# Mean Deviation

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Mean deviation is the measure of variability. It is deviation from the average of a data set.
Mean deviation of the population = ∑ | x - µ | / N

µ = Population mean
N= Population size.

A manager of a company can find the mean deviation by taking the deviations and averaging these values. Because it is computed using the absolute values, the mean deviation is less useful in statistics than other measure of dispersion. However, in the field of forecasting, it is used occasionally as measure of error.
Note: - Sum of deviation from arithmetic mean is always zero.

∑ (x - µ) = 0

This property requires considering alternative ways to obtain measure of variability.
T get the non-zero sum value we take the absolute value so that we can ignore the negative sign of the deviation value.

Example: - Find the deviation from arithmetic mean of the given data set.
5          9          16        17        18

Solution:-

 X x- µ 5 -8 9 -4 16 3 17 4 18 5 ∑x = 65 ∑ (x- µ) =0

µ= ∑x / N = 65 /5 =13

So ∑ ( x - µ ) = 0

Example 2: - Find the mean deviation for the same above data.
Solution: - Take the absolute value and then find the sum of absolute deviation.
Mean deviation= ∑ | x - µ | / N=24/5 = 4.8