How to use it· 4 steps
- Paste your numbers, separated by commas, spaces, tabs, semicolons or new lines. A column copied from a spreadsheet works as it is.
- If your numbers use thousands separators (1,234) or decimal commas (3,5), say so under “Commas in the data”.
- Read the mean, median and mode, then choose the quartile method your course or software uses.
- Check the outliers and the sorted list, and copy the sorted data if you need it elsewhere.
Step by step
How to use the mean, median and mode calculator
- 1Paste your numbers, separated by commas, spaces, tabs, semicolons or new lines. A column copied from a spreadsheet works as it is.
- 2If your numbers use thousands separators (1,234) or decimal commas (3,5), say so under “Commas in the data”.
- 3Read the mean, median and mode, then choose the quartile method your course or software uses.
- 4Check the outliers and the sorted list, and copy the sorted data if you need it elsewhere.
Mean, median and mode — what each one tells you
The mean is the sum divided by the count. For the example data — 12, 15, 11, 18, 15, 21, 14, 15, 30, 13 — the sum is 164 and the count is 10, so the mean is 16.4. The median is the middle value once the data is sorted: 11, 12, 13, 14, 15, 15, 15, 18, 21, 30. With an even count there are two middle values, and the median is their average — here (15 + 15) ÷ 2 = 15. The mode is the value that occurs most often: 15, three times.
The three disagree for a reason. The mean uses every value, so a single extreme one pulls it: the 30 in the example lifts the mean above the median. The median ignores how far out the extremes are, which makes it the better summary of a typical value for skewed data — incomes, house prices, response times. The mode is the only one of the three that works for categories, such as the most common shoe size sold.
When the mean and the median are close, the data is roughly symmetric. When the mean is well above the median, a long tail of large values is pulling it up — worth knowing before quoting an average.
When there is no mode, or more than one
If every value appears once, there is no mode, and the calculator says so rather than picking one. If two or more values tie for the highest count, they are all modes — the data is bimodal or multimodal — and all of them are listed with how often each occurs.
One case is a matter of convention. When every distinct value appears equally often — 1, 1, 2, 2 — no value is more typical than another, so this calculator reports no mode, which is the usual textbook rule. Spreadsheets behave differently: Excel's MODE returns only the first mode it finds and an error when there is none, and MODE.MULT is needed to see ties.
Mode is also sensitive to rounding. 4.99 and 5.00 are different values, so measured data with many decimals often has no mode at all until it is rounded or grouped.
Quartiles, the IQR and outliers — and why the methods differ
The first and third quartiles, Q1 and Q3, mark the 25th and 75th percentiles; the interquartile range, IQR = Q3 − Q1, is the spread of the middle half of the data. For large data sets every method agrees closely, but for small ones they can differ noticeably, and statisticians have catalogued nine definitions in common software (Hyndman and Fan, 1996). Three are offered here, each labelled with where you will meet it.
Inclusive is what Excel's QUARTILE.INC and QUARTILE, Google Sheets and R use by default: it interpolates at position (n − 1) × p. Exclusive is Excel's QUARTILE.EXC, also used by Minitab and SPSS: it interpolates at (n + 1) × p and cannot place quartiles in very small data sets. Median of halves is what the TI-83 and TI-84 calculators and most introductory textbooks teach: split the sorted data in two, leaving out the median when the count is odd, and take the median of each half.
For the data 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49, the inclusive method gives Q1 = 25.5 and Q3 = 42.5, while the exclusive and median-of-halves methods both give Q1 = 15 and Q3 = 43. Neither answer is wrong; they are different definitions, which is why a homework answer can disagree with a spreadsheet. Outliers use Tukey's fences — anything below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR — so they inherit the chosen method. In the pre-filled example the fences are 7.25 and 23.25 under the inclusive method, and the 30 is flagged.
Entering data without surprises
Values can be separated by commas, spaces, tabs, semicolons or new lines, in any mix. Commas are a hazard, because 1,234 can mean one number or two. By default a comma separates values, so 1,234 is read as 1 and 234 — and when the data looks like it contains thousands separators, a warning says so. If your data does use them, or uses commas as decimal points as much of Europe does, switch the setting and the values are read accordingly.
Anything that is not a number — a heading, a unit, a stray word — is skipped and listed under the box, rather than dropped silently or allowed to break the calculation. Negative numbers and scientific notation such as 1e3 are accepted, and lists of many thousands of values are fine. The sum uses compensated summation, so a long column of decimals does not drift the way a simple running total does.
The range is maximum minus minimum, and the sorted list can be copied out in one click. For the spread of the data in more detail — standard deviation, variance and z-scores, with the working — use the standard deviation calculator. Everything is computed in your browser; pasted data is never uploaded.
Answers
Frequently asked questions
How do I find the median of an even number of values?
Sort the values and average the two in the middle. For 3, 5, 8, 10 the middle pair is 5 and 8, so the median is 6.5.
What if two numbers tie for the mode?
Then both are modes and the data is bimodal. The calculator lists every tied value and how many times each appears.
Why does my textbook give a different Q1 from Excel?
They use different quartile methods. Textbooks and TI calculators usually take the median of each half; Excel's QUARTILE.INC interpolates. Choose the method that matches your course.
Is the average the same as the mean?
In everyday use, yes — “average” usually means the arithmetic mean. Strictly, the median and mode are averages too, which is why reports should say which one they mean.
How are outliers identified?
By Tukey's rule: values more than 1.5 times the interquartile range below Q1 or above Q3. The fences are shown so you can see exactly where the line falls.
Can I paste a column from Excel or Google Sheets?
Yes. A copied column arrives as one value per line, which is read directly. Headings and blank cells are skipped.