1. The problem is to understand what variance is in statistics. 2. Variance measures how much a set of numbers is spread out from their average (mean). 3. The formula for variance $\sigma^2$ of a population 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 data points, and $\mu$ is the mean. 4. For a sample variance $s^2$, the formula is: $$s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$$ where $n$ is the sample size, $x_i$ are the sample points, and $\bar{x}$ is the sample mean. 5. Variance tells us how data points differ from the mean; a higher variance means data is more spread out. 6. To calculate variance: - Find the mean. - Subtract the mean from each data point and square the result. - Sum all squared differences. - Divide by $N$ for population or $n-1$ for sample. 7. Variance is always non-negative because squared differences cannot be negative. This explanation covers the concept and calculation of variance.