76.2
71
62.5
71.5
77.6
91.6
78.8
78
83.3
69.4
92.2
78.3
75.7 find the standard deviation

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.

76.2 71 62.5 71.5 77.6 91.6 78.8 78 83.3 69.4 92.2 78.3 75.7 find the standard deviation

Learn how to calculate the standard deviation for the data set {76.2, 71, 62.5, 71.5, 77.6, 91.6, 78.8, 78, 83.3, 69.4, 92.2, 78.3, 75.7}. This solution covers key statistical concepts such as mean, variance, and standard deviation, making it suitable for students in Grades 9-12.

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