Question

Compute the Arithmetic Mean of the following frequency distribution with the step down approach.                                       

Marks

20-29

30-39

40-49

50-59

60-69-

70-79

No. of Students

5

11

18

22

16

8​

Answer 1

Answer:

42.42

Explanation:

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

x  

i

​  

=mid value of class interval

Assumed mean a=44.5

class interval c=10

ci  f  

i

​  

  x  

i

​  

  d  

i

​  

=  

c

x  

i

​  

−a

​  

   f  

i

​  

d  

i

​  

 

9.5−19.5 5  14.5  

10

14.5−44.5

​  

=−3  −15

19.5−29.5 15  24.5  −2  −30

29.5−39.5 28  34.5  −1  −28

39.5−49.5 42  44.5  0  0

49.5−59.5 15  54.5  1  15

59.5−69.5 12  64.5  2  24

69.5−79.5 3  74.5  3  9

N=Σf  

i

​  

=120          

Σf  

i

​  

d  

i

​  

=−25

Mean  

x

=a+  

N

Σf  

i

​  

d  

i

​  

 

​  

×c

∴  

x

=44.5+  

120

−25

​  

×10=42.4166667⇒42.42