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प्रश्न
Obtain standard deviation for the following date:
| Height (in inches) | 60 – 62 | 62 – 64 | 64 – 66 | 66 – 68 | 68 – 70 |
| Number of students | 4 | 30 | 45 | 15 | 6 |
उत्तर
We prepare the following table for the calculation of standard deviation.
| Height (in inches) | Number of students fi |
Mid value xi |
fixi | fixi2 |
| 60 – 62 | 4 | 61 | 244 | 14884 |
| 62 – 64 | 30 | 63 | 1890 | 119070 |
| 64 – 66 | 45 | 65 | 2925 | 190125 |
| 66 – 68 | 15 | 67 | 1005 | 67335 |
| 68 – 70 | 6 | 69 | 414 | 28566 |
| Total | N =100 | ∑fixi = 6478 | ∑fixi2 = 419980 |
`bar"x"= (sum"f"_"i""x"_"i")/"N"=6478/100` = 64.78
Var(X) = `sigma_"x"^2 = (sum"f"_"i""x"_"i"^2)/"N"- (bar"x")^2`
= `419980/100-(64.78)^2`
= 4199.80 – 4196.4484
= 3.3516
∴ S.D. = `sigma_"x"=sqrt("Var"("X"))=sqrt3.3516`
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