Maharashtra State BoardHSC Science (Electronics) 11th
Advertisement Remove all ads

Find variance and S.D. for the following set of numbers: 7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6 - Mathematics and Statistics

Sum

Find variance and S.D. for the following set of numbers:

7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6

Advertisement Remove all ads

Solution

Tabulated form of the above data is

xi fi
2 3
3 2
4 1
5 1
6 3
7 2
8 3
9 1
11 2

Calculation of variance and S.D.;

xi fi fixi xi2 fixi2
2 3 6 4 12
3 2 6 9 18
4 1 4 16 16
5 1 5 25 25
6 3 18 36 108
7 2 14 49 98
8 3 24 64 192
9 1 9 81 81
11 2 22 121 242
Total N = 18 `sumf_"i"x_"i"` = 108   `sumf_"i"x_"i"^2` = 792

`bar(x) = (sumf_"i"x_"i")/"N" = 108/18` = 6

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

= `792/18 - (6)^2`

= 44 – 36

= 8

∴ S.D. = `sigma_x = sqrt("Var"(X)`

= `sqrt(8)`

= 2.82

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×