How to Calculate Mean Deviation About Mean (for Ungrouped Data)

Let's learn how to calculate mean deviation about mean for raw or ungrouped data.

Steps

Say we need to find the mean deviation about mean for the following data set:

6, 7, 10, 12, 13, 4, 8, 12
Find the mean of the given data.

Mean = (Sum of observations) / (Number of observations)

= (6 + 7 + 10 + 12 + 13 + 4 + 8 + 12) / 8 = 72/8 = 9
Subtract the mean from each of the observations and record your results. These results are the respective deviations of the observations from the mean.

6 – 9, 7 – 9, 10 – 9, 12 – 9, 13 – 9, 4 – 9, 8 – 9, 12 – 9

or, -3, –2, 1, 3, 4, –5, –1, 3
Find absolute values of the deviations obtained above.

|-3|, |–2|, |1|, |3|, |4|, |–5|, |–1|, |3|

or, 3, 2, 1, 3, 4, 5, 1, 3
Add the absolute values obtained above.

3 + 2 + 1 + 3 + 4 + 5 + 1 + 3 = 22
Divide the result of last step by the number of observations. This will give you the final answer.

Thus, the mean deviation about mean for the given ungrouped data is = 22/8 = 2.75