Maharashtra State BoardHSC Science (Electronics) 11th
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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

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
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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

  Is there an error in this question or solution?
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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
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