Question

The number of words Mr. Ahmad’s students read per minute is 109, 89, 112, 98, 101, 105, 120, 106. What is the mean absolute deviation of the dataset? Round the answer to the nearest tenth

Answer 1

To find the mean absolute deviation (MAD) of the dataset, we need to find the mean and then subtract each value from the mean, take the absolute value, and find the average of those differences.

First, we find the mean:
Mean = (109 + 89 + 112 + 98 + 101 + 105 + 120 + 106) / 8
Mean = 840 / 8
Mean = 105

Next, we find the differences between each value and the mean:
|109 - 105| = 4
|89 - 105| = 16
|112 - 105| = 7
|98 - 105| = 7
|101 - 105| = 4
|105 - 105| = 0
|120 - 105| = 15
|106 - 105| = 1

Next, we find the average of these differences:
(4 + 16 + 7 + 7 + 4 + 0 + 15 + 1) / 8
54/8
6.75

Therefore, the mean absolute deviation (MAD) of the dataset is 6.8 (rounded to the nearest tenth).