Question

The marks obtained by 60 students in an examination are as follows. Find the mean mark
marks
0-10
10 - 20
20 - 25
25 - 30
30 - 35
35 - 40
no.of students
3
8
20
16
9
4.​

Answer 1

Answer:

ANSWER

C-I F x Fx Step deviation d=

c

x−A

d

2

fd fd

2

5-15 8 10 80 -2 4 -16 32

15-25 12 20 240 -1 1 -12 12

25-35 20 30 600 0 0 0 0

35-45 10 40 400 +1 1 +10 10

45-55 7 50 350 +2 4 +14 28

55-65 3 60 180 +3 9 +9 27

n=60 Σ=1850 Σfd=+5 Σfd

2

=109

The mid-point of class intervals have C=10 as a common factor and the mean is not an integer.

∴ Let us follow step deviation method.

(i) Mean=

n

∑fx

=

60

1850

=30.8

(ii) S.D=

n

∑fd

2

−(

n

∑fd

)

2

×C=

60

109

−(

60

5

)

2

×10=

1.81

×10=1.34×10,σ=13.4.

This means, on an average each score deviates from the mean value 30.8 by 13.4.