Mean Deviation Formula
Mean deviation formula is defined for/about a central value ‘x’ and is the mean of absolute values of the deviations of the observations from the central value ‘x’. We can obtain mean deviation from any measure of central tendency. But, generally, in the statistical study mean deviation from mean and median are used. Let us learn this mean deviation formula and a few solved examples in the upcoming sections.
What Is Mean Deviation Formula?
The mean deviation formula is the mean of absolute values of the deviations of the observations from the central value ‘x’. In the statistical study mean deviation from mean and median are used. The mean deviation formula is given as,
M.D. = Sum of absolute values of deviations from x / Number of observations
Generally in the statistical study mean deviation from mean and median are used.
M.D.(X) \(= \dfrac{1}{n}\sum^n_{i=1} x_i  M \) , where M = median
Let us have a look at a few solved examples on the mean deviation formula to understand the concept better.
Solved Examples Using Mean Deviation Formula

Example 1: Find the mean deviation about the mean for the following data:
5, 8, 10, 12, 13, 4, 8, 12Solution:
To find: Mean deviation for the given data set.
Given:
Data set = {5, 8, 10, 12, 13, 4, 8, 12}
Mean of the data (m) = (5+8+10+12+13+4+8+12)/8 = 72/8 = 9
Now, we will find the deviations of each observation from the mean X, i.e, xX,
59,89,109,129,139,49,89,129
4, 1, 1, 3, 4, 5, 1, 3
Absolute values of the deviations from mean i.e., ǀxi Xǀ
4, 1, 1, 3, 4, 5, 1, 3
Required mean deviation about mean is,
Using Mean Deviation Formula,
M.D.(X) \(= \dfrac{1}{n}\sum^n_{i=1} x_i  X \)
M.D.(X) \(= \dfrac{1}{8}\sum^8_{i=1} x_i  X \)= (4+1+1+3+4+5+1+3)/8
= 22/8
= 2.75Answer: Mean deviation of the data about mean is 2.75.

Example 2 : Find the mean deviation about the median for the following data,
3, 10, 4, 3, 12, 10, 18, 4, 7, 19, 21Solution:
To find: Mean deviation about the median.
According to the formula,
M.D.(X)= \(= \dfrac{1}{n}\sum^n_{i=1} x_i  M \)We need to find the median first.
To find median we will first arrange the observation into ascending order,
3,3,4,4,7,10,10,12,18,19,21Median = \(\dfrac{(n+1)}{2}\) ( for odd observation)
= \(\dfrac{(11 + 1)}{2}\)
= 6
Median is the sixth observation, i.e.,10.
The absolute values of the respective deviations from the median, i.e.,ǀxi Mǀ,
7,7,6,6,3,0,0,2,8,9,11
Also,
M.D.(X) = \(= \dfrac{1}{n}\sum^n_{i=1} x_i  M \)= (1/11) × (59)
= 5.36
Answer: Mean deviation about median is 5.36.