# What is the sample mean for the data?

## Attached screenshot: http://prntscr.com/jl73nw

May 23, 2018

The sample mean of the last 10 data points is $\overline{x} = 8.4$.

#### Explanation:

It is unclear from the wording of the question, but since the second data set contains only 10 data points out of a possible 24, I am assuming these 10 members is what we're calling our "sample".

Under this assumption, the sample mean for these 10 data is

$\overline{x} = \frac{8 + 8 + 8.5 + 8 + 9 + 8 + 9 + 9 + 8.5 + 8}{10}$
$\textcolor{w h i t e}{\overline{x}} = \frac{84}{10}$

$\textcolor{w h i t e}{\overline{x}} = 8.4$

### Note:

While these 10 members are a sample from a population, they are not a sample from the first set of 24 data points. This is because the second set of measurements was taken on a different night, and so the hours of sleep for each member might have changed.

If we treat the $24 + 10 = 34$ data points as a sample from a worldwide population of "hours of sleep the night before a musical", then we'd get a sample mean of

$\overline{x} = \frac{8 + 8.5 + 8 + 7.5 + \ldots + 9 + 8.5 + 8}{34}$
$\textcolor{w h i t e}{\overline{x}} = \frac{275.5}{34}$

$\textcolor{w h i t e}{\overline{x}} \approx 8.10$

It all depends on which population we're trying to estimate the mean from.