Which statement best describes standard deviation?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a dataset. When we refer to standard deviation, we are highlighting how much individual data points differ from the mean (average) of the dataset. A high standard deviation indicates that the data points are spread out over a wider range of values, whereas a low standard deviation suggests that the data points are closer to the mean.

In the context of explaining variance, standard deviation is effectively the square root of variance. Variance itself measures the average squared deviations from the mean, and standard deviation provides a more interpretable value by bringing the units back to the original scale of the data.

The other options mention concepts that do not accurately represent what standard deviation measures. For instance, measurement of central tendency focuses on averages (mean, median, mode) rather than variability. Calculating the average of a set of numbers is a different concept altogether. The shape of a distribution typically relates to measures such as skewness and kurtosis, not to standard deviation specifically. Understanding standard deviation is crucial for grasping how data points relate to each other in terms of variability, making option B the most accurate choice.