Question

Find the mean for the following frequency distribution :
Class
1-5
6-10
11-15
16-20
21-25
26-30
31-35

Frequency
18
32
30
40
25
15
40

Answer 1

Dear Student,

Solution: let a = 18 , h = 5

True class ---freq------xi------di --------ui= di/h

0.5 -5.5-------18----------3------(-15) ------. -3

5.5-10.5 ------32--------- 8-----(-10)-------. -2

10.5-15.5 ------30---------13-----(-5) ------. -1

15.5- 20.5------40--------18-----(0)-------. 0

20.5-25.5------25--------23----(5)------. 1

25.5-30.5-------15--------28---(10) -------. 2

30.5-35.5------40--------33------(15)------3

summation of fiui= -54-64-30+0+25+30+120

= 27

sum of Frequencies= 18+32+30+40+25+15+40

= 200

step deviation method= a +( sum of fiui/sum of fi)h

= 18+(27/200)5

= 18+0.675

= 18.675

Mean = 18.675

Hope it helps you.

Answer 2

Mean = 18 + ( 27/200 ) × 5

= 18 + 0.675

= 18.675

Therefore ,

Mean = 18.675

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