Statistics Calculator

One paste, seven answers

Most questions about a list of numbers reduce to a small family of statistics: the centre (mean and median), the spread (range and standard deviation) and the repeated values (mode). This page computes the whole family from data separated by commas, spaces or new lines. That puts it between two habits people already have — squinting at a list and hoping for the best, and opening a spreadsheet to build formulas cell by cell. You paste the values, press Calculate, and the panel reports the count, sum, median, mode, minimum, maximum, range and both standard deviations in one pass, in the same order every time, so repeat runs of the same data are trivially comparable.

Two readers get particular value. The first is building a report slide and needs a defensible spread figure, which is where the population-versus-sample choice earns its keep: the panel prints both, labelled, and you pick the one that matches your story. The second is investigating a data set with one suspicious value — a typo, a cancelled order, a genuinely unusual Saturday — and wants to see exactly how far that value drags the centre before deciding to trim it.

A worked example, step by step

Problem: a market stall recorded Saturday takings of 12, 15, 13, 11, 14 and 40 (the fair brought an exceptional crowd). What is the centre, and how much does the outlier move it?

1. Sort the list: 11, 12, 13, 14, 15, 40.
2. Sum: 105, so the mean is 105 ÷ 6 = 17.5.
3. Median: with an even count, average the 3rd and 4th sorted values — (13 + 14) ÷ 2 = 13.5.
4. Spread: the population standard deviation (dividing by 6) is about 10.14; the sample version (dividing by 5) is about 11.11.
5. Mode: no value repeats, so the tool reports "none (no repeated value)" — that is an answer, not a failure.
6. The outlier test: remove 40 and the mean of the remaining five values is 65 ÷ 5 = 13.0.

Read the last step honestly: the outlier moves the mean from 13 to 17.5 but leaves the median at either 13.5 or 13 by comparison. When a business question asks "what is a typical Saturday?", the median of 13.5 is the fairer headline; when the question is "what did we take?", the mean of 17.5 is still the correct total-based figure. The calculator gives both precisely so you never have to fake that distinction.

Three small sets and what they teach

The middle row is the same relation the market-stall example shows, compressed to its essentials: 38 is not "wrong", but every statistic inherited from it — mean, range and standard deviation — absorbs its weight. Whether that is distortion or information depends on the question, and the point of seeing both figures side by side is being able to argue the choice instead of guessing it.

The standard deviation choice, stated plainly

Population standard deviation divides the squared deviations by n and answers "the spread of exactly these values". Sample standard deviation divides by n − 1 and answers "the spread of the wider population this list is drawn from", inflating the figure slightly to pay for the uncertainty of not seeing everything. If your list is literally the whole group — the six Saturdays you actually had — quote the population figure (about 10.14 for the stall example). If the list is a sample of a bigger group you did not measure, quote the sample figure (about 11.11), which the tool only prints when there is more than one value. Quoting the sample number for a complete census overstates your honesty; quoting the population number for a sample understates your spread.

Mistakes that quietly skew a statistics readout

• Pasting thousands separators. "1,200" splits into two numbers, so count the reported values against what you pasted before reading anything else.
• Letting blank entries count. Empty strings are filtered, but stray characters make the tool reject the list — clean the paste and resend.
• Comparing means across different-sized lists. A mean of 6 values and a mean of 600 are different kinds of evidence; weight them accordingly.
• Quoting a median from a list with repeats in it wrong. The tool averages the two middle values for even counts; doing that by eye on a sorted list with duplicates is where copy mistakes happen.
• Reporting the sample figure for a census. If the list is not a sample, dividing by n − 1 is an unnecessary inflation that reviewers will catch.

Keep exploring

• Average Calculator — the mean alone, when the list is part of a running conversation.
• Percentage Change — percentage movement over time when the story is growth, not spread.
• What Percent Is X of Y? — shares of a whole, useful when the list describes parts of a budget.
• Guide: How to Calculate Percentages.