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Free average calculator. Paste numbers to get mean, median, mode, min, max, and count.
Last updated 6 October 2026
Ten people work at a small firm. Nine of them are paid between $31,000 and $44,000. The tenth founded it and is paid $900,000. Paste those ten salaries into the panel above and it returns both of the figures that get called the average:
Nine of the ten staff earn less than the mean, and not one person at the firm is paid anything near it. The median, by contrast, points at a salary a real employee recognises.
Now delete the founder. The nine remaining salaries have a mean of $36,000 and a median of $35,000, which sit almost on top of each other because nothing is pulling them apart. One row of data moved the mean by $86,400 and the median by $500. That gap in sensitivity is the whole subject of this page.
The Census Bureau’s Income in the United States: 2025, issued September 2026, reports that “In 2025, median household income was $87,460, an increase of 2.6 percent from the 2024 estimate of $85,210”. The same report gives how the total is divided: “In 2025, households in the lowest quintile received 3.0 percent of aggregate household income, while households in the highest quintile received 52.4 percent of aggregate household income”, and “The top 5 percent of households received 23.5 percent of aggregate household income.”
Those shares are enough to place the mean without anyone printing it. A fifth of households holding 52.4% of all household income have an average income of 52.4 ÷ 20 = 2.62 times the national average. The bottom fifth, on 3.0%, averages 0.15 times it. So the top fifth’s average household income is about 17 times the bottom fifth’s, and the top 5% average about 4.7 times the national mean. Those three multiples are arithmetic performed here on the published shares; the report does not print them.
A distribution with that much weight in its upper tail has a mean well above its median, which is why the headline figure in that report is a median. Had it led with a mean instead, the same year would have read as a richer country, truthfully, using a different statistic.
The definitions below are quoted from the NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.1, which is the authority this page follows.
“the mean is the sum of the data points divided by the number of data points”, and “The mean is that value that is most commonly referred to as the average.” It is the only one of the three that recovers a total: mean × count gives you the sum back, so if the question is what the payroll costs, the mean is the statistic that answers it and the median cannot.
“the median is the value of the point which has half the data smaller than that point and half the data larger than that point.” For an even-sized list the handbook averages the two middle values, (YN/2 + Y(N/2)+1) / 2, and that is what the panel above does. A consequence worth noticing: the median of an even-sized list need not be one of your numbers. The median of 1, 2, 3, 4 is 2.5.
“the mode is the value of the random sample that occurs with the greatest frequency. It is not necessarily unique.” Not necessarily unique is doing real work there: 1, 2, 2, 3, 3 has two modes, and the panel lists both rather than picking one.
Take the ten salaries again and pay the founder $9,000,000 instead of $900,000. The mean goes from $122,400 to $932,400, a move of $810,000. The median does not move at all; it stays at $35,500. The handbook explains why in one sentence: “Extreme values in the tails distort the mean. However, these extreme values do not distort the median since the median is based on ranks.”
Ranks are the key. The median asks each value only which side of the middle it falls on, and a very large number and a merely large number give the same answer. The mean asks each value how large it is, and then believes it. The handbook draws the conclusion plainly: “In general, for data with extreme values in the tails, the median provides a better estimate of location than does the mean.”
The comparison is also a measurement in its own right. For skewed data, “The mean will be pulled in the direction of the skewness. That is, if the right tail is heavier than the left tail, the mean will be greater than the median.” So a mean above the median tells you the long tail is on the high side, before you plot anything.
The usual answer to a wobbly average is to gather more of it. There are distributions where that fails, and the handbook works one through. For 10,000 draws from a Cauchy distribution it reports a mean of 3.70 and a median of −0.016. The two statistics do not merely differ in size; they disagree about which side of zero the typical value sits on. The full sample runs from about −29,000 to about 89,000.
“The Cauchy distribution has the interesting property that collecting more data does not provide a more accurate estimate of the mean,” the handbook notes, because “the sampling distribution of the mean is equivalent to the sampling distribution of the original data.” Its verdict: “for the Cauchy distribution the mean is useless as a measure of the typical value”, while “the median does provide a useful measure for the typical value.”
Cauchy data is an extreme case and you are unlikely to be holding any. The transferable lesson is narrower and more useful: the stability of a mean depends on the shape of the tail, and no amount of sample size substitutes for looking at that shape.
This page is not an argument for the median. For data without heavy tails, the mean is the better estimator and uses more of the information you have. The handbook is direct about the symmetric case: for a normal distribution “the mean, median, and mode are actually equivalent”, and “if a histogram or normal probability plot indicates that your data are approximated well by a normal distribution, then it is reasonable to use the mean as the location estimator.”
It is also honest about the awkward middle, which most pages tidy away: “For skewed distributions, it is not at all obvious whether the mean, the median, or the mode is the more meaningful measure of the typical value. In this case, all three measures are useful.” Three numbers and no single right answer is a legitimate result. Reporting all three, as the panel above does, is usually better than defending a choice between them.
