Maharashtra State BoardHSC Commerce 11th
Advertisement Remove all ads

Find the various 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, 8, 2, 6 - Mathematics and Statistics

Sum

Find the various 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, 8, 2, 6

Advertisement Remove all ads

Solution

Given data: 7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6
The tabulated form of the above data is as given below:

x1 2 3 4 5 6 7 8 9 11
f1 3 2 1 1 3 2 3 1 2

We prepare the following table for the calculation of variance and S. D.

xi fi fixi fixi2
2 3 6 12
3 2 6 18
4 1 4 16
5 1 5 25
6 3 18 108
7 2 14 98
8 3 24 192
9 1 9 81
11 2 22 242
Total N = 18 ∑fixi = 108 ∑fixi2 = 792

`bar"x"`= `(sum"f"_"i""x"_"i")/"N"=108/18` = 6

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

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

= 44 – 36
= 8
∴ S.D. `sigma_x = sqrt("Var"("X")`

= `sqrt(8)`

= `2sqrt(2)`

  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×