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The following table gives weights of the students of class A. Calculate the Coefficient of variation. (Given:0.8=0.8944) Weight (in kg) Class A 25 – 35 8 35 – 45 4 45 – 55 8 - Mathematics and Statistics

Sum

The following table gives weights of the students of class A. Calculate the Coefficient of variation. `("Given": sqrt0.8 = 0.8944)`

Weight (in kg) Class A
25 – 35 8
35 – 45 4
45 – 55 8
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Solution

Weight
(in kg)
Class A
(fi)
Mid value
(xi)
fixi fixi2
25 – 35 8 30 240 7200
35 – 45 4 40 160 6400
45 – 55 8 50 400 20000
Total N = 20   ∑fixi = 800 ∑fixi2 = 33600

`bar"x" = (sum"f"_"i""x"_"i")/"N"`

= `(800)/(20)`
= 40

Var(X) = `sigma_"x"^2=(sum"f"_"i""x"_"i"^2)/"N"-(bar"x")^2`

= `33600/20-(40)^2`

= 1680 − 1600
= 80
∴ S.D. = σx = `sqrt80`

= `sqrt((100xx8)/10)`

= `10sqrt0.8 `

= 10(0.8944)
= 8.944

C.V. (X) = `sigma_"x"/bar"x" xx 100`

= `(8.944)/(40) xx 100`

= 22.36%

Concept: Coefficient of Variation
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