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

Answer 1

Mean Absolute deviation for (set 1): 4

Mean Absolute deviation for (set 2): 9

Set 2 has a lower (MAD) mean absolute deviation that Set 1.

Explanation:

(set 1)

Mean: 80 + 82 + 90 = 252/3 = 84

84 - 80 = 4

84 - 82 = 2

84 - 90 = 6

Mean Absolute Deviation: 2 + 4 + 6 = 12/3 = 4

(set 2)

Mean: 60 + 80 + 82 + 90 = 312/4 = 78

78 - 60 = 18

78 - 80 = 2

78 - 82 = 4

78 - 90 = 12

Mean Absolute Deviation: 2 + 4 + 12 + 18 = 36/4 = 9

Answer 2

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

Explanation:

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