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) = = 

Example 1: 

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

Solution:

Median = 

Median = 

Median = Size of 10^th item

So, the median class lies in the group 4-6.

Hence, l₁ = 4, c.f. = 6, f = 8, i = 2.

Median = 

Median = 

Median = 5

Mean Deviation from Median (MD_Me) = 

Mean Deviation from Median (MD_Me) =  

Mean Deviation from Median (MD_Me) = 1.4

Coefficient of Mean Deviation from Median = 

Coefficient of Mean Deviation from Median = 

Coefficient of Mean Deviation from Median = 0.28

Example 2: 

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

Solution:

Median = 

Median = 

Median = Size of 25^th item

So, the median class lies in the group 80-100

Hence, l₁ = 80, c.f. = 9, f = 20, i = 20

Median = 

Median = 

Median = 96

Mean Deviation from Median (MD_Me) = 

Mean Deviation from Median (MD_Me) = 

Mean Deviation from Median (MD_Me) = 17.76

Coefficient of Mean Deviation from Median = 

Coefficient of Mean Deviation from Median = 

Coefficient of Mean Deviation from Median = 0.185