The table lists the test scores William and Andre received on five math assessments. William’s Scores Andre’s Scores
89
90
97
74
78
73
81
87
91
82
Which statement best describes the difference of the mean of the two data sets?

A.
It is equal to about 0.5 times the mean absolute deviation of either data set.
B.
It is equal to about 1 times the mean absolute deviation of either data set.
C.
It is equal to about 1.5 times the mean absolute deviation of either data set.
D.
It is equal to about 2 times the mean absolute deviation of either data set.

B.) It is equal to about 1 times the mean absolute deviation of either data set.

Explanation:

Given the scores :

Williams :

89,97, 78, 81, 91

Andre :

90, 74, 73, 87, 82

The mean scores :

Mean = ΣX / n

William's mean score = 436 / 5 = 87.2

Mean absolute deviation :

[|89-87.2| + |97-87.2| + |78-87.2| +|81-87.2| + |91-87.2|] / 5

William's mean absolute deviation = 6.16

Andre's mean score = 406 / 5 = 81.2

Andre's mean absolute deviation =

[|90-81.2| + |74-81.2| + |73-81.2| +|87-81.2| + |82-81.2|] / 5 = 6.16

Difference of the mean = 87.2 - 81.2 = 6

Mean absolute deviation of each dataset = 6.16

The closest relationship between the mean difference and the mean absolute deviation is :

Mean difference is about 1 times the mean absolute deviation