Average Calculator

What this tool is used for

• Getting mean, median, mode and range together so you can see which describes the data.
• Spotting that a mean and median disagree, which is the first sign of skew.
• Summarising a short set of measurements without a spreadsheet.
• Finding whether a dataset has a mode at all, or several.
• Checking a summary figure quoted in a report against the raw numbers.

Frequently Asked Questions

Which average should I use?

The mean when the data is roughly symmetric, the median when it is skewed or has outliers, and the mode when the values are categories rather than magnitudes. On the sample list 12, 7, 9, 12, 21, 7, 12, 3 the mean is 10.375 and the median is 10.5 — close, because nothing in it is extreme.

Why is no mode reported for some lists?

Because when every value appears exactly once, no value is more frequent than the others, so a mode would be an arbitrary pick. The tool leaves it blank in that case and lists ALL tied values when several share the top frequency — a set can genuinely be bimodal, and collapsing that to one number hides the shape.

How are the quartiles defined?

By the exclusive method: sort, split at the median, and take the median of each half — excluding the median itself when the count is odd. This is Tukey's hinge convention. Tools using an inclusive rule report slightly different Q1 and Q3 on the same data — a definitional difference, not a bug.

What does the box plot actually show?

The five-number summary: minimum, Q1, median, Q3 and maximum. The box spans the interquartile range — the middle half of the data — so its width is a measure of spread that ignores extremes entirely, and a median sitting off-centre inside the box is a direct visual reading of skew.

Which standard deviation does it show?

Both. The population version divides by n and is right when your list IS the whole group; the sample version divides by n−1 (Bessel's correction) and is right when the list is a sample of something larger. The correction matters most on small lists — with 5 values the sample figure is about 12% higher.

Common errors and gotchas

• Quoting the mean for skewed data, where a single large value drags it away from anything typical.
• Assuming there is one mode, when a set can have none or many.
• Treating the range as a measure of spread, when two outliers determine it entirely.
• Averaging values that already are averages, without weighting by how many each covered.
• Including a placeholder value such as zero or 999, which silently distorts every statistic.