Statistics Calculator — Mean, Median, Std Dev, Quartiles

The mean and the median hide different things

Take six salaries: 40,000 · 42,000 · 45,000 · 48,000 · 50,000 · 250,000. The mean is 79,167. The median is 46,500.

Note what the mean has done — it sits above five of the six actual salaries. A single large value has dragged it somewhere nobody in the dataset earns, which is exactly the failure mode people mean when they say averages mislead.

The rule that follows: for skewed data — income, house prices, response times, medical costs — the median describes a typical case and the mean does not. But the mean keeps a property the median lacks: mean × count = the total. If you need the payroll figure, the mean is the one that reconstructs it. Neither is better; they answer different questions.

This tool divides by n−1

For variance and standard deviation the calculator uses the sample formula, dividing by n−1 rather than n, and the interface says so.

The reason is worth understanding rather than memorising. A sample's own mean is computed from that sample, so it sits closer to those particular data points than the true population mean would. Measuring spread around a mean fitted to your own data therefore understates the real spread systematically — not randomly. Dividing by n−1 compensates for that bias.

The correction is substantial at small n and fades as the dataset grows, which is why it matters most in exactly the situations where people are hand-checking results. If your figures disagree with a textbook or another tool, check which formula it used before assuming an error — this is the most common cause of two correct calculations disagreeing.

Standard deviation assumes a shape

It describes spread well for roughly symmetric, single-peaked data and poorly for anything else. Two datasets can share a mean and a standard deviation while looking nothing alike — one clustered around the middle, the other piled at both ends with nothing between.

So treat summary statistics as a compressed description rather than a substitute for looking. A histogram of thirty numbers takes seconds and routinely reveals structure that no single statistic reports.

What the tool computes

Paste numbers separated by commas, spaces or newlines and it returns thirteen figures: count, sum, mean, median, mode (or none where nothing repeats), range, minimum, maximum, sample variance, sample standard deviation, Q1, Q3 and the interquartile range. Values show up to four decimal places with trailing zeros trimmed.

The interquartile range deserves a mention as the least-used useful statistic here: it is the spread of the middle half of the data, and unlike standard deviation it is barely affected by outliers — which makes it the natural companion to the median in exactly the skewed cases described above.

A mean without a sense of spread is close to useless, and a spread without a sense of sample size is worse. For deciding how much data a comparison actually needs, see the A/B test sample size calculator.