The square of the standard deviation is called the variance. The standard deviation measures the spread or dispersion of a set of data points around the mean, while the variance quantifies the same concept but on a squared scale. Mathematically, the variance is the average of the squared differences from the mean.

If $\sigma$ is the standard deviation, then the variance $\sigma^2$ is:

$\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2$

Where:

• $n$ is the number of data points,
• $x_i$ are the individual data points,
• $\mu$ is the mean of the data points.

So, the square of the standard deviation is simply the variance of the dataset.

Would you like more details or clarification on this concept?

Here are 5 related questions to explore this concept further:

1. What is the relationship between variance and standard deviation?
2. How is the variance calculated in a sample versus a population?
3. Why do we square the differences when calculating variance?
4. How does the variance change when data is more spread out?
5. Can standard deviation or variance ever be negative?

Tip: The variance amplifies outliers because squaring large deviations increases their effect.