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: 82, 80, 90
Set 2: 82, 80, 60, 90

The MAD of set 1 is 6 less than the MAD of set 2.
The MAD of set 1 is 5 less than the MAD of set 2.
The MAD of set 1 is 5 more than the MAD of set 2.
The MAD of set 1 is 6 more than the MAD of set 2.

Answer 1

The MAD of set 1 is 5 less than the MAD of set 2.

took the test

Answer 2

Set 1: 82, 80, 90
n=3
Mean=(82+80+90)/3=252/3→Mean=84
Absolute Value: AV
MAD=[AV(82-84)+AV(80-84)+AV(90-84)]/3
MAD=[AV(-2)+AV(-4)+AV(6)]/3
MAD=(2+4+6)/3
MAD=12/3
MAD=4

Set 2: 82, 80, 60, 90
n=4
Mean=(82+80+60+90)/4=312/4→Mean=78
Absolute Value: AV
MAD=[AV(82-78)+AV(80-78)+AV(60-78)+AV(90-78)]/4
MAD=[AV(4)+AV(2)+AV(-18)+AV(12)]/4
MAD=(4+2+18+12)/4
MAD=36/4
MAD=9

MAD of set 2 - MAD of set 1 = 9-4=5

Answer: Second option: The MAD of set 1 is 5 less than the MAD of set 2.