1
Consider the following three sets of data
50, 50, 50
Mean = 50
48, 50, 52
Mean = 50
1, 49, 100
Mean = 50
Measures of dispersion help us to study how spread or
varied or scattered is the data.
2
Variance is the average of the sum of squares of
deviations of observations from their mean.
Variance =
 x
i
x

2
n
Standard Deviation =
Variance
To compare two or more sets of data we calculate the
Coefficient of Variation
Coefficient of Variation = Standard Deviation x 100
Mean
3
Consider the following data representing the distribution
of salaries of 3 companies A, B and C each having 76
employees:
Class Mark
Salary
X
(in Rs)
Company A
Company B
Company C
250
200-300
3
3
3
350
300-400
8
8
9
450
400-500
16
15
13
550
500-600
22
23
23
650
600-700
16
18
20
750
700-800
8
6
5
850
800-900
3
2
2
950
900-1000
0
1
1
76
76
76
Total
Number of employees
4
For the above data the following results are observed:
Mean Salary (in Rs)
S.D. (in Rs)
C.V . 
S .D.
 100
Mean
Company A
Company B
Company C
550
550
550
140.49
140.49
140.49
25.54
25.54
25.54
In order to compare such types of data we use a measure
called SKEWNESS.
Skewness means lack of symmetry.
5
6
7
8
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.
9
Consider the following data representing the
distribution of salaries of 3 companies A, D and E each
having 76 employees:
Class Mark
Salary
X
(in Rs)
Company A
Company D
Company E
250
200-300
3
2
4
350
300-400
8
10
6
450
400-500
16
17
15
550
500-600
22
18
26
650
600-700
16
17
15
750
700-800
8
10
6
850
800-900
3
2
4
76
76
76
Total
Number of employees
10
30
25
20
15
Company A
Company D
Company E
10
5
0
0
100
200
300
400
500
600
700
800
900
11
12
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.
13