To calculate the sample variance for the given data set, follow these steps:

**Data set**: 11, 3, 2, 12, 6, 14

### Step 1: Find the mean (average)

\[
\text{Mean} = \frac{11 + 3 + 2 + 12 + 6 + 14}{6} = \frac{48}{6} = 8
\]

### Step 2: Calculate the squared deviations from the mean

For each data point, subtract the mean and square the result:
\[
(11 - 8)^2 = 9, \quad (3 - 8)^2 = 25, \quad (2 - 8)^2 = 36
\]
\[
(12 - 8)^2 = 16, \quad (6 - 8)^2 = 4, \quad (14 - 8)^2 = 36
\]

### Step 3: Sum the squared deviations

\[
9 + 25 + 36 + 16 + 4 + 36 = 126
\]

### Step 4: Divide by \(n - 1\) (since this is a sample, not a population)

\[
\text{Sample variance} = \frac{126}{6 - 1} = \frac{126}{5} = 25.2
\]

So, the sample variance is **25.2**.

Would you like more details or clarification on any step?

Here are 5 related questions for further exploration:
1. How do you compute the population variance, and how does it differ from sample variance?
2. What are the units of variance, and how is it interpreted?
3. How do you calculate the standard deviation from the variance?
4. What is the significance of using \(n - 1\) for sample variance instead of \(n\)?
5. Can variance be negative, and why or why not?

**Tip**: Variance measures the spread of data. A higher variance indicates data points are spread out more from the mean.

Learn how to calculate the sample variance for the data set {11, 3, 2, 12, 6, 14}. This problem covers core statistical concepts, including mean, squared deviations, and the sample variance formula. Suitable for students in Grades 9-12.

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