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.