Chapter 14.3, Problem 2CFU

To determine

To calculate: The variance of a set of data if we know the standard deviation.

Answer to Problem 2CFU

The variance is ${\sigma }^2.$

Explanation of Solution

Given information:

We know the standard deviation.

Formula used:

A measure of variability associated with the arithmetic mean is the standard deviation.

  $\sigma =\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(X_i-\overline{X}\right)}^2}}$

The variance is the mean of the squares of the deviations from $\overline{X}$ .

The standard deviation is the positive square root of the variance.

Calculation:

According to the question ,

The standard deviation is denoted as $\sigma$ and variance is denoted as ${\sigma }^2.$

By definition, we get

  $\text{Variance = }{\left(\text{Standard Deviation}\right)}^2$

Hence, the variance is ${\sigma }^2.$