Understanding Standard Deviation
Standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
Sample vs. Population
Use the **Population** mode if your data represents the entire group you are studying. Use the **Sample** mode (most common in research) if your data is a subset of a larger population. The sample calculation uses **Bessel's correction** (dividing by $n-1$ instead of $n$) to provide an unbiased estimate.
The Formula
For a sample, the formula is: $s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$
Where $\bar{x}$ is the mean and $n$ is the number of data points.