What is the population variance of the following set of numbers: 3, 5, 8, 9, 10?

Solution:

Given, the data set is 3, 5, 8, 9, 10

We have to find the population variance of the given set of numbers.

Population variance can be calculated using the formula,

\(\sigma =\frac{1}{N}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}\)

Here, \(\bar{x}\) = sample average

x = individual values in sample

N = count of values in the sample.

Mean = (3 + 5 + 8 + 9 + 10)/5

= 35/5

= 7

N = 5

On substituting the values,

\(\sigma =\frac{1}{5}((3-7)^{2}+(5-7)^{2}+(8-7)^{2}+(9-7)^{2}+(10-7)^{2})\)

\(\sigma =\frac{1}{5}((-4)^{2}+(-2)^{2}+(1)^{2}+(2)^{2}+(3)^{2})\)

\(\sigma =\frac{1}{5}(16+4+1+4+9)\)

\(\sigma =\frac{1}{5}(34)\)

\(\sigma =6.8\)

Therefore, the population variance is \(\sigma =6.8\).

What is the population variance of the following set of numbers: 3, 5, 8, 9, 10?

Summary:

The population variance of the following set of numbers: 3, 5, 8, 9, 10 is \(\sigma =6.8\).