Thank you for visiting 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. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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).
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
