Question

I need help with the sample standard deviation and the sample variance

Answer 1

The sample standard deviation is 29.3

The sample variance is 859.2

Explanation:

We have the following data set:

`77,\:68,\:32,\:26,\:47,\:6,\:34,\:99,\:27,\:15,\:72`

To determine the sample standard deviation and the sample variance we must first calculate the mean of the data, like so:

`\begin{gathered} \bar{x}=(1)/(n)\sum_(i=1)^na_i\: \\ \\ n=11 \\ \\ \sum_(i=1)^na_i=77+68+32+26+47+6+34+99+27+15+72=503 \\ \\ \bar{x}=(1)/(11)(503) \\ \\ \bar{x}=45.7 \end{gathered}`

Now we proceed to calculate the sample standard deviation and the sample variance: