# 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.

#### 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