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: 5, 10, 7, 2
set 2: 5, 10, 7, 42

the mad of set 1 is 10.5 more than the mad of set 2.
the mad of set 1 is 2.5 more than the mad of set 2.
the mad of set 1 is 10.5 less than the mad of set 2.
the mad of set 1 is 2.5 less than the mad of set 2.

Explanation:

Step1: Calculate mean of Set 1

Mean of Set 1: $\frac{5 + 10 + 7 + 2}{4} = \frac{24}{4} = 6$

Step2: Calculate MAD of Set 1

Absolute deviations: $|5 - 6| = 1$, $|10 - 6| = 4$, $|7 - 6| = 1$, $|2 - 6| = 4$
MAD of Set 1: $\frac{1 + 4 + 1 + 4}{4} = \frac{10}{4} = 2.5$

Step3: Calculate mean of Set 2

Mean of Set 2: $\frac{5 + 10 + 7 + 42}{4} = \frac{64}{4} = 16$

Step4: Calculate MAD of Set 2

Absolute deviations: $|5 - 16| = 11$, $|10 - 16| = 6$, $|7 - 16| = 9$, $|42 - 16| = 26$
MAD of Set 2: $\frac{11 + 6 + 9 + 26}{4} = \frac{52}{4} = 13$

Step5: Compare MADs

Difference: $13 - 2.5 = 10.5$ → MAD of Set 1 is 10.5 less than MAD of Set 2.

Answer:

The MAD of set 1 is 10.5 less than the MAD of set 2.