Question

For the following set of data, find the number of data within 1 population standard deviation of the mean.52, 60, 60, 59, 52, 65, 57, 55

Answer 1

For this problem, we are given a certain a data set and we need to find the number of data within 1 population standard deviation of the mean.

The data set is:

$52,60,60,59,52,65,57,55$

The first step we need to take is to reorder the data set.

$52,52,55,57,59,60,60,65$

Now we need to determine the mean:

$\mu=\frac{52+52+55+57+59+60+60+65}{8}=\frac{460}{8}=57.5$

Finally, we have to find the standard deviation:

$\begin{gathered} \sigma=\sqrt{\frac{(52-57.5)^2+(52-57.5)^2+(55-57.5)^2+(57-57.5)^2+(59-57.5)^2+(60-57.5)^2+(60-57.5)^2+(65-57.5)^2}{8}}\\ \\ \sigma=\sqrt{\frac{138}{8}}=\sqrt{17.25}=4.15 \end{gathered}$

Now we need to find the range within 1 standard deviation from the mean:

$\begin{gathered} [57.5-4.15,57.5+4.15\rbrack\\ \\ \lbrack53.35,61.65\rbrack \end{gathered}$

The range of values within one standard deviation goes from 53.35 to 61.65. Therefore there are a total of 5 values within this range.