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Question
Calculate coefficient of variation for the data given below [Given : `sqrt(3.3)` = 1.8166]
| C.I. | 5 – 15 | 15 – 25 | 25 – 35 | 35 – 45 | 45 – 55 | 55 – 65 | 65 – 75 |
| f | 6 | 7 | 15 | 25 | 8 | 18 | 21 |
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Solution
| C.I. | Mi value (xi) |
Frequency (fi) |
fixi | fixi2 |
| 5 – 15 | 10 | 6 | 60 | 600 |
| 15 – 25 | 20 | 7 | 140 | 2800 |
| 25 – 35 | 30 | 15 | 450 | 13500 |
| 35 – 45 | 40 | 25 | 1000 | 40000 |
| 45 – 55 | 50 | 8 | 400 | 20000 |
| 55 – 65 | 60 | 18 | 1080 | 64800 |
| 65 – 75 | 70 | 21 | 1470 | 102900 |
| Total | N = 100 | `sum"f"_"i""x"_"i"` = 4600 | `sum"f"_"i""x"_"i"^2` = 244600 |
`bar"x" = (sum"f"_"i""x"_"i")/"N" = 4600/100` = 46
Var (X) = `sigma_"x"^2`
= `1/"N" sum"f"_"i""x"_"i"^2 - (bar"x")^2`
= `1/100 xx 244600 - (46)^2`
= 2446 – 2116
= 330
S.D. = `sigma_"x"^2`
= `sqrt(330)`
= `sqrt(3.3 xx 100)`
= `10sqrt(3.3)`
= 10 × 1.8166
= 18.166
∴ C.V. = `100 xx sigma_"x"/bar"x"`
= `100 xx (18.166)/46`
= 39.49%
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