Question

Find standard deviation and coefficient of variance for the following data.


Class interval
0-10
10-20
20-30
30-40
40-50

frequency
11
15
25
12
7

​

Answer 1

Answer:

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Answer 2

ANSWER
Class interval f
i
​
x
i
​
u
i
​
=
h
x
i
​
−A
​
u
i
2
​
f
i
​
u
i
​
f
i
​
u
i
2
​

0-10 5 5 -2 4 -10 20
10-20 8 15 -1 1 -8 8
20-30 15 25 0 0 0 0
30-40 16 35 1 1 16 16
40-50 6 45 2 4 12 24
Total 50 10 68
We have N=∑f
i
​
=50
Width of class h=10
Assumed mean A=25(say)

Mean,
x
ˉ
=A+
N
∑
i=1
5
​
f
i
​
u
i
​

​
×h
=25+
50
10
​
×10=25+2=27
⇒
x
ˉ
=27

Variance σ
2
=h
2

⎣
⎢
⎡
​

N
∑
i=1
5
​
f
i
​
u
i
2
​

​
−(
N
∑
i=1
5
​
f
i
​
u
i
​

​
)
2

⎦
⎥
⎤
​

σ
2
=10
2

⎣
⎢
⎡
​

50
68
​
−(
50
10
​
)
2

⎦
⎥
⎤
​

=10
2

(50)
2

[50×68−(10)
2
]
​

=
25
1
​
[3400−100]
=
25
3300
​

=132
this is the answer