1. The problem is to understand what variance means in statistics. 2. Variance measures how spread out a set of numbers is around the mean (average). 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 and $\bar{x}$ is the sample mean. 5. Variance tells us the average squared distance of each data point from the mean. 6. A small variance means data points are close to the mean; a large variance means they are spread out. 7. Variance is always non-negative because squared differences cannot be negative. 8. Understanding variance helps in statistics to measure data variability and risk in fields like finance and science.