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Calculate the sample standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given.

[tex]
\[
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{5}{|c|}{Body Temperatures (in ${ }^{\circ} F$) of Adult Males} \\
\hline
98.2 & 97.6 & 96.5 & 96.6 & 97.8 \\
\hline
98.7 & 98.3 & 99.3 & 98.2 & 98.0 \\
\hline
96.4 & 98.5 & 98.9 & 99.1 & 97.2 \\
\hline
97.3 & 99.0 & 96.6 & 98.5 & 96.5 \\
\hline
\end{tabular}
\]
[/tex]

Answer :

To find the sample standard deviation for the given data set of body temperatures, follow these steps:

1. List the Data:
The body temperatures are:
98.2, 97.6, 96.5, 96.6, 97.8, 98.7, 98.3, 99.3, 98.2, 98.0, 96.4, 98.5, 98.9, 99.1, 97.2, 97.3, 99.0, 96.6, 98.5, and 96.5.

2. Calculate the Mean (Average):
Add up all the temperatures and then divide by the number of temperatures (20 in this case).

Mean = (98.2 + 97.6 + 96.5 + 96.6 + 97.8 + 98.7 + 98.3 + 99.3 + 98.2 + 98.0 + 96.4 + 98.5 + 98.9 + 99.1 + 97.2 + 97.3 + 99.0 + 96.6 + 98.5 + 96.5) ÷ 20

The mean temperature is approximately 97.86°F.

3. Calculate Each Temperature's Deviation from the Mean:
For each temperature, subtract the mean and record the result.
For example, the first deviation is [tex]\(98.2 - 97.86\)[/tex].

4. Square Each Deviation:
After finding the deviation of each temperature from the mean, square each of those results.

5. Calculate the Variance:
To find the variance, sum up all the squared deviations and then divide by the number of temperatures minus one (n-1) since this is a sample.

Variance = (Sum of squared deviations) ÷ (20 - 1)

6. Calculate the Standard Deviation:
The standard deviation is the square root of the variance. This gives you the sample standard deviation.

The sample standard deviation for this data set is approximately 0.97°F.

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