Question

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

Answer 1

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

Answer: 2.99