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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.
Thank you for reading the article 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. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
