Here you will learn what is the mean deviation formula with examples.
Let’s begin –
Mean Deviation Formula
(i) For Ungrouped distribution :
Definition : If x1, x2, ….. , xn 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) = ∑ni=1|xi–A|n
M.D = ∑din, where di = xi – 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.
xi | |di| = |xi–300| |
340 | 40 |
150 | 150 |
210 | 90 |
240 | 60 |
300 | 0 |
310 | 10 |
320 | 20 |
Total | di = 370 |
∴ Mean Deviation (M.D.) = ∑din = 3707 = 52.8
Also Read : What is the Formula for Mean Median and Mode
(ii) For discrete frequency distribution :
Definition : If xi/fi; 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) = ∑ni=1fi|xi–A|N
where ∑ni=1fi = N
Example : Calculate the mean deviation about mean from the following data :
xi | 3 | 9 | 17 | 23 | 27 |
fi | 8 | 10 | 12 | 9 | 5 |
Solution : Calculation of mean deviation about mean.
xi | fi | fixi | |xi–15| | fi|xi–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 = ∑fi = 44 | ∑fixi = 660 | ∑fi|xi–15| = 312 |
Mean = ∑fixiN = 66044 = 15
Mean Deviation = M.D. = ∑ni=1fi|xi–15|N = 31244 = 7.09