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)

Question

Responses

1.7
1.7

9.3
9.3

11.8
11.8

7.0

Answer 1

To find the mean absolute deviation (MAD), you first need to find the mean of the dataset:

(8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 9.5

Next, find the absolute deviations from the mean for each data point:

|8.4 - 9.5| = 1.1
|9.4 - 9.5| = 0.1
|14.2 - 9.5| = 4.7
|5.6 - 9.5| = 3.9
|8.3 - 9.5| = 1.2
|9.0 - 9.5| = 0.5
|10.2 - 9.5| = 0.7

Now, find the mean of these absolute deviations:

(1.1 + 0.1 + 4.7 + 3.9 + 1.2 + 0.5 + 0.7) / 7 ≈ 1.84

Rounded to the nearest tenth, the mean absolute deviation is 1.8. None of the provided responses are exactly 1.8, but 1.7 is the closest answer.