1. Measures of Dispersion

2. Consider the following three sets of data 50, 50, 50 Mean = 50 48, 50, 52 1, 49, 100 Measures of dispersion help us to study how spread or varied or scattered is the data.

3. Variance is the average of the sum of squares of deviations of observations from their mean.
Standard Deviation =
To compare two or more sets of data we calculate the Coefficient of Variation
Coefficient of Variation = Standard Deviation x 100
Mean

4. Skewness
Consider the following data representing the distribution of salaries of 3 companies A, B and C each having 76 employees:
Class Mark
Salary
Number of employees X
(in Rs)
Company A
Company B
Company C
250 3
350 8 9
450 16 15 13
550 22 23
650 18 20
750 6 5
850 2
950 1
Total 76

5. Skewness means lack of symmetry.
For the above data the following results are observed:
In order to compare such types of data we use a measure called SKEWNESS.
Skewness means lack of symmetry.
Company A
Company B
Company C
Mean Salary (in Rs)
550
S.D. (in Rs)
140.49
25.54

9. Skewness is measured with the help of COEFFICIENT OF SKEWNESS
Skewness is measured with the help of COEFFICIENT OF SKEWNESS. If the value of coefficient of skewness is zero, the data is symmetric. If the value of coefficient of skewness is less than zero, the data is negatively skewed. If the value of coefficient of skewness is greater than zero, the data is positively skewed.

10. Kurtosis
Consider the following data representing the distribution of salaries of 3 companies A, D and E each having 76 employees:
Class Mark
Salary
Number of employees X
(in Rs)
Company A
Company D
Company E
250 3 2 4
350 8 10 6
450 16 17 15
550 22 18 26
650
750
850
Total 76

12. Kurtosis means peakedness of the curve.

13. Kurtosis is measured by coefficient of kurtosis
Kurtosis is measured by coefficient of kurtosis. Coefficient of Kurtosis characterizes the relative peakedness or flatness of data. Positive coefficient of kurtosis indicates a relatively peaked or leptokurtic data. Negative coefficient of kurtosis indicates a relatively flat or platykurtic data. Zero coefficient of kurtosis indicates mesokurtic data.