Average calculator
The set above averages 5, and its median is 4.5, and its mode is 4. All three are correct answers to "the average". The mean is pulled by extreme values, the median is not, and the mode is the only one that works on things you cannot add up.
The mean is the sum of the values divided by how many there are. The median is the middle value once they are sorted, or the midpoint of the two middle values in an even-length list. The mode is whichever value appears most often, and this page shows a dash for it when no value in the list repeats.
How to use it
Two standard deviations are reported because they answer different questions. The sample figure divides by one less than the count and belongs on numbers that are a sample of something larger; the population figure divides by the count itself and is right only when you have measured every case there is. The gap between them is the square root of n over n minus one, so it closes as the list grows. On the eight numbers this page opens with, the sample deviation of 2.1381 sits 6.9 per cent above the population figure of 2. At fifty values the gap is 1 per cent, and at five hundred it is a tenth of that. On a short list the choice moves the number far enough to change what you would conclude from it.
The input box is blunt about what counts as a separator, and it is the one thing to watch. Spaces, tabs, newlines, semicolons and commas all split values, so a comma is never read as a decimal mark and never as a thousands separator. Paste 1,200 1,300 and you get four numbers rather than two, and a mean of 125.5 rather than 1250. The count field is the check: if it disagrees with how many values you thought you pasted, the separators are the reason. Text that is not a number at all is dropped rather than rejected, so a column carrying n/a loses those rows quietly; a unit or a currency symbol stuck to a number is stripped and the number kept, so 12kg reads as 12 and $5.50 as 5.5. A time does not survive that treatment: 12:30 reads as 1230, and a date reads as its year.
Which average to quote is a judgement the arithmetic cannot make for you. The mean uses every value and is the only one of the three you can add up or scale, so almost every further statistic is built on it. The median cares only where the middle sits and not how far away the extremes are, so one wild reading leaves it untouched. The mode is the only one that means anything for values you cannot do arithmetic on at all: shoe sizes, survey answers, the most common colour in a column.
What people use it for
- Getting a class or exam average out of a pasted mark list
- Deciding whether the mean or the median describes a skewed set better
- Checking a figure quoted as “the average” against the other two
- Finding the middle value of an even-length list without sorting it by hand
- Reading the most common answer out of a column of survey responses
- Seeing how far a set of repeated measurements actually spreads
Questions
One large value drags the mean up and leaves the median where it was. Incomes are the classic case, and median income is the figure normally quoted for exactly that reason.
Yes. Every value tied for the highest frequency is listed, so 1 1 2 2 3 comes back as 1, 2.
Only when no value repeats at all. A list where every value happens to appear twice is not treated as having no mode: 1 1 2 2 3 3 reports 1, 2, 3, because all three are tied at the top.
Both, and scientific notation as well: 1e3 reads as 1000. Write one and a half as 1.5, because a comma is a separator here.
A comma inside a number split it. 1,200 becomes 1 and 200. Strip the thousands separators before pasting, or export the column without them.
Yes. A copied column arrives as one number per line, and newlines are separators, so it works untouched.
It is dropped and the rest is used. A row reading n/a or blank simply does not count, and the count field shows how many values actually made it through.
No. Anything that is not a digit, a decimal point, a sign or an exponent marker is stripped off, so 12kg reads as 12 and $5.50 as 5.5.
Not reliably. 12:30 has its colon stripped and reads as 1230, and 2026-09-07 reads as 2026. Convert times to minutes first and average those.
The sample one, unless your numbers are the entire population you care about. Measuring every machine in one factory is a population; measuring twenty of them to describe the factory is a sample.
By the square root of n over n minus one. That is 6.9 per cent at eight values, 2.6 per cent at twenty, 1 per cent at fifty and 0.1 per cent at five hundred.
Roughly how far a typical value sits from the mean, in the same units as the data. For a bell-shaped set about two thirds of values fall within one deviation of the mean.
Because a sample deviation needs at least two values to divide by, and the page reports zero rather than an error. Treat any deviation from a one-value list as meaningless.
No. The range is only the largest minus the smallest, so it is decided by two values and ignores everything between them. The deviation uses all of them.
The median. Both distributions have a long upper tail that pulls the mean above what most people experience, and the median describes the middle of the market instead.
Not directly. Repeat each value as many times as its weight and paste the longer list, which gives the same answer for whole-number weights.
Only average them directly when each one covers the same size of group. Two rates over groups of 10 and 1,000 need weighting by group size, otherwise the small group counts as much as the large one.
No. The list is sorted internally before the median and the extremes are read off, so a shuffled column gives identical answers.
Several thousand values stay instant. The work is one pass for the sums and one sort, both of which your device does far faster than you can paste.
So a mean that is not a round number is not silently rounded into one. Round it yourself to whatever precision your measurements justify.
No. The whole calculation happens in this page, which is also the reason it stays instant on a long column.