Question

find mean for the following data by using step deviation method
x 100-200 f 10
x200-300 f 18
x300-400 f 12
x400-500 f 20
x500-600 f 40
​

Answer 1

Consider the following table, to calculate mean by "step deviation method":

x  i =mid value of class interval

Assumed mean a=35

class interval c=10

ci  f i​     di​ = cxi −a   f di

0−10  15  5  −3  −45

10−20  10  15  −2  −20

20−30  15  25  −1  −15

30−40  20  35  0  0

40−50  25  45  1  25

50−60  30  55  2  60

60−70  35  65  3  105

N=Σf  i =150          

Σf  i d  i =110

Mean  x =a+  N

Σf  i d  i ×c

∴  x =35+  150110 ×10=42.3334≈42

Hence, option B is correct.

hope it will help you