"Average" is ambiguous, and choosing the wrong one distorts the story. The mean is pulled around by outliers, the median describes the typical middle case, and the mode finds the most common value. Paste your numbers once and this tool reports all of them, plus range and standard deviation.
Whenever the data is skewed or has extreme outliers. Household income is the classic example: a handful of very high earners lifts the mean well above what a typical household actually receives.
Yes. If two or more values tie for the highest frequency the data is bimodal or multimodal, and the tool lists each of them.
Population standard deviation, dividing by n. If you are working with a sample and need the unbiased estimate, use n − 1 instead.
Just the distance between the smallest and largest value. It is simple but fragile — one extreme reading can make the range enormous while most of the data sits tightly together.
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