Question

5. Calculate the mean of the following frequency distribution by step-deviation method:
x: 15, 20 ,25,30,35,40,45,50,55
f:5,8,11,20,23,18,13,3,1​

Answer 1

Answer:

Step-by-step explanation:

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

​  

  x  

i

​  

  d  

i

​  

=  

c

x  

i

​  

−a

​  

   f  

i

​  

d  

i

​  

 

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+  

150

110

​  

×10=42.3334≈42