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Find Standard Deviation(S.D.) and Coefficient of Variation for grouped data
Calculate Coefficient of variation from the follwing grouped data
Class
Frequency
2 - 4
3
4 - 6
4
6 - 8
2
8 - 10
1
Solution:
Class
`(1)`
Frequency `(f)`
`(2)`
Mid value `(x)`
`(3)`
`f*x`
`(4)=(2)xx(3)`
`f*x^2=(f*x)xx(x)`
`(5)=(4)xx(3)`
2-4
3
3
`3=(2+4)/2`
9
`9=3xx3`
`(4)=(2)xx(3)`
27
`27=9xx3`
`(5)=(4)xx(3)`
4-6
4
5
`5=(4+6)/2`
20
`20=4xx5`
`(4)=(2)xx(3)`
100
`100=20xx5`
`(5)=(4)xx(3)`
6-8
2
7
`7=(6+8)/2`
14
`14=2xx7`
`(4)=(2)xx(3)`
98
`98=14xx7`
`(5)=(4)xx(3)`
8-10
1
9
`9=(8+10)/2`
9
`9=1xx9`
`(4)=(2)xx(3)`
81
`81=9xx9`
`(5)=(4)xx(3)`
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`n = 10`
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`sum f*x=52`
`sum f*x^2=306`
Mean `bar x = (sum fx)/n`
`=52/10`
`=5.2`
`sigma = sqrt((sum f*x^2)/n - ((sum f*x)/n)^2)`
`=sqrt(306/10 - (52/10)^2)`
`=sqrt(306/10 - 2704/100)`
`=sqrt(30.6 - 27.04)`
`=sqrt(3.56)`
`=1.89`
Co-efficient of Variation `=sigma / bar x * 100 %`
`=1.89/5.2 * 100 %`
`=36.28 %`