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प्रश्न
Answer the following :
Following data gives no. of goals scored by a team in 100 matches. Compute the standard deviation
| No. of Goals Scored | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 5 | 20 | 25 | 15 | 20 | 5 |
उत्तर
We construct the following table to compute S.D. :
| xi | fi | fixi | fixi2 = fixi × xi |
| 0 | 5 | 0 | 0 |
| 1 | 20 | 20 | 20 |
| 2 | 25 | 50 | 100 |
| 3 | 15 | 45 | 135 |
| 4 | 20 | 80 | 320 |
| 5 | 5 | 25 | 125 |
| `sumf_"i"` = 90 | `sumf_"i"x_"i"` = 220 | `sumf_"i"x_"i"^2` = 700 |
From the table,
`sumf_"i"` = 90,`sumf_"i"x_"i"` = 220, `sumf_"i"x_"i"^2` = 700.
`bar(x) = (sumf_"i"x_"i")/(sumf_"i") = 220/90` = 2.44
Var (x) = `sigma_x^2 = (sumf_"i"x_"i"^2)/(sumf_"i") - (barx)^2`
= `700/90 - (2.44)^2`
= 7.78 – 5.95
= 1.83
S.D. = `sigma_x = sqrt(1.83)` = 1.35
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