How is standard deviation best defined?

Standard deviation is best defined as a measure of "typical" deviation from the mean because it quantifies how much individual data points vary or deviate from the average value of a dataset. It provides insight into the dispersion or spread of the data, indicating whether the data points tend to cluster closely around the mean or spread out over a wider range.

When analyzing data, understanding standard deviation is critical because a smaller standard deviation suggests that the data points are generally closer to the mean, while a larger standard deviation indicates greater variability. This characteristic makes it particularly useful in statistics, as it helps researchers and analysts understand the reliability of the mean as a representation of the data set.

In contrast, while total variance in data represents a measure of variability, it is the square of the standard deviation and does not give a direct interpretation of deviation from the mean. Data range refers merely to the difference between the maximum and minimum values in a dataset, which does not provide information about the distribution of the data itself. Lastly, median values relate to the middle point of a dataset but do not address variability or dispersion in the same systematic manner as standard deviation does.