1. The problem is to understand what the standard deviation is. 2. Standard deviation is a measure of how spread out numbers are in a data set. 3. The formula for the standard deviation $\sigma$ of a population is: $$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2}$$ where $N$ is the number of data points, $x_i$ are the data points, and $\mu$ is the mean (average) of the data. 4. For a sample standard deviation $s$, the formula is: $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ where $n$ is the sample size, $x_i$ are the sample data points, and $\bar{x}$ is the sample mean. 5. The standard deviation tells us how much the data varies from the mean: a small standard deviation means data points are close to the mean, a large one means they are spread out. 6. To calculate it, first find the mean, then subtract the mean from each data point and square the result, find the average of these squared differences, and finally take the square root.