What does the sample standard deviation measure?

The sample standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of sample values relative to their sample mean. Specifically, it provides insight into how much the individual data points deviate from the average value of the sample. A higher standard deviation indicates that the data points are more spread out from the mean, while a lower standard deviation suggests that they are closer to the mean.

This measure is essential in statistics as it helps assess the consistency and reliability of data. For instance, in quality control or experiment analysis, knowing the variability of a set of measurements can inform decision-making and improve processes. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

Other options, such as the average of sample values, total count of sample observations, and the difference between population and sample, do not accurately describe what the sample standard deviation measures. Each of these options relates to distinct statistical concepts that do not pertain specifically to the dispersion of values around an average.