Mean, Median & Mode Calculator
Paste a list of numbers for the mean, median, and mode plus quartiles, IQR, standard deviation, variance, and the full five-number summary, all copyable.
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- No usage limit
About the Mean Median Mode Calculator
Most mean, median, and mode calculators hand you three numbers and quit. Then you need the standard deviation, so you open a second tab. Then a quartile calculator to draw a box plot, so you open a third. This one refuses to do that to you. Paste your numbers once and you get the three averages, the full five-number summary (min, Q1, median, Q3, max), the interquartile range, and variance and standard deviation in both the sample and population versions. One paste, the whole descriptive-statistics picture, and a Copy all results button so it drops into your homework or report in a single click.
Everything runs in your browser. Nothing you type gets uploaded or stored anywhere, which actually matters when the numbers are grades, salaries, or lab readings you would rather not hand to some stranger's server. The bare calculators stop at three averages and send you tab-hopping for the rest, and honestly that always seemed like a lazy way to build one.
How to use
- Enter your numbers in the box. Separate them with commas, spaces, or new lines, paste a whole column copied out of a spreadsheet, or drop a
.csvor.txtfile straight onto the box. - Read the three averages at the top: mean, median, and mode, each labeled with how it was worked out.
- Check the five-number summary and the spread block. The quartiles, the IQR, and both standard deviations show how spread out your data is, not just where its center sits.
- Copy or share. One button copies every result as clean text. The Share link carries your exact numbers after the hash, which is the one part of a web address a browser never sends to a server, so a bookmark reopens the same data set and nothing about it travels.
- Edit and watch. Add, remove, or fix a value and every result recalculates instantly. There is no submit button.
Decimals and negative numbers both work. Any token that is not a number, a stray word, a currency symbol, a blank line, is quietly skipped, so a messy paste still gives clean results.
Three averages, and why you want all of them
"Average" is a loose word. In statistics it splits into three precise ideas, each a measure of central tendency, a single number standing in for a whole set.
The mean adds everything up and divides by the count. It uses every value, which is its strength and its weakness, because one wild number can drag it a long way from the pack. The median is the middle of the sorted list, half your data below it and half above, and it barely notices outliers. The mode is the value that shows up most often, and it is the only one of the three that works on things you cannot add up, like shirt sizes or favorite colors.
The same data can give three answers. Ask for the average salary at a company and the mean might say $95,000 while the median says $58,000, because two executives at the top pull the mean up and away from what a typical person earns. That gap is worth paying attention to. When the mean and median sit close your data is balanced, and when they spread apart it is skewed, with the size of the gap telling you the shape of your numbers before you have drawn a single chart.
The five-number summary and quartiles
The averages tell you where your data sits. The five-number summary tells you how it is spread across its whole range: the minimum, the first quartile (Q1), the median (which is the second quartile), the third quartile (Q3), and the maximum. Those five numbers are exactly what a box plot is drawn from, so this hands you every value the diagram needs.
Quartiles cut your sorted data into four equal-sized chunks. Q1 sits a quarter of the way in, Q3 three quarters of the way in, and the interquartile range is Q3 minus Q1, the spread of the middle half of your data. The IQR is a stubborn measure of spread. Because it throws away the top and bottom quarters, a lone billionaire or a typo of 9999 leaves it unmoved, the same reason the median barely shifts when an outlier drags the mean around.
One honest gotcha: there is more than one way to compute a quartile, and the methods disagree. This calculator uses the median-of-halves method (split at the median, and for an odd count leave the median out of both halves), which is what most textbooks and graphing calculators teach. Spreadsheets that interpolate, like Excel's QUARTILE.INC, can report a Q1 or Q3 that is a touch different on the same numbers. Neither is broken, they are different conventions. If your answer has to match a specific class or piece of software, check which one it expects first.
Standard deviation and variance, sample versus population
Variance is the average squared distance of your values from the mean, and standard deviation is simply its square root, which brings the number back into the same units as your data. A small standard deviation means your numbers sit close to the mean, and a large one means they are spread out.
The part people get wrong is sample versus population. The population versions divide the squared distances by the count, n. The sample versions divide by (n - 1) instead, which nudges the estimate slightly upward. That (n - 1) is Bessel's correction, there because a sample tends to underestimate the true spread of the bigger group it came from, so you compensate. Rule of thumb: if your numbers are a sample you are using to reason about a larger population (the usual situation), use the sample standard deviation. If your data is the entire group you care about, use the population one. This tool shows both, so you are never stuck guessing which your assignment wanted. For the full step-by-step working, the standard deviation calculator lays out the whole table.
Which number should you actually quote?
Use the mean when your data is roughly symmetric with no wild outliers, since it uses every value and gives the richest summary. Switch to the median the moment your data is skewed, with income and house prices as the textbook cases. That is exactly why official reports quote median household income. And reach for the mode when you care about the most common value or a non-numeric category, like the most-sold product size or the answer picked most on a survey.
Frequently asked questions
What is the interquartile range actually used for?
Two things, mostly. It is a spread measure that ignores outliers, so it describes messy real-world data more honestly than the plain range does. And it powers the standard outlier test: anything below Q1 minus 1.5 times the IQR, or above Q3 plus 1.5 times the IQR, gets flagged as a probable outlier. Those cutoffs are the "whiskers" and dots you see on a box plot.
Should I use the sample or population standard deviation?
Use the sample version (dividing by one less than the count) when your numbers are a sample and you want to generalize to a larger group. Use the population version when your data is the complete set, nobody left out. Most of the time the honest answer is "sample," which is why spreadsheet defaults like STDEV.S lean that way, so when unsure, pick sample.
Can I paste a whole column from a spreadsheet or drop a file?
Yes to all three. Paste a column straight from a spreadsheet and the line breaks are read as separators. Drag a .csv or .txt file onto the box to load its contents. Or type by hand. Whatever is fastest, and nothing you load ever leaves your device.
Formatted numbers survive the trip. A cell showing 12,500 reads as twelve thousand five hundred rather than a 12 and a 500, which is the quiet way a pasted column ends up holding more values than it had rows. That is why the count sits right under the box. Paste 40 rows and it should say 40. The shape nobody can settle is a line with nothing on it but digits and commas, like 100,200,300, since that is three values or one depending on who typed it. This one reads three, tells you which way it went, and gives you a link to flip it.
What is the five-number summary good for beyond box plots?
Comparing two data sets fast. Line up the five-number summaries of, say, two classes' test scores and you can see which group scored higher (compare medians), which was more consistent (compare the IQRs), and whether either had a rough tail (look at the gap between Q3 and the max). It is a compact profile of a distribution that a single average can never give you.
Does the mode work on things that are not numbers, like colors or shirt sizes?
The concept does, even though this box takes numbers. You cannot compute a mean or median of "favorite color" because those cannot be added or ranked into an average. But you can count which one comes up most, and that count is the mode. Most-picked survey answer, best-selling size, most-common complaint, all valid modes. For non-numeric categories, tally the frequencies and the winner is your mode.
Is my data private, and does it work offline?
Both yes. Every calculation happens locally in your browser, no numbers are uploaded, logged, or sent anywhere. Once the page has loaded it keeps working with no connection at all, so you can crunch sensitive figures like salaries or medical results without a single value leaving your machine.