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Three different numbers are called “the average”, and the gap between them is the information.
The mean is the total over the count. The median is the middle value once sorted. The mode is whichever occurs most often.
On Philippine salary data the mean sits well above the median, because a handful of very large values drag it up. Quote the mean alone and you have described a country almost nobody lives in. So the median is the figure at the top here, with the mean immediately beside it so the gap is visible.
There is a second choice that changes the answer: sample or population. Dividing by n describes exactly the numbers in front of you. Dividing by n − 1 estimates the spread of a wider population you sampled. On five values that is a 12% difference. Most calculators pick one without saying. This one asks, and labels the answer.
All three are, which is why all three are shown. The mean is the total divided by the count. The median is the middle value once they are sorted. The mode is whichever value occurs most often. On a tidy, symmetric set they land close together; when they do not, the gap is the interesting part.
Because on the kind of data people paste — salaries, prices, response times — a few very large values pull the mean upward and it stops describing anybody. Average salary figures are the standard example: the mean can sit above what three quarters of people earn. The mean is shown right beside the median so you can see the gap rather than have it hidden by a choice somebody else made.
Sample if these numbers are a subset of a larger group you are drawing conclusions about; population if they are the entire set you care about. It genuinely changes the answer: sample variance divides by n − 1 (Bessel's correction) and population divides by n, which on a handful of values differs by ten per cent or more. Most calculators pick one without telling you. This one asks, defaults to sample, and labels the result.
Because every value appeared exactly once. Listing all of them as modes would be technically defensible and practically useless. Equally, a set can have two modes — this reports both rather than picking one, because "the mode" as a single figure forces a wrong answer whenever there is a tie.
A value more than 1.5 times the interquartile range beyond the first or third quartile — the usual rule of thumb, and the same one that draws the whiskers on a box plot. It is a prompt to look at those values, not a licence to delete them. Quartiles use the R type-7 definition, which is what Excel's QUARTILE and NumPy's default both use; there are several accepted methods and they disagree on small sets, so it matters which one is named.
No, only the mean. A weighted median does exist, but it is a different and less standardised measure, and returning one under the label "median" would mislead more than it helped. The page says so whenever weights are in use.
Runs entirely in your browser; nothing is transmitted. Standard deviation defaults to the sample formula (dividing by n − 1) and the page says which one it used. Quartiles use the R type-7 definition, as Excel and NumPy do. Nothing you type here is sent to our servers — the calculation runs entirely in your browser.
