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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 in the data.

[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
\multicolumn{5}{|c|}{\text{Body Temperatures (in °F)}} \\
\hline
98.1 & 98.0 & 98.4 & 97.2 & 99.2 \\
\hline
97.7 & 98.2 & 96.5 & 97.1 & 97.9 \\
\hline
96.6 & 97.8 & 97.8 & 99.2 & 97.0 \\
\hline
97.9 & 97.1 & 99.2 & 97.1 & 97.7 \\
\hline
\end{array}
\][/tex]

Answer :

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

### Step 1: List the Data
Here are the body temperatures provided:
- 98.1, 98.0, 98.4, 97.2, 99.2
- 97.7, 98.2, 96.5, 97.1, 97.9
- 96.6, 97.8, 97.8, 99.2, 97.0
- 97.9, 97.1, 99.2, 97.1, 97.7

### Step 2: Calculate the Mean
Add all the temperatures together and divide by the number of temperatures to find the mean.

[tex]\[
\text{Mean} = \frac{(98.1 + 98.0 + \ldots + 97.7)}{20} = 97.785
\][/tex]

### Step 3: Calculate the Deviations
Subtract the mean from each individual temperature to find the deviations.

[tex]\[
\text{Deviations: } (98.1 - 97.785), (98.0 - 97.785), \ldots, (97.7 - 97.785)
\][/tex]

### Step 4: Square the Deviations
Square each of the deviations obtained in the previous step.

### Step 5: Calculate the Sample Variance
Sum all the squared deviations and divide by the number of temperatures minus one (which is 20 - 1 = 19) to get the sample variance.

[tex]\[
\text{Sample Variance} = \frac{\sum (\text{Squared Deviations})}{19} = 0.6403
\][/tex]

### Step 6: Calculate the Sample Standard Deviation
Take the square root of the sample variance to find the sample standard deviation.

[tex]\[
\text{Sample Standard Deviation} = \sqrt{0.6403} = 0.8
\][/tex]

### Conclusion
Therefore, the sample standard deviation of the body temperatures is approximately 0.8 (rounded to one decimal place).

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