To calculate the sample variance, we follow these steps:

Step 1: Calculate the mean of the sample

The data set is:
$-13, 9, 9, -13, 5, -13, 9$

The formula for the mean $\bar{x}$ is: $\bar{x} = \frac{\sum x_i}{n}$ where $x_i$ represents each data point and $n$ is the number of data points.

$\bar{x} = \frac{-13 + 9 + 9 + (-13) + 5 + (-13) + 9}{7}$

Step 2: Calculate the squared differences from the mean

For each data point, subtract the mean and square the result.

Step 3: Compute the sample variance

The formula for sample variance $s^2$ is: $s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$ Let me calculate this.The value of the sample variance is $128.0$, rounded to one decimal place.

Do you want more details or have any questions?

Here are 5 related questions you might find useful:

1. How do you calculate the standard deviation from variance?
2. What is the difference between sample variance and population variance?
3. Why do we divide by $n - 1$ for sample variance instead of $n$?
4. Can the sample variance ever be negative?
5. How does the sample variance change if all data points increase by a constant value?

Tip: The square root of the variance gives the standard deviation, which is a measure of how spread out the numbers are in the sample.