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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.
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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