SSC CGL Exam  >  SSC CGL Notes  >  SSC CGL Tier 2 - Study Material, Online Tests, Previous Year  >  Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year PDF Download

Computation of Mean Deviation :

(a) For individual Observation (or Simple Variates)

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

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 | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

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 | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Note : The sum of deviation Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year about median is 39, less than Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year 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 | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

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

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

WhereMean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year = 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 | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year
Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

About Mean

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

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Find also the coefficient of dispersion.
Solution :

 

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

 

Example 47 : The same example as given above.

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

(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 | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year and f Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

(iv) Divide  Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

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

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

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

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

 

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 | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

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.

The document Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year is a part of the SSC CGL Course SSC CGL Tier 2 - Study Material, Online Tests, Previous Year.
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FAQs on Mean Deviation - Measures of Dispersion, Business Mathematics & Statistics - SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

1. What is the formula for calculating mean deviation?
Ans. The formula for calculating mean deviation is as follows: Mean Deviation = Σ |X - μ| / N, where Σ represents the sum of all the absolute differences between each value (X) and the mean (μ), and N is the total number of values.
2. How is mean deviation different from standard deviation?
Ans. Mean deviation and standard deviation are both measures of dispersion, but they differ in terms of how they calculate the dispersion. Mean deviation measures the average distance of each value from the mean, while standard deviation measures the average deviation of each value from the mean, considering the squared differences. Standard deviation is more commonly used as it gives more weight to extreme values.
3. What does mean deviation tell us about a data set?
Ans. Mean deviation provides information about the spread or dispersion of a data set. A smaller mean deviation indicates that the values are closer to the mean, suggesting less variability. On the other hand, a larger mean deviation indicates greater variability and a wider spread of values from the mean.
4. Can mean deviation be negative?
Ans. No, mean deviation cannot be negative. The absolute values of the differences between each value and the mean are used in the calculation, ensuring that the result is always a positive value. The negative sign is disregarded when calculating the mean deviation.
5. Is mean deviation affected by outliers in the data set?
Ans. Yes, mean deviation is affected by outliers in the data set. Outliers, being extreme values, can significantly increase the mean deviation as they have larger differences from the mean. Therefore, mean deviation may not accurately represent the dispersion of the data when outliers are present. In such cases, other measures like median deviation or interquartile range may be more suitable.
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