What is the approximate variance of the data set {0,0,1,2,3}

Question

A) 1.17

B) 1.36

C) 2.34

D) 2.72

Answer 1

The formula for variance on a finite set of numbers is:

 

(s²) = (∑(x_i-x_m)²)/(n-1)

 

S² = variance

x_i = the individual numbers in the data set = {0,0,1,2,3}

x_m = arithmetic average or 'mean' of the data set = (0+0+1+2+3)/6 = 1.2

n = # items in the set = 5

 

x_i     x_i-x_m      (x_i-x_m)²

 

0      -1.2        1.44

0      -1.2        1.44

1      -0.2        0.04 

2       0.8        0.64

3       1.8        3.24

                   --------

                    6.8

 

The sum of the squared differences is 6.8

6.8/(n-1) = 6.8/4 = 1.7

 

Variance = 1.7