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

Business Mathematics and Statistics

Created by: Arshit Thakur

B Com : Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev

The document Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev is a part of the B Com Course Business Mathematics and Statistics.
All you need of B Com at this link: B Com

Computation of Mean Deviation :

(a) For individual Observation (or Simple Variates)

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

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 B Com Notes | EduRev

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 B Com Notes | EduRev

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

Note : The sum of deviation Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev about median is 39, less than Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev 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 B Com Notes | EduRev

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

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

WhereMean Deviation - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev = 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 B Com Notes | EduRev
Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev

About Mean

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

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

Find also the coefficient of dispersion.
Solution :

 

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

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

 

Example 47 : The same example as given above.

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

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

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

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

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

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

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

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

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

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

 

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 B Com Notes | EduRev

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

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.

Dynamic Test

Content Category

Related Searches

pdf

,

study material

,

Sample Paper

,

MCQs

,

Business Mathematics & Statistics B Com Notes | EduRev

,

past year papers

,

Business Mathematics & Statistics B Com Notes | EduRev

,

Mean Deviation - Measures of Dispersion

,

Important questions

,

Viva Questions

,

Business Mathematics & Statistics B Com Notes | EduRev

,

video lectures

,

shortcuts and tricks

,

Exam

,

Objective type Questions

,

Mean Deviation - Measures of Dispersion

,

practice quizzes

,

ppt

,

Semester Notes

,

Free

,

Summary

,

mock tests for examination

,

Mean Deviation - Measures of Dispersion

,

Extra Questions

,

Previous Year Questions with Solutions

;