To find the mean absolute deviation (MAD), we first need to find the mean of the data set:
Mean = (25 + 28 + 20 + 22 + 32 + 28 + 35 + 34 + 30 + 36) / 10
= 290 / 10
= 29
Now, we find the absolute deviation for each data point by subtracting the mean from each value and taking the absolute value:
|25 - 29| = 4
|28 - 29| = 1
|20 - 29| = 9
|22 - 29| = 7
|32 - 29| = 3
|28 - 29| = 1
|35 - 29| = 6
|34 - 29| = 5
|30 - 29| = 1
|36 - 29| = 7
Next, we find the average of these absolute deviations:
MAD = (4 + 1 + 9 + 7 + 3 + 1 + 6 + 5 + 1 + 7) / 10
= 44 / 10
= 4.4
Therefore, the mean absolute deviation is 4.4.
Interpretation: On average, the values in the data set differ from the mean by approximately 4.4 units. This indicates the typical amount of variation or spread in the data set.