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Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

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Computation of Mean Deviation :

(a) For individual Observation (or Simple Variates)

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Where | d | within two vertical lines denotes deviations from mean (or median), ignoring algebraic signs (i.e., + and –).

Coefficient of Mean Deviation :

Coefficient of Mean Deviation =   Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Steps to find M. D.
(1) Find mean or median
(2) Take deviation ignoring ± signs
(3) Get total of deviations
(4) Divide the total by the number of items.

Example 45 : To find the mean deviation of the following data about mean and median : (`) 2, 6, 11, 14, 16, 19, 23.

Solution :

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Note : The sum of deviation Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com about median is 39, less than Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com about mean (= 40). Also M.D. about median.(i.e.5.57) is less than that about mean, (i.e., 5.71) Coefficient of Mean Deviation :

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

(b) For Discrete Series (or Simple Frequency Distribution) The formula for computing M.D. is

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

WhereMean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com = deviations from mean (or median) ignoring ± signs.

Steps of find M.D.
(i) Find weighed A.M. or median.
(ii) Find deviations ignoring ± signs. i.e., Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com
Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

About Mean

Example 46 : To calculate mean deviation of the following series :

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Find also the coefficient of dispersion.
Solution :

 

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

 

Example 47 : The same example as given above.

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

(c) For Class Intervals (or Group Distribution) Steps to compute (M.D.)
(i) Find mid-value of the class intervals
(ii) Compute weighted A.M. or median
(iii) Find Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com and f Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

(iv) Divide  Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Example 48 : Find M.D. about A.M. of the following frequency distribution.

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Calculate also M.D. about median and hence find coefficient of mean dispersion.
Solution :

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

 

Median = value of N/2th item = value of 50/2, i.e., 25 th item. So median class is (7.50 – 9.50)

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics Notes | Study Business Mathematics and Statistics - B Com

Advantages of Mean Deviation :
(1) It is based on all the observations. Any change in any item would change the value of mean deviation.
(2) It is readily understood. It is the average of the deviation from a measure of central tendency.
(3) Mean Deviation is less affected by the extreme items than the standard deviation.
(4) It is simple to understand and easy to compute.

Disadvantages of Mean Deviation :
(1) Mean deviation ignores the algebraic signs of deviations and as such it is not capable of further algebraic treatment.
(2) It is not an accurate measure, particularly when it is calculated from mode.
(3) It is not popular as standard deviation.

Uses of Mean Deviation :

Because of simplicity in computation, it has drawn the attention of economists and businessmen. It is useful reports meant for public.

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