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)
First, find the mean of the dataset:
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7
Mean = 65.1 / 7
Mean = 9.3
Next, find the absolute deviation of each data point from 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
|9.0 - 9.3| = 0.3
|10.2 - 9.3| = 0.9
Now, find the mean of these absolute deviations:
Mean absolute deviation = (0.9 + 0.1 + 4.9 + 3.7 + 1 + 0.3 + 0.9) / 7
Mean absolute deviation = 11.8 / 7
Mean absolute deviation ≈ 1.7
Therefore, the mean absolute deviation of the dataset is approximately 1.7.