# Answer the following : Compute the variance and S.D. for the following data: X 62 30 64 47 63 46 35 28 60 F 5 8 3 4 5 7 8 3 7 - Mathematics and Statistics

Sum

Compute the variance and S.D. for the following data:

 X 62 30 64 47 63 46 35 28 60 F 5 8 3 4 5 7 8 3 7

#### Solution

 xi fi fixi xi2 fixi2 62 5 310 3844 19220 30 8 240 900 7200 64 3 192 4096 12288 47 4 188 2209 8836 63 5 315 3969 19845 46 7 322 2116 14812 35 8 280 1225 9800 28 3 84 784 2352 60 7 420 3600 25200 N = 50 sumf_"i"x_"i" = 2351 sumf_"i"x_"i"^2 = 119553

bar(x) = (sumf_"i"x_"i")/"N" = 2351/50 = 47.02

Var (X) = sigma_x^2 = (sumf_"i"x_"i"^2)/"N" - (barx)^2

= 119553/50 - (47.02)^2

= 2391.06 – 2210.88

= 180.18

S.D. = sigma_x = sqrt("Var(X)")

= sqrt(180.18)

= 13.42

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 8 Measures of Dispersion
Miscellaneous Exercise 8 | Q II. (8) | Page 191