A sample of size [tex]$n=10$[/tex] is drawn from a population. The data is shown below:

[tex]
\[
\begin{array}{ccccc}
59.1 & 69 & 49 & 76.8 & 85.2 \\
85.2 & 61.9 & 69.4 & 85.2 & 56.1
\end{array}
\]
[/tex]

1. What is the range of this data set?
[tex]
\[
\text{range} = \square
\]
[/tex]

2. What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, reporting 2 more decimal places than the original data.

[tex]
\[
\text{stdev} = \square
\]
[/tex]

To find the range and standard deviation of the given data set, follow these steps:

1. Determine the Range:
- The range of a data set is found by subtracting the smallest value from the largest value in the set.
- For the given data:
- Identify the smallest value, which is 49.
- Identify the largest value, which is 85.2.
- Calculate the range: [tex]$ 85.2 - 49 = 36.2 $[/tex].
- So, the range of the data set is 36.2.

2. Calculate the Sample Standard Deviation:
- The standard deviation measures the amount of variation or dispersion in a data set.
- Since this is a sample, we use the formula for the sample standard deviation which accounts for one less degree of freedom.
- The standard deviation is calculated using the following steps (in practice, a calculator or software is typically used):
- Find the mean of the data set.
- Subtract the mean from each data value to find the deviations.
- Square each of these deviations.
- Find the average of these squared deviations by dividing by [tex]$ n-1 $[/tex] (where [tex]$ n $[/tex] is the number of data points, here [tex]$ n=10 $[/tex]).
- Take the square root of this average to get the sample standard deviation.

- For the given data set, the standard deviation is approximately 13.1588 when rounded to four decimal places.

Thus, the results are:
- Range: 36.2
- Standard deviation: 13.1588