One calculator for the whole descriptive toolkit
Descriptive statistics is the art of summarising a dataset honestly: where is its centre, how wide is its spread, what shape does it take? This calculator computes the standard summary in one pass: count, sum, mean, median, mode, range, quartiles, IQR, variance, standard deviation and standard error, from a single paste of your data.
The three questions every summary must answer
Location. Mean or median: where does the dataset live? Spread. Standard deviation or IQR: how much do values disagree with each other? Shape. Comparing mean with median (and, in fuller analyses, skewness) tells you whether the data leans left, leans right, or stands symmetric.
A summary that answers all three questions can be trusted. One that reports a lone mean (no spread, no shape) is hiding most of the story, which is exactly why this tool refuses to calculate one without the others.
Nine innings: 45, 12, 78, 33, 45, 0, 56, 45, 21 summarise to: mean ≈ 37.2, median 45, mode 45, range 78, standard deviation ≈ 22.9. Location says "mid-40s on a typical day", spread says "but hold on, the typical deviation is huge", shape says "the mean sits below the median, dragged down by the failures". Three numbers deep and you already understand this batsman better than a season's worth of single averages.
Descriptive vs inferential statistics
Everything on this page is descriptive: it describes the data you have. Inferential statistics (confidence intervals, hypothesis tests, p-values) goes further and reasons about data you don't have, using a sample to make claims about a population. The descriptive summary always comes first; no test result means anything until you know your data's centre, spread and shape.
Frequently asked questions
What does descriptive statistics include?
Measures of location (mean, median, mode), spread (range, IQR, variance, standard deviation) and shape (skewness), plus summaries like quartiles and the five-number summary.
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarises the data you collected. Inferential statistics uses a sample to draw conclusions about a larger population, with confidence intervals and hypothesis tests.
Which measures should I report together?
At minimum a location and a spread: mean with standard deviation for symmetric data, or median with IQR for skewed data.