Mean, Median and Mode Calculator
Find the mean, median, mode, range, quartiles, IQR and outliers of any data set, with a box plot and quartiles matched to Excel, R or TI-84 methods.
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About this toolWhat is the Mean, Median and Mode Calculator?
Type or paste a data set and this calculator gives the three averages at once: the mean (sum divided by count), the median (the middle value once sorted) and the mode (the most frequent value, or values). It also reports the range, minimum and maximum, the first and third quartiles, the interquartile range, the 1.5 x IQR fences and any outliers beyond them, and it draws a box plot so you can see the shape of the data at a glance.
Quartiles are where calculators quietly disagree. A TI-84, Excel's QUARTILE.INC, Excel's QUARTILE.EXC and R's boxplot all use different rules, and on a small data set they can give different Q1 and Q3. Instead of picking one silently, this tool lets you choose the method and shows a table of all four, labelled with the software each one matches, so your answer lines up with your textbook or spreadsheet.
- Mean, median, mode (including bimodal, multimodal and no mode)
- Range, quartiles, IQR, fences and outliers
- Box plot with whiskers, mean marker and outlier points
- Four quartile methods matched to TI-84, Excel, R and SPSS
- Geometric and harmonic means
- Sorted data listing, copy and share link
How to use the Mean, Median and Mode Calculator
- Enter your numbers in the box, separated by commas, spaces or new lines.
- Pick a quartile method. If your course uses a TI-84 or a textbook, keep the default; if you need to match Excel, choose the inclusive or exclusive interpolation method.
- Read the mean, median and mode cards. The median card says which sorted position it came from, and the mode card says how many times the mode appears.
- Check the box plot and the outlier card, then compare quartile methods in the table if your answer differs from someone else's.
- Copy the summary or share a link to the same data.
Worked examples
A data set with a clear mode and an outlier
Input
12, 15, 15, 18, 21, 22, 15, 25, 27, 30, 64
Output
Mean 24, median 21, mode 15 (3 times), Q1 15, Q3 27, IQR 12, upper fence 45, outlier 64
The value 64 pulls the mean three units above the median. It sits beyond Q3 + 1.5 x 12 = 45, so it is flagged as an outlier and drawn as a circle on the box plot.
Two modes
Input
3, 7, 7, 2, 9, 4, 4
Output
Mean 5.142857, median 4, modes 4 and 7 (bimodal)
Both 4 and 7 appear twice and nothing appears more often, so the data are bimodal and both values are reported.
Why quartile methods differ
Input
Same 11 values as the first example
Output
Q3 = 27 by the TI-84 and QUARTILE.EXC rules, 26 by Tukey hinges and QUARTILE.INC
Each rule draws the line at a slightly different position between 25 and 27. With hundreds of values the methods converge; with a dozen they can differ noticeably.
Background and insight
The mean uses every value, which makes it efficient but sensitive to extremes: one income of $10 million in a room of teachers drags the mean far above what anyone typically earns. The median ignores how far the extremes are and only cares about order, so it is the usual summary for skewed data such as house prices and salaries. The mode is the only average that works for categories (the most common shoe size, the most common answer) and can have several values or none at all; this calculator reports "no mode" when every value appears equally often.
There is no single definition of a quartile. Hyndman and Fan (1996) catalogued nine sample quantile rules used by statistical packages. The four offered here are the ones people meet most: the median of each half with the overall median excluded (TI-83/84 and most school textbooks), Tukey's hinges with the median included in both halves (R's fivenum and boxplot), linear interpolation at position (n - 1)p + 1 (Excel QUARTILE.INC, Google Sheets, R type 7, NumPy), and linear interpolation at (n + 1)p (Excel QUARTILE.EXC, R type 6, Minitab and SPSS). The tests check all four against the worked examples on Wikipedia's Quartile article.
Outliers use Tukey's rule: anything below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR is flagged, and the box-plot whiskers stop at the most extreme values inside those fences. The geometric and harmonic means are shown too, for growth rates and for averaging rates such as speeds.
Common use cases
Homework and exams
Get the five-number summary and box plot for a textbook problem and confirm you used the same quartile rule as your teacher.
Salary and price data
Compare the mean and median to see how much a few large values skew a pay survey or a list of house prices.
Quality checks
Spot readings outside the 1.5 x IQR fences before they distort a report or a control chart.
Survey answers
Find the most common rating on a 1 to 5 scale and see whether responses split into two camps.
Tips and limitations
- If the mean and median are far apart, the data are skewed. Report the median for typical values and the mean when totals matter.
- An outlier flag is a prompt to investigate, not a reason to delete. Check for typos and unit mix-ups first.
- Excel's older QUARTILE function is the same as QUARTILE.INC.
- With an even count the median is the average of the two middle values, so it may not be one of your data points.
- The geometric mean needs every value above zero; it is the right average for growth factors such as 1.05, 0.97, 1.12.
Frequently asked questions
How do you find the mean, median and mode?
The mean is the sum divided by how many values there are. The median is the middle value after sorting (or the average of the two middle values when the count is even). The mode is the value that appears most often. For 3, 7, 7, 2, 9 the mean is 5.6, the median is 7 and the mode is 7.
What if there is no mode?
If every value appears the same number of times, there is no mode, and the calculator says so. Some teachers prefer to say every value is a mode; the meaning is the same: no value stands out.
Can a data set have two modes?
Yes. When two values tie for the highest frequency the data are bimodal, and with three or more ties they are multimodal. The calculator lists every tied value.
Why does my calculator give a different Q1 and Q3?
Quartiles have several accepted definitions. A TI-84 excludes the median from each half, Excel QUARTILE.INC interpolates at (n - 1)p + 1 and QUARTILE.EXC at (n + 1)p. Pick the matching method in the dropdown, or read the comparison table.
When should I use the median instead of the mean?
Use the median when the data are skewed or contain outliers, such as incomes, house prices or response times. Use the mean when the values are roughly symmetric or when you need a figure that multiplies back to the total.
How are outliers determined?
With Tukey's rule: any value below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR. Because the fences depend on the quartiles, the outlier list can change with the quartile method on small data sets.
What is the interquartile range?
The IQR is Q3 minus Q1, the width of the middle half of the data. Unlike the range it ignores the extremes, so a single outlier does not change it.
Is there an in-depth guide to the Mean, Median and Mode Calculator?
Yes. “Mean, Median, Standard Deviation and Z-Scores Explained” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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