Question

Calculate the mean deviation of the following income groups of five and seven members from their medians:

I Income in Rs.	II Income in Rs.
4000	3800
4200	4000
4400	4200
4600	4400
4800	4600
	4800
	5800

Answer 1

Given, Numbers of observations are given in two groups. 

To Find: Calculate the Mean Deviation from their Median. 

Formula Used: Mean Deviation = \(\frac{\Sigma d_i}{n}\)

For Group 1: Since, Median is the middle number of all the observation, 

So, To Find the Median, Arrange the Income of Group 1 in Ascending order, we get 4000, 4200, 4400, 4600, 4800 

Therefore, The Median = 4400

Deviation |d| = |x-Median| 

Now, The Mean Deviation is

X1	|di|=|xi-4400|
4000	400
4200	200
4400	0
4600	200
4800	400
Total	1200

Mean Deviation = \(\frac{\Sigma d_i}{n}\)

Mean Deviation Of Group 1 = \(\frac{1200}{5}\) = 240

For Group 2: Since, Median is the middle number of all the observation, 

So, To Find the Median, Arrange the Income of Group 2 in Ascending order, we get 3800,4000,4200,4400,4600,4800,5800 

Therefore, The Median = 4400 

Deviation |d| = |x-Median| 

Now, The Mean Deviation is

X1	|di|=|xi-4400|
3800	600
4000	400
4200	200
4400	0
4800	200
5800	1400
Total	3200

Mean Deviation = \(\frac{\Sigma d_i}{n}\)

Mean Deviation Of Group 2 = \(\frac{3200}{7}\) = 457.14

Hence, The Mean Deviation of Group 1 is 240 and Group 2 is 457.14