1.

Calculate the mean deviation about the median of the following observation : 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

Answer»

Given, Numbers of observations are given. 

To Find: Calculate the Mean Deviation. 

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

Explanation: Here, Observations 22, 24, 30, 27, 29, 31, 25, 28, 41, 42are Given.

Since, Median is the middle number of all the observation, 

So, To Find the Median, Arrange the numbers in Ascending order, we get 

22, 24, 25, 27, 28, 29, 30, 31, 41, 42 

Here the Number of observations are Even then the middle terms are 28 and 29 

Therefore, The Median = \(\frac{28+29}{2}\) = 28.5

Deviation |d| = |x-Median| 

And, The number of observations is 10. 

Now, The Mean Deviation is

Xi|di| = |xi-28.5|
226.5
244.5
301.5
271.5
290.5
312.5
253.5
280.5
4112.5
4313.5
Total Σdi 47

Hence, The Mean Deviation is 8.7

Mean Deviation = \(\frac{47}{10}\) = 4.7


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