To calculate the mean (average) of a set of numbers, follow these steps:

1. Add all the numbers together.
2. Divide the sum by the number of values.

Here are the steps for your data set:

Numbers: $5, 6, 9, 10, 3, 4, 7, 5, 6, 8$

Step 1: Add the numbers: $5 + 6 + 9 + 10 + 3 + 4 + 7 + 5 + 6 + 8 = 63$

Step 2: Count the number of values: There are 10 values.

Step 3: Divide the sum by the number of values: $\text{Mean} = \frac{63}{10} = 6.3$

So, the mean is $6.3$.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you calculate the median of this data set?
2. What is the mode of this data set?
3. How would you calculate the range of this data set?
4. Can you calculate the standard deviation for this data set?
5. What would the mean be if you added 2 to each number?

Tip: The mean gives a good overall measure, but it can be affected by very high or low values in the data set.