Find the sample standard deviation (round to 3 decimal places):  180.34, 172.72, 175.26, 190.5, 187.96, 175.26, 170.18, 185.42

To find the sample standard deviation, follow these steps:

1. **Find the mean**:
   \[
   \text{Mean} = \frac{\sum X}{n}
   \]
   where \(X\) is the sum of the data values, and \(n\) is the number of data points.

2. **Calculate each deviation from the mean** (i.e., \( x_i - \text{Mean} \)), then square the result.

3. **Find the sum of squared deviations**.

4. **Divide by \(n-1\)** to account for the sample standard deviation (where \(n\) is the number of data points).

5. **Take the square root** of the result to find the standard deviation.

Let's compute it.

The data set is:
\[
180.34, 172.72, 175.26, 190.5, 187.96, 175.26, 170.18, 185.42
\]

I'll now calculate.The sample standard deviation is approximately \( 7.529 \) (rounded to three decimal places).

Would you like more details on this calculation, or do you have any other questions?

Here are 5 related questions to explore further:
1. What is the difference between sample and population standard deviation?
2. How do you calculate the variance from a data set?
3. What is the significance of using \(n-1\) for sample standard deviation?
4. Can the standard deviation ever be negative?
5. How does standard deviation relate to the normal distribution?

**Tip**: Always use the sample standard deviation formula for small data sets or when you have a sample, not the entire population.

Find the sample standard deviation (round to 3 decimal places): 180.34, 172.72, 175.26, 190.5, 187.96, 175.26, 170.18, 185.42

Learn how to calculate the sample standard deviation for the data set: 180.34, 172.72, 175.26, 190.5, 187.96, 175.26, 170.18, 185.42. This problem demonstrates key statistical concepts such as finding the mean and applying the standard deviation formula. Suitable for students in Grades 10-12.

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