To calculate the standard deviation of a data set, follow these steps:

Steps:

1. Find the mean (average) of the data.
2. Subtract the mean from each data point and square the result.
3. Find the average of these squared differences (this is called the variance).
4. Take the square root of the variance to get the standard deviation.

Now, let's calculate it step by step:

Data:

$76.1, 85.3, 87.3, 94.4, 96, 99.6, 107.1, 114.6, 114.6, 114.6$

Step 1: Calculate the mean

$\text{Mean} = \frac{76.1 + 85.3 + 87.3 + 94.4 + 96 + 99.6 + 107.1 + 114.6 + 114.6 + 114.6}{10}$

Let me compute that for you.The mean of the data set is approximately $98.96$.

Step 2: Subtract the mean from each data point and square the result

Now, we'll compute the squared differences for each value from the mean.

Let me do this next step for you.The squared differences from the mean for each data point are:

$[522.58, 186.60, 135.96, 20.79, 8.76, 0.41, 66.26, 244.61, 244.61, 244.61]$

Step 3: Calculate the variance

The variance is the average of these squared differences. Let's calculate that next.The variance of the data set is approximately $167.52$.

Step 4: Calculate the standard deviation

Finally, we'll take the square root of the variance to find the standard deviation. Let me compute that for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can take the square root of the variance $167.52$ to find the standard deviation:

$\text{Standard Deviation} = \sqrt{167.52} \approx 12.94$

If you have any questions or want more details, feel free to ask!

Here are 5 related questions for further practice:

1. How do you calculate variance from raw data?
2. What is the difference between population and sample standard deviation?
3. How does the standard deviation help in understanding data spread?
4. How would removing an outlier affect the standard deviation?
5. Can two data sets have the same mean but different standard deviations?

Tip: Always check if you're dealing with a sample or population, as it affects the divisor (n or n-1) in the variance formula.