Question

10. Find the mean of the following distribution by step deviation method.
Class boundary 0-30 30-60 60-90 90-120 120-150
Frequency
12
15
20
25
8.​

Answer 1

Answer:

Let us find the class marks x

i

of each class by taking the average of upper class limit and lower class limit and put them in a table.

Let us assume a=35 and h=10

Class Interval Frequency Class marks (x

i

) d

i

=x

i

−a u

i

=

h

x

i

−a

f

i

u

i

0.5−9.5 8 5 −30 −3 −24

9.5−19.5 10 15 −20 −2 −20

19.5−29.5 22 25 −10 −1 −22

29.5−39.5 26 35 0 0 0

39.5−49.5 18 45 10 1 18

49.5−59.5 9 55 20 2 18

59.5−69.5 7 65 30 3 21

Total ∑f

i

=100 ∑f

i

u

i

=−9

Using step deviation method,

x

=a+

∑f

i

∑f

i

u

i

×h

=35+

100

−9

×9

=35−0.81

= 34.19