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Question
Compute arithmetic mean and S.D. and C.V.
(Given `sqrt(296)` = 17.20)
| C.I. | 45 – 55 | 55 – 65 | 65 – 75 | 75 – 85 | 85 – 95 | 95 – 105 |
| f | 4 | 2 | 5 | 3 | 6 | 5 |
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Solution
We prepare the following table for the calculation of arithmetic mean and S.D.:
| C.I. |
Mid value |
fi | fixi | fixi2 |
| 45 – 55 | 50 | 4 | 200 | 10000 |
| 55 – 65 | 60 | 2 | 120 | 7200 |
| 65 – 75 | 70 | 5 | 350 | 24500 |
| 75 – 85 | 80 | 3 | 240 | 19200 |
| 85 – 95 | 90 | 6 | 540 | 48600 |
| 95 – 105 | 100 | 5 | 500 | 50000 |
| Total | N = 25 | `sum"f"_"i""x"_"i"` = 1950 | `sum"f"_"i""x"_"i"^2` = 159500 |
Arthmetic mean = `bar"x" = (sum"f"_"i""x"_"i")/"N" = 1950/25` = 78
Var (X) = `sigma_"x"^2`
= `(sum"f"_"i""x"_"i"^2)/"N" - (bar"x")^2`
= `159500/25 - (78)^2`
= 6380 – 6084
= 296
∴ S.D. = `sigma_"x"`
= `sqrt("Var (X)")`
= `sqrt(296)`
= 17.20
C.V. = `100 xx (sigma_"x")/bar"x"`
= `100 xx (17.20)/78`
= 22.05%
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