Mean Deviation from Median | Individual, Discrete, and Continuous Series

Last Updated : 25 Oct, 2023

What is Mean Deviation from Median?

Mean Deviation of a series can be defined as the arithmetic average of the deviations of various items from a measure of central tendency (mean, median, or mode). Mean Deviation is also known as the First Moment of Dispersion or Average Deviation. Mean Deviation is based on all the items of the series. Theoretically, the mean deviation can be calculated by taking deviations from any of the three averages. But in actual practice, the mean deviation is calculated either from mean or median. While calculating deviations from the selected average, the signs (+ or -) of deviations are ignored and are taken as positive.

Table of Content

Mean Deviation from Median in Case of Individual Series
Mean Deviation from Median in Case of Discrete Series
Mean Deviation from Median in Case of Continuous Series

Coefficient of Mean Deviation

Mean Deviation is an absolute measure of dispersion. In order to transform it into a relative measure, it is divided by the average, from which it has been calculated. It is known as the Coefficient of Mean Deviation.

Coefficient of Mean Deviation from Median (MD_Me) = $\frac{MD_{Me}}{Me}$

Mean Deviation from Median in Case of Individual Series

Step 1: Calculate the specific average (Median) from which the mean deviation is to be found.

Step 2: Obtain absolute (positive) deviations of each observation from the median.

Step 3: Absolute deviations are totalled up to find out ∑|D|.

Step 4: Apply the formula

Mean Deviation from Median (MD_Me) = $\frac{\Sigma|X-Me|}{N} = \frac{\Sigma|D|}{N}$

Example 1:

Calculate the mean deviation from median for the given data: 10, 16, 22, 24, 28.

Solution:

Mean Deviation from Median in Case of Individual Series

Median = $Size~of~[\frac{N+1}{2}]^{th}~item$

Median = $Size~of~[\frac{5+1}{2}]^{th}~item$

Median = Size of 3^rd item

Median = 22

Mean Deviation from Median (MD_Me) = $\frac{\Sigma|D|}{N}$

Mean Deviation from Median (MD_Me) = $\frac{26}{5}$

Mean Deviation from Median (MD_Me) = 5.2

Coefficient of Mean Deviation from Median = $\frac{MD_{Me}}{Median}$

Coefficient of Mean Deviation from Median = $\frac{5.2}{22}$

Coefficient of Mean Deviation from Median = 0.23

Example 2:

Calculate the mean deviation from median for the given data: 20, 24, 32, 40, 50, 54, 60.

Solution:

Mean Deviation from Median in Case of Individual Series

Median = $Size~of~[\frac{N+1}{2}]^{th}~item$

Median = Size~of~[\frac{7+1}{2}]^{th}~item

Median = Size of 4^thitem

Median = 40

Mean Deviation from Median (MD_Me) = $\frac{\Sigma|D|}{N}$

Mean Deviation from Median (MD_Me) = $\frac{88}{7}$

Mean Deviation from Median (MD_Me) = 12.57

Coefficient of Mean Deviation from Median = $\frac{MD_{Me}}{Median}$

Coefficient of Mean Deviation from Median = $\frac{12.57}{40}$

Coefficient of Mean Deviation from Median = 0.31

Mean Deviation from Median in Case of Discrete Series

Step 1: Calculate the specific average (Median) from which the mean deviation is to be found.

Step 2: Obtain the absolute deviations |D| of each observation from the specific average (Median).

Step 3: Multiple absolute deviations |D| with respective frequencies (f) and obtain the sum of products to get ∑f |D|.

Step 4: Divide ∑f |D| by the number of items to get the mean deviation.

Mean Deviation from Median (MD_Me) = $\frac{\Sigma f|X-Me|}{N}=\frac{\Sigma f|D|}{N}$

Example 1:

Calculate the mean deviation from median of the following series.

Mean Deviation from Median in Case of Discrete Series

Solution:

Mean Deviation from Median in Case of Discrete Series

Median = $Size~of~[\frac{N+1}{2}]^{th}~item$

Median = $Size~of~[\frac{61+1}{2}]^{th}~item$

Median = Size of 31^th item

Median = 150

Mean Deviation from Median (MD_Me) = $\frac{\Sigma f|D|}{N}$

Mean Deviation from Median (MD_Me) = $\frac{2410}{61}$

Mean Deviation from Median (MD_Me) = 39.5

Coefficient of Mean Deviation from Median = $\frac{MD_{Me}}{Median}$

Coefficient of Mean Deviation from Median = $\frac{39.5}{150}$

Coefficient of Mean Deviation from Median = 0.26

Example 2:

Calculate the mean deviation from median and coefficient of mean deviation.

MD-md-4

Solution:

Mean Deviation from Median in Case of Discrete Series

Median = $Size~of~[\frac{N+1}{2}]^{th}~item$

Median = $Size~of~[\frac{16+1}{2}]^{th}~item$

Median = Size of 8.5^th item

Median = 11

Mean Deviation from Median (MD_Me) = $\frac{\Sigma f|D|}{N}$

Mean Deviation from Median (MD_Me) = $\frac{10}{16}$

Mean Deviation from Median (MD_Me) = 0.625

Coefficient of Mean Deviation from Median = $\frac{MD_{Me}}{Median}$

Coefficient of Mean Deviation from Median = $\frac{0.625}{11}$

Coefficient of Mean Deviation from Median = 0.056

Mean Deviation from Median in Case of Continuous Series

In the case of continuous series, the formula for mean deviation is the same as that of the discrete series. For the given frequency distribution, the mid-points of class intervals have to be found out, and they are taken as ‘m’. In this way, a continuous series assumes the shape of a discrete series. After that, all the steps of discrete series are applied. Symbolically,

Mean Deviation from Median (MD_Me) = $\frac{\Sigma f|m-Me|}{N}$ = $\frac{\Sigma f|D|}{N}$