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? if necessary, round any values for the mad to the nearest tenth to help answer the question.

set 1: 30, 25, 5, 32
set 2: 25, 30, 32

○ the mad of set 1 is 29 more than the mad of set 2.
○ the mad of set 1 is 6.3 more than the mad of set 2.
○ the mad of set 1 is 23 less than the mad of set 2.
○ the mad of set 1 is 6.3 less than the mad of set 2.

Explanation:

Step1: Calculate mean of Set 1

$\text{Mean}_1 = \frac{30 + 25 + 5 + 32}{4} = \frac{92}{4} = 23$

Step2: Calculate MAD of Set 1

$\text{MAD}_1 = \frac{|30-23| + |25-23| + |5-23| + |32-23|}{4}$
$= \frac{7 + 2 + 18 + 9}{4} = \frac{36}{4} = 9.0$

Step3: Calculate mean of Set 2

$\text{Mean}_2 = \frac{25 + 30 + 32}{3} = \frac{87}{3} = 29$

Step4: Calculate MAD of Set 2

$\text{MAD}_2 = \frac{|25-29| + |30-29| + |32-29|}{3}$
$= \frac{4 + 1 + 3}{3} = \frac{8}{3} \approx 2.7$

Step5: Compare the two MADs

$\text{MAD}_1 - \text{MAD}_2 = 9.0 - 2.7 = 6.3$

Answer:

The MAD of set 1 is 6.3 more than the MAD of set 2.