calculate standard deviation class intervals 10-20 ,20-30,30-50,50-70 , 70-80 frequency 5,8,16,8,3
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Class 11
>>Applied Mathematics
>>Descriptive Statistics
>>Data interpretation
>>Calculate the variance and standard devi
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Calculate the variance and standard deviation of the following continuous frequency distribution
Class interval 30−40 40−50 50−60 60−70 70−80 80−90 90−100
Frequency 3 7 12 15 8 3 2
Easy
Solution
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Class Interval Mid Value (x) frequency (f) fx fx
2
30−40 35 3 105 3675
40−50 45 7 315 14175
50−60 55 12 660 36300
60−70 65 15 957 63375
70−80 75 8 600 45000
80−90 85 3 255 21675
90−100 95 2 190 18050
n=∑f=50
x
ˉ
=
n
1
∑fx
i
=
50
3082
=61.64
Variance (σ
2
)=
n
1
∑fx
2
−(
x
ˉ
)
2
=
50
202250
−(61.64)
2
=245.5104
Standard deviation (σ)=
245.5104
=15.67