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

Question

9.3
7.0
11.8
1.7

Answer 1

To find the mean absolute deviation, we first calculate the mean of the dataset:

(8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 9.31428571429

Next, we find the absolute deviation of each data point from the mean:

|8.4 - 9.31428571429| = 0.91428571429
|9.4 - 9.31428571429| = 0.08571428571
|14.2 - 9.31428571429| = 4.88571428571
|5.6 - 9.31428571429| = 3.71428571429
|8.3 - 9.31428571429| = 1.01428571429
|9.0 - 9.31428571429| = 0.31428571429
|10.2 - 9.31428571429| = 0.88571428571

Now, we find the mean absolute deviation by taking the average of these absolute deviations:

(0.91428571429 + 0.08571428571 + 4.88571428571 + 3.71428571429 + 1.01428571429 + 0.31428571429 + 0.88571428571) / 7 ≈ 1.7

Therefore, the mean absolute deviation of the dataset is approximately 1.7.