You cannot take the mean of blue. For data whose values are labels rather than magnitudes, the most frequent value is the only measure of a typical one that is even defined: the commonest blood type, the commonest reason given for cancelling, the commonest answer on a multiple-choice form. Sorting is meaningless there too, so the median goes with the mean.
The handbook flags the matching limitation for continuous measurements: “any specific value may not occur more than once if the data are continuous. What may be a more meaningful, if less exact measure, is the midpoint of the class interval of the histogram with the highest peak.” The panel above counts exact repeats, so a column of measured weights or times will usually report no mode at all. That is a true statement about your data and not a failure of the tool, but it is also not the histogram-peak mode the handbook describes, and this page does not compute one.
Whether you pasted a sample or a population. If these numbers are a sample, the mean shown is an estimate of something you did not measure. The handbook calls that “a point estimate or a sample estimate” and points out that “different samples from the same population will generate different values for the sample mean”. Quantifying that spread needs an interval estimate. The panel shows none, so treat every figure on it as a description of the numbers you typed rather than a claim about the world they came from.
Whether an extreme value is a fact or a typing error. That decision is yours and it is not a statistical one. A tool that silently dropped outliers would be worse than one that does not, because you would never learn they were there. The min and max rows are there so you can see the ends of your own data before you trust the middle.
How much each number stands for. Every value you paste counts exactly once. A class of 30 averaging 60 and a class of 10 averaging 90 average to 75 if you feed the panel the two class averages, while the real figure across all 40 students is 67.5. Where your numbers are themselves summaries of different-sized groups, you need a weighted mean and this is the wrong tool.
What your numbers measure. It will average a temperature against a share price without complaint, and it will average percentages, which is its own trap: the mean of several percentage changes is not the overall percentage change.
How your numbers were punctuated. It reads numbers out of whatever text you
paste, and the comma is the hard case, because in a pasted column it is doing two jobs at once:
separating your numbers from each other, and grouping digits inside them. Until 6 October 2026 this
panel only knew the first job, so 1,234 arrived as two numbers and the advice here was
to strip your separators before pasting. It now decides by context. A comma counts as a thousands
separator when a digit sits before it and exactly three digits follow, with no fourth digit after
them, so 1,234 is one number and 1, 2 and 1,2345 are both
lists. That reading is a judgement made on your behalf, so when any comma is read as a grouping the
panel says how many in a Notes row rather than leaving you to infer it from the count.
Three other things it now accepts rather than misreading. The minus sign Excel, Word and most
spreadsheets emit is U+2212, not the ASCII hyphen, and the old scanner
knew only the hyphen, so a negative silently came back positive. The accounting form,
(1234) for a negative, is read as one. Currency symbols are ignored, so a money column
pastes directly. And a value too large for a double to hold, such as 1e999, used to be
discarded without a word, which quietly shrank the denominator and made a wrong mean look right; it
is now subtracted from the count in plain sight, in the same Notes row.
Part of the QuikUtil tools collection. Your numbers are never uploaded; the arithmetic runs in your browser.
If the numbers are roughly symmetric, the mean, and the NIST/SEMATECH handbook agrees: for a normal distribution “the mean, median, and mode are actually equivalent”. If the data has a long tail, the median, because “for data with extreme values in the tails, the median provides a better estimate of location than does the mean”. If the answers are categories rather than numbers, the mode is the only one of the three that exists.
Easily. In the ten-salary firm above, nine of the ten are paid less than the mean of $122,400, because one $900,000 salary carries it. The median of $35,500 always has half the list on each side, by construction. “Below average” is a claim about the mean and it says nothing about whether someone is unusual.
The mean adds every value, so a single number can push it as far as that number is large. The median counts positions. Raise the founder’s $900,000 to $9,000,000 and the mean of the ten goes from $122,400 to $932,400, a move of $810,000, while the median stays at exactly $35,500. NIST puts it this way: “Extreme values in the tails distort the mean. However, these extreme values do not distort the median since the median is based on ranks.”
Because every value you entered appeared once, so no value is more frequent than any other. That is the normal state of measured data. NIST notes that with continuous quantities “any specific value may not occur more than once if the data are continuous”, and that the more meaningful mode is then “the midpoint of the class interval of the histogram with the highest peak”. This panel counts exact repeats; it does not build a histogram.
Yes, and the panel lists all of them. NIST’s definition is explicit that the mode “is not necessarily unique”. Entering 1, 2, 2, 3, 3 gives two modes, 2 and 3, and that pair is the honest answer rather than a tie to be broken.
It averages the two middle values after sorting, which is the handbook definition: for even N the median is (Y[N/2] + Y[(N/2)+1]) / 2. So the median of 1, 2, 3, 4 is 2.5, a value that is not in your data at all. For an odd count the median is always one of your own numbers.
Only if the groups are the same size. A class of 30 averaging 60 and a class of 10 averaging 90 give an average-of-averages of 75, while the real average across all 40 students is (30 × 60 + 10 × 90) ÷ 40 = 67.5. This panel weights every number you paste equally, because it cannot see how many observations each one stands for.