What is the variance of the following data? if necessary, round your answer to two decimal places.
12, 13, 8, 13, 9, 11, 12, 9, 11
a)2.99
b)3.02
c)3
d)3.01

The formula of the variance, s^2, is

s^2 = sum [ value i - average]^2 for all the data i / (number of data)

Average = [12 + 13 + 8 + 13 + 9 + 11 + 12 + 9 + 11] / 9 = 98 / 9 = 10.889

data     value - average     (value - average)^2

12        12 - 10.889              1.2346

13        13 - 10.889              4.4568

8           8 - 10.889               8.3467

13         13 - 10.889             4.4568   

9           9 - 10.889               3.5679  

11         11 - 10.889              0.0123

12         12 - 10.889             1.2346

9           9 - 10.889               3.5679          

11         11 - 9.667              0.0123
                                        
                      sum             26.8889

s^2 = 26.8889 / (n) = 26.8889 / (9) = 2.988 ≈ 2.99

2.99

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