Question

Sleep Notation Consider a sample of sleep times taken from the population of all adults living in Alaska. Identify the symbols used for the sample mean, population mean, sample standard deviation, population standard deviation, sample variance, and the population variance.

Short answer

The symbols used are

$\overline{x},\mu$: for sample and population mean, respectively,

$s,\sigma$: for sample and population standard deviation, respectively, and

$s^2,{\sigma }^2$: for sample and population variance, respectively.

Step-by-step solution

Given information

The sampled values are sleep times from all adults that live in Alaska.

Determine the symbols used for each measure

For any set of observations x, the following symbols are used:

Sample mean uses the symbol $\overline{x}$, which is read as x-bar.

Population mean uses the symbol $\mu$, which is read as mu.

Sample standard deviation uses the symbol $s$.

Population standard deviation uses the symbol $\sigma$, which is read as sigma.

Since variance is the square of the standard deviation measure, the following notations are implied.

Sample variance uses the symbol $s^2$. And population variance uses the symbol ${\sigma }^2$, which is read as sigma square.