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Answer :
To calculate the sample standard deviation for the given data set of body temperatures, follow these steps:
1. List the Data Set:
The body temperatures are as follows:
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.
2. Calculate the Mean:
To find the mean, add all the temperatures together and divide by the number of values.
[tex]\[
\text{Mean} = \frac{98.1 + 98.0 + 98.4 + \ldots + 97.7}{20} = 97.785
\][/tex]
3. Calculate Each Deviation:
Subtract the mean from each data point to find the deviation of each.
4. Square Each Deviation:
After finding each deviation, square these values.
5. Calculate the Variance:
Add up all the squared deviations and divide by the number of data points minus one (because it's a sample, not a population):
[tex]\[
\text{Variance} = \frac{\sum (\text{Each value} - \text{Mean})^2}{n - 1} = 0.6403
\][/tex]
6. Calculate the Standard Deviation:
The sample standard deviation is the square root of the variance:
[tex]\[
\text{Standard Deviation} = \sqrt{0.6403} \approx 0.800
\][/tex]
Therefore, the sample standard deviation for the body temperatures is approximately 0.800.
1. List the Data Set:
The body temperatures are as follows:
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.
2. Calculate the Mean:
To find the mean, add all the temperatures together and divide by the number of values.
[tex]\[
\text{Mean} = \frac{98.1 + 98.0 + 98.4 + \ldots + 97.7}{20} = 97.785
\][/tex]
3. Calculate Each Deviation:
Subtract the mean from each data point to find the deviation of each.
4. Square Each Deviation:
After finding each deviation, square these values.
5. Calculate the Variance:
Add up all the squared deviations and divide by the number of data points minus one (because it's a sample, not a population):
[tex]\[
\text{Variance} = \frac{\sum (\text{Each value} - \text{Mean})^2}{n - 1} = 0.6403
\][/tex]
6. Calculate the Standard Deviation:
The sample standard deviation is the square root of the variance:
[tex]\[
\text{Standard Deviation} = \sqrt{0.6403} \approx 0.800
\][/tex]
Therefore, the sample standard deviation for the body temperatures is approximately 0.800.
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
