Question-42

If the sample variance of a data of size \(10\) is \(23\), then what is the population variance of this data\(?\)

• \(25.56\)

• \(19\)

• \(20.7\)

• \(23\)

Hint

Sample variance, \(s^2 = \dfrac{\sum_{i=1}^n(x_i - \bar{x})^2}{n-1}\) and

Population variance, \(\sigma^2 = \dfrac{\sum_{i=1}^n(x_i - \bar{x})^2}{n}\)

Find the relation between \(s^2\) and \(\sigma^2\) by using the above formula and calculate the value of population variance.

Answer

• \(25.56\)

• \(19\)

• \(20.7\)

• \(23\)

Solution