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
