Mean Deviation About Mean and Median – Formula and Examples

Here you will learn what is the mean deviation formula with examples.

Let’s begin – 

Mean Deviation Formula

(i) For Ungrouped distribution :

Definition : If $x_1$, $x_2$, ….. , $x_n$ are n values of a variable X, then the mean deviation from an average A (median or arithmetic mean) is given by

Mean Deviation (M.D)  = ${\sum_{i=1}^{n}{|x_i – A|}}\over n$

M.D = ${\sum{d_i}}\over n$,  where $d_i$ = $x_i$ – A

Example : Calculate the mean deviation about median from the following data : 340, 150, 210, 240, 300, 310, 320

Solution : Arranging the observations in ascending order of magnitude, we have 150, 210, 240, 300, 310, 320, 340.

Clearly, the middle observation is 300. So, median is 300.

$x_i$	$|d_i|$ = $|x_i – 300|$
340	40
150	150
210	90
240	60
300	0
310	10
320	20
Total	$d_i$ = 370

$\therefore$ Mean Deviation (M.D.) = ${\sum{d_i}}\over n$ = $370\over 7$ = 52.8

Also Read : What is the Formula for Mean Median and Mode

(ii) For discrete frequency distribution :

Definition : If $x_i$/$f_i$; i = 1, 2, …. , n is the frequency distribution, then the mean deviation from an average A (median or arithmetic mean) is given by

Mean Deviation (M.D)  = ${\sum_{i=1}^{n}{f_i|x_i – A|}}\over N$

where ${\sum_{i=1}^{n}{f_i}}$ = N

Example : Calculate the mean deviation about mean from the following data :

$x_i$	3	9	17	23	27
$f_i$	8	10	12	9	5

Solution : Calculation of mean deviation about mean.

$x_i$	$f_i$	$f_i x_i$	$|x_i – 15|$	$f_i|x_i – 15|$
3	8	24	12	96
9	10	90	6	60
17	12	204	2	24
23	9	207	8	72
27	5	135	12	60
	N = $\sum{f_i}$ = 44	$\sum{f_ix_i}$ = 660		$\sum{f_i|x_i – 15|}$ = 312

Mean = $\sum{f_ix_i}\over N$ = $660\over 44$ = 15

Mean Deviation = M.D. = ${\sum_{i=1}^{n}{f_i|x_i – 15|}}\over N$ = $312\over 44$ = 7.09