Paste any list of numbers — marks, measurements, survey responses — and this calculator returns the full set of descriptive statistics at once: mean, median, mode, range, and both forms of standard deviation.
It shows sample and population standard deviation separately, because choosing the wrong one is one of the most common errors in student results chapters and the two can differ noticeably in small samples.
The mean is the arithmetic average and uses every value, which makes it sensitive to extremes: one very high mark pulls it upward. The median is the middle value once sorted, and is barely affected by outliers — which is why income is almost always reported as a median.
The mode is the most frequent value, and it is the only one of the three that works for categories rather than numbers. Where a distribution is skewed, reporting the mean alone can be actively misleading; reporting mean and median together tells the reader how skewed it is.
If no value repeats, the set has no mode. This tool says so rather than listing every value, because "every value is a mode" is not a useful statement and is not how the term is normally used.
Where several values tie for the highest frequency, all of them are modes and the set is bimodal or multimodal. That is worth noticing rather than glossing over: two clear peaks often means you have two distinct groups mixed together in one dataset.
Population standard deviation divides by n and is correct only when your data covers every member of the group you are describing — every student in one class, if the class is the whole population of interest.
Sample standard deviation divides by n−1 and is correct when your numbers are a sample from a larger group you want to say something about. That is almost always the situation in student research, so the sample figure is the default you should report. Dividing by n−1 corrects a bias that would otherwise make a sample look less variable than the population it came from.
The range is the highest value minus the lowest. It is simple and easily distorted — a single unusual value changes it completely — so it describes the extremes rather than the typical spread.
Standard deviation is the better measure of spread because it accounts for every value. Roughly, a standard deviation of 2 on a mean of 10 means most values sit between 8 and 12. Reporting a mean without a measure of spread tells a reader very little: identical means can hide entirely different distributions.
The mean is the arithmetic average, the median is the middle value once sorted, and the mode is the most frequent value. The median resists outliers; the mean does not.
Sample (n−1) in almost all student work, because your numbers are a sample from a larger group. Use population (n) only when you have measured everyone in the group you are describing.
Then the set has no mode. That is a genuine result rather than an error, and it is not the case that every value counts as a mode.
Yes. Commas, spaces, tabs and new lines all work, and anything that is not a number is ignored and counted for you.
Comparing them reveals skew. When they differ noticeably, the distribution is lopsided and the mean alone would misrepresent it.