Question

Find the mean of the following data, by direct method.

Class internal Frequency

1 - 5

5 - 9

9 - 13

13 - 17

17 - 21

4

3

5

7

1

N = 20​

Answer 1

Answer:

Solution :

xi=10,30,50,70,90xi=10,30,50,70,90

fi=15,18,21,29,17fi=15,18,21,29,17

A=50,L=20A=50,L=20

di=−40,−20,0,20,40di=-40,-20,0,20,40

ui=(di−h)=−2,−1,0,1,2ui=(di-h)=-2,-1,0,1,2

fi⋅ui=−30,−18,0,29,34fi⋅ui=-30,-18,0,29,34

∑(fi⋅ui)=15∑(fi⋅ui)=15

∑fi=N=100∑fi=N=100

Mean=A+h⋅(∑fi⋅uiN)Mean=A+h⋅(∑fi⋅uiN)

=50+20⋅(15100)=50+20⋅(15100)

=50+3=53=50+3=53