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Question
Following data gives no. of goals scored by a team in 100 matches:
| No. of goals scored | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 15 | 20 | 25 | 15 | 20 | 5 |
Compute the variance and standard deviation for the above data.
Solution
We prepare the following table for the calculation of variance and S.D:
| No. of goals scored (xi) |
No. of matches (fi) |
fixi | fixi2 |
| 0 | 15 | 0 | 0 |
| 1 | 20 | 20 | 20 |
| 2 | 25 | 50 | 100 |
| 3 | 15 | 45 | 135 |
| 4 | 20 | 80 | 320 |
| 5 | 5 | 25 | 125 |
| Total | N = 100 | `sum"f"_"i""x"_"i"` = 220 | `sum"f"_"i""x"_"i"^2` = 700 |
`bar"x" = (sum"f"_"i""x"_"i")/"N" = 220/100` = 2.2
Var (X) = `sigma_"x"^2`
= `(sum"f"_"i""x"_"i"^2)/"N" - (bar"x")^2`
= `700/100 - (2.2)^2`
= 7 - 4.84
= 2.16
S.D. = `sigma_"x"`
= `sqrt("Var (X)")`
= `sqrt(2.16)`
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