Question

Find the mean absolute deviation of the following dataset: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2. Round the answer to the nearest tenth.(1 point)
Responses

11.8
11.8

1.7
1.7

7.0
7.0

9.3

Answer 1

To find the mean absolute deviation, you need to find the average of the absolute differences between each data point and the mean of the dataset.

First, find the mean (average) of the dataset:
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2)/7 = 65.1/7 ≈ 9.3.

Next, find the absolute difference between each data point and the mean:
|8.4 - 9.3| = 0.9
|9.4 - 9.3| = 0.1
|14.2 - 9.3| = 4.9
|5.6 - 9.3| = 3.7
|8.3 - 9.3| = 1.0
|9.0 - 9.3| = 0.3
|10.2 - 9.3| = 0.9

Find the average of these absolute differences:
(0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9)/7 ≈ 2.143.

Rounded to the nearest tenth, the mean absolute deviation is 2.1.

Therefore, the correct response is:
2.1