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

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