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).
### 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).