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The problem is asking for the variance of the given data set, which represents the ages of five children: 8, 9, 10, 11, and 12. It also provides the mean (average) of these ages, which is 10. 

To calculate the variance, we use the following formula:

\[
\text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n}
\]

Where:
- \(x_i\) are the data points,
- \(\bar{x}\) is the mean,
- \(n\) is the number of data points.

### Step-by-step Calculation:

1. **Data points (ages):** 8, 9, 10, 11, 12
2. **Mean (\(\bar{x}\)):** 10
3. **Calculate the squared differences from the mean:**

\[
(8 - 10)^2 = (-2)^2 = 4
\]
\[
(9 - 10)^2 = (-1)^2 = 1
\]
\[
(10 - 10)^2 = (0)^2 = 0
\]
\[
(11 - 10)^2 = (1)^2 = 1
\]
\[
(12 - 10)^2 = (2)^2 = 4
\]

4. **Sum of squared differences:**

\[
4 + 1 + 0 + 1 + 4 = 10
\]

5. **Calculate the variance:**

\[
\text{Variance} = \frac{10}{5} = 2
\]

### Answer:
The variance of the ages of the five children is **2**.

Would you like more details on variance or any other questions related to this topic?

### Related Questions:
1. What is the standard deviation of these data points?
2. How do we calculate variance for a different set of data?
3. What is the difference between variance and standard deviation?
4. How does changing one data point affect the variance?
5. How can variance be used in real-world applications?

### Tip:
Remember that variance gives us an idea of how spread out a set of data is around the mean. A small variance indicates that the data points are close to the mean, while a large variance indicates that they are spread out over a wider range of values.

Los siguientes datos representan las edades de cinco niños: 8, 9, 10, 11 y 12. Si la media es 10, ¿cuál es la varianza de estos datos?

Learn how to calculate the variance of a data set representing the ages of five children: 8, 9, 10, 11, and 12. The mean of the data is 10, and the variance calculation involves finding the squared differences from the mean. Suitable for students in Grades 6-8.

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