The mean absolute deviation is calculated by finding the mean of the data set, then finding the absolute difference between each data point and the mean, and finally finding the mean of those absolute differences.
First, find the mean:
(4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4) / 6 = 5.55
Next, find the absolute differences between each data point and the mean:
|4.8 - 5.55| = 0.75
|5.9 - 5.55| = 0.35
|6.2 - 5.55| = 0.65
|10.8 - 5.55| = 5.25
|1.2 - 5.55| = 4.35
|6.4 - 5.55| = 0.85
Now, find the mean of these absolute differences:
(0.75 + 0.35 + 0.65 + 5.25 + 4.35 + 0.85) / 6 ≈ 2.5
So, the mean absolute deviation of the data set is 2.5 (rounded to the nearest tenth).