Set 1's MAD is 13 more than Set 2's)

Answer:

The MAD of set 1 is 13 more than the MAD of set 2.