Average Deviation Formula

How to Calculate Average Deviation from Mean

The arithmetic average of the deviations (all taking positive) from the mean, median or mode is known as average deviation or mean deviation.

Average deviation from ungrouped data or individual series is given by 

Average deviation = $\frac{1}{N}\sum\limits_{i = 1}^n {\left| {{x_i} - m} \right|} $
where $\sum\limits_{i = 1}^n {\left| {{x_i} - m} \right|} $ is the sum of modulus of the deviation of the variate from the mean (mean, median or mode) and N is number of terms.

Example:
The score of batsmen in ten innings are 38, 70, 48, 34, 42, 55, 63, 46, 54, 44. Find the mean deviation about the median.
Sol: Arranging the data in ascending order.
We have
34, 38, 42, 44, 46, 48, 54, 55, 63, 70.
Here n = 10. So, median is the A.M. of 5th and 6th observation.
⸫ Median M = $\left( {\frac{{46 + 48}}{2}} \right) = 47$
Average deviation
 $\begin{gathered}
   = \frac{{\left| {38 - 47} \right| + \left| {70 - 47} \right| + \left| {48 - 47} \right| + \left| {34 - 47} \right|}}{{10}} \hfill \\
   + \frac{{\left| {42 - 47} \right| + \left| {55 - 47} \right| + \left| {63 - 47} \right| + \left| {46 - 47} \right|\left| {34 - 47} \right|}}{{10}} \hfill \\
   + \frac{{\left| {54 - 47} \right| + \left| {44 - 47} \right|}}{{10}} \hfill \\
\end{gathered} $
=$\frac{{86}}{{10}} = 8.6$ 

Practice question

Calculate the average deviation about mean for the given data 4, 6, 8, 10, 12, 14.
a. 37.5
b. 38
c. 40
d. 42.