1. The problem is to understand and calculate the standard deviation of a data set. 2. Standard deviation measures how spread out numbers are from the mean (average). 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. 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 points, and $\bar{x}$ is the sample mean. 5. Steps to calculate: - Find the mean $\mu$ or $\bar{x}$. - Subtract the mean from each data point to find deviations. - Square each deviation. - Sum all squared deviations. - Divide by $N$ (population) or $n-1$ (sample). - Take the square root of the result. 6. This gives a measure of spread; a small standard deviation means data points are close to the mean, large means more spread out. This explanation covers the concept and formulas for standard deviation.