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

1. Find the mean (average) of the data set.
2. Subtract the mean from each number and square the result.
3. Find the average of those squared differences.
4. Take the square root of that average.

Let's calculate:

Step 1: Find the mean

The data set is:
76.2, 71, 62.5, 71.5, 77.6, 91.6, 78.8, 78, 83.3, 69.4, 92.2, 78.3, 75.7

To find the mean: $\text{mean} = \frac{76.2 + 71 + 62.5 + 71.5 + 77.6 + 91.6 + 78.8 + 78 + 83.3 + 69.4 + 92.2 + 78.3 + 75.7}{13}$

Step 2: Subtract the mean and square the differences.

I'll calculate that for you.The mean of the data set is approximately $77.39$.

The standard deviation is approximately $7.97$.

Would you like further details or clarifications?

Here are 5 related questions you might explore:

1. What is the variance of this data set?
2. How does standard deviation differ from variance?
3. Can you calculate the z-scores for each data point?
4. What does the standard deviation tell us about the data spread?
5. How would the standard deviation change if we added or removed a data point?

Tip: A small standard deviation means the data points are close to the mean, while a large one indicates they are spread out.