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Following data gives no. of goals scored by a team in 90 matches: No. of goals scored 0 1 2 3 4 5 No. of matches 5 20 25 15 20 5 Compute the variance and standard deviation for the above data. - Mathematics and Statistics

Sum

Following data gives no. of goals scored by a team in 90 matches:

No. of goals scored 0 1 2 3 4 5
No. of matches 5 20 25 15 20 5

Compute the variance and standard deviation for the above data.

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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 5 0 0
1 20 20 20
2 25 50 100
3 15 45 135
4 20 80 320
5 5 25 125
Total N = 90 `sum"f"_"i""x"_"i"` = 220 `sum"f"_"i""x"_"i"^2` = 700

`bar"x" = (sum"f"_"i""x"_"i")/"N" = 220/90` = 2.44

Var (X) = `sigma_"x"^2`

= `(sum"f"_"i""x"_"i"^2)/"N" - (bar"x")^2`

= `700/90 - (2.44)^2`

= 7.78 – 5.9536
= 1.83
S.D. = `sigma_"x"`
= `sqrt("Var (X)")`
= `sqrt(1.83)`

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 2 Measures of Dispersion
Miscellaneous Exercise 2 | Q 9 | Page 35
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