# 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

(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