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Example Calculate s.d. of the marks of 100 students.

Marks

No. of students

(fi)

Mid-values

(xi)

fi xi

fi xi2

0-2

10

1

10

10

2-4

20

3

60

180

4-6

35

5

175

875

6-8

30

7

210

1470

8-10

5

9

45

405

 

n = 100

 

Sfi xi = 500

Sfi xi2 = 2940

Solution

1)


2)

Example Calculate s.d. of the marks of 100 students.

 

Marks

No. of students

(fi)

Mid-values

(xi)

fi xi

fi xi2

0-2

10

1

10

10

2-4

20

3

60

180

4-6

35

5

175

875

6-8

30

7

210

1470

8-10

5

9

45

405

 

n = 100

 

Sfi xi = 500

Sfi xi2 = 2940


Solution

1)

 

2)

 

Combined Standard deviation : If two sets containing n1 and n2 items having means x1 and x2 and standard deviations s1 and s2 respectively are taken together then,

(1) Mean of the combined data is

 

(2) s.d. of the combined set is


 

[next page]

Index

5.1 Introduction
5.2 Methods of computing dispersion
5.3 Range
5.4 Mean Deviation
5.5 Variance
5.6 Coefficient of Variation
5.7 Percentile
5.8 Quartiles and interquartile range
5.9 Skewness moments and Kurtosis
5.10 Kurtosis

Chapter 6





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