What can a standard deviation tell us about the usefulness of the mean?

Standard deviation measures the dispersion or variability of data points around the mean. A low standard deviation indicates that the data points are closely clustered around the mean, suggesting that the mean is a reliable representation of the dataset. Conversely, a high standard deviation signifies greater variability, which may diminish the mean’s usefulness as a summary statistic, as it may not accurately reflect the data's central tendency. Thus, understanding standard deviation helps assess how well the mean represents the underlying data.