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To find the sample standard deviation, let's go through the calculation step-by-step.

### Given Data:
Fuel efficiency values (mpg):  
\( 22, 24, 24, 26, 14, 23, 23, 31, 23, 21, 25, 21 \)

### Steps:

1. **Calculate the Mean (already given as 23.08)**:  
   \[
   \text{Mean} = 23.08
   \]

2. **Find the Deviations**:  
   Subtract the mean from each data point to find the deviations.

3. **Square Each Deviation** and Sum the Results:
   
   \[
   \sum (x - \text{mean})^2
   \]

4. **Calculate the Sample Variance**:  
   Divide by \( n - 1 \), where \( n = 12 \) (the sample size).
   \[
   \text{Variance} = \frac{\sum (x - \text{mean})^2}{n - 1}
   \]

5. **Take the Square Root of the Variance** to get the standard deviation.

Let me calculate this value.The mean of the fuel efficiency data is \( 23.08 \), which matches the given value. The sample standard deviation, rounded to the nearest hundredth, is \( 3.92 \).

Would you like more details on the calculations or have any questions?

### Further Related Questions
1. What is the difference between sample and population standard deviation?
2. How would the standard deviation change if one of the fuel efficiency values was significantly higher?
3. What other statistical measures can describe the spread of this data set?
4. How can we interpret the standard deviation in the context of fuel efficiency?
5. What does a low versus high standard deviation imply in fuel efficiency studies?

**Tip:** The sample standard deviation uses \( n-1 \) in the denominator to account for the sample's variability and make it an unbiased estimator of the population standard deviation.

Find the mean and sample standard deviation of the fuel efficiency data set [22, 24, 24, 26, 14, 23, 23, 31, 23, 21, 25, 21]. Round to the nearest hundredth.

Learn how to calculate the mean and sample standard deviation of a fuel efficiency data set [22, 24, 24, 26, 14, 23, 23, 31, 23, 21, 25, 21] with a detailed step-by-step solution. This guide covers statistical concepts like mean and sample standard deviation, suitable for high school students in Grades 10-12.

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