Mean Absolute Deviation Quick Check 1 of 51 of 5 Items 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 9.3 9.3 7.0
The mean absolute deviation can be calculated by finding the average of the absolute differences between each data point and the mean of the dataset.
First, calculate the mean of the dataset:
(8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 65.1 / 7 = 9.3
Next, find the absolute differences 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
Now, find the average of these absolute differences:
(0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9) / 7 = 11.8 / 7 ≈ 1.7
Therefore, the mean absolute deviation of the dataset is 1.7, rounded to the nearest tenth.
The correct response is: 1.7