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# What is Mean Deviation?

## Introduction

Mean deviation is the measure of dispersion. Mean deviation measures the average difference between the elements of the data from any fixed value, mean, median or mode.

Suppose ‘x’ is a data point or observation from the data set, and ‘a’ is a fixed value in the data set., then the difference (x – a) is called deviation.

In order to find the mean deviation we use the term ‘absolute values of the deviations’.

Here the reason behind taking absolute values is that the measure of central tendency ranges between the highest and lowest values, so that we may get some deviations negative and some positive.

The mean deviation about ‘a’ is the mean of absolute values of the deviations of the data set from ‘a’.

We can find the mean deviation from mean, median or mode as well.

## How do we calculate mean deviation (MD)?

We find the mean deviation for ungrouped data as below-

Let us suppose we have a data set say- x1, x2, x3, x4, x5………xn, then the mean deviation from a fixed point ‘a’ is defined as-

Mean deviation from mean and median

For grouped data we use the following formulae to find the mean deviation-

Let us suppose we have a data set say- x1, x2, x3, x4, x5……..xn, with the corresponding frequencies f1, f2, f3, f4, f5………fn, respectively, the the mean deviation from mean and median is defined as-

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