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Question
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%
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