Question

Sleep Variance The standard deviation of the sample values in Exercise 1 is 1.3 hours. What is the variance (including units)?

Short answer

The variance is 1.7 ${\text{hours}}^2$

Step-by-step solution

Given information

The sleep hours reported by the respondents are8, 7, 5, 7, 4, 7, 6, 7, 8, 8, 8, 6.

The standard deviation is 1.3 hours.

Relationship between standard deviation and variance

Variance is a measure of variation, which is the squared result of the standard deviation measure.

Mathematically, the relation can be expressed $\text{Var}\left(x\right)={s_x}^2$, for standard deviation s and sample outcomes.

Compute the variance from the standard deviation

Let x be the given set of observations (sleep hours).

Then the variance of x is

$$\begin{gathered} Var\left(X\right)={\left(1.3\right)}^2 \\ =1.69 \\ \approx 1.7 \end{gathered}$$

The unit of variance is squared times the unit of standard deviation.

Thus, the variance is 1.7 ${\text{hours}}^2$.