For the data below, which represents a sample with n = 8, answer the questions. Round to 4 decimal places where possible.

x
27.7
10.9
18.9
18
11.7
27.2
10.3
4.8
Find the standard deviation 

To find the standard deviation of the given data set, we'll follow these steps:

1. **Calculate the mean** (\(\bar{x}\)):
   \[
   \bar{x} = \frac{\sum x}{n}
   \]
   where \(\sum x\) is the sum of all data points, and \(n\) is the sample size.

2. **Find the squared deviations** from the mean:
   \[
   (x_i - \bar{x})^2
   \]
   for each data point \(x_i\).

3. **Calculate the variance**:
   \[
   \text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n-1}
   \]
   Since this is a sample, we use \(n-1\) in the denominator for the sample variance.

4. **Find the standard deviation**:
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}}
   \]

Let's perform the calculations.The calculations are as follows:

1. **Mean** (\(\bar{x}\)): \(16.1875\)
2. **Variance**: \(68.1270\)
3. **Standard deviation**: \(8.2539\)

The standard deviation of the sample is approximately **8.2539**.

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. How do the mean and standard deviation help in understanding the data set?
2. What is the difference between population and sample standard deviation?
3. How does the standard deviation change if we add a new data point?
4. Why do we divide by \(n-1\) instead of \(n\) in the sample variance formula?
5. What does a higher standard deviation indicate in a data set?

**Tip:** The standard deviation measures how spread out the numbers are from the mean—larger values indicate more variability in the data.

For the data below, which represents a sample with n = 8, answer the questions. Round to 4 decimal places where possible.

x
27.7
10.9
18.9
18
11.7
27.2
10.3
4.8

Find the standard deviation.

Learn how to find the standard deviation for a sample of 8 data points: 27.7, 10.9, 18.9, 18, 11.7, 27.2, 10.3, and 4.8. This solution walks through calculating the mean, variance, and standard deviation, with all answers rounded to four decimal places. Suitable for high school students studying statistics.

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