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Question
Answer the following :
Calculate the coefficient of variation for the data given below:
| Size (cm) | 5 - 8 | 8 - 11 | 11 - 14 | 14 - 17 | 17 - 20 | 20 - 23 | 23 - 26 |
| No of items | 3 | 14 | 13 | 16 | 19 | 24 | 11 |
Solution
| Size (cm) | Mid value (xi) |
No. of students (fi) |
fixi | fixi2 |
| 5 - 8 | 6.5 | 3 | 19.5 | 126.75 |
| 8 - 11 | 9.5 | 14 | 133 | 1263.5 |
| 11 - 14 | 12.5 | 13 | 162.5 | 2031.25 |
| 14 - 17 | 15.5 | 16 | 248 | 3844 |
| 17 - 20 | 18.5 | 19 | 351.5 | 6502.75 |
| 20 - 23 | 21.5 | 24 | 516 | 11094 |
| 23 - 26 | 24.5 | 11 | 269.5 | 6602.75 |
| N = 100 | `sumf_"i"x_"i"` = 1700 | `sumf_"i"x_"i"^2` = 31465 |
`bar(x) = (sumf_"i"x_"i")/"N" = 1700/100` = 17
Var(X) = `sigma_x^2 = 1/"N" sumf_"i"x_"i"^2 - (barx)^2`
= `1/100 (31465) - (17)^2`
= 314.65 − 289
= 25.65
`sigma_x = sqrt(25.65)` = 5.06
∴ C.V. = `100 xx sigma_x/bar(x)`
= `100 xx 5.06/17`
= 29.76%
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