Mean, Median & Mode Calculator
Paste your numbers to see the mean, median and mode side by side.
| # | Value |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 |
Report the median, 15. The mean, 17.8, is pulled up by 41, which lies beyond Tukey's fences.
Where the three centers fall
Dashed lines: median and mode10 values from 9 to 41 in 5 classes: 9 to 15.4: 6; 15.4 to 21.8: 2; 21.8 to 28.2: 1; 28.2 to 34.6: 0; 34.6 to 41: 1. The mean is 17.8, the median 15 and the mode 15.
Working
- 1Sort the 10 values9, 11, 12, 15, 15, 15, 18, 20, 22, 41
- 2Mean: add the values and divide by how many there arex̄ = 17810 = 17.8
- 3Check: deviations from the mean always sum to 0Σ(x − x̄) = 0
- 4Median: n = 10 is even, so average values 5 and 6median = 15 + 152 = 15
- 5Mode: the most frequent value15, appearing 3 times
- 6Range: largest minus smallest41 − 9 = 32
- 7Answerx̄ = 17.8, median = 15, mode = 15
Pull one value
Drag the brass point to move itMoving the largest value, now 41, from −23 to 73: the mean runs from 11.4 to 21, while the median only runs from 15 to 15. At its current value the mean is 17.8 and the median 15.
Every measure of center
- Mean
- 17.8
- Median
- 15
- Mode
- 15
- Midrange
- 25
- Trimmed mean (drops 1 each end)
- 16
- Geometric mean
- 16.27
- Harmonic mean
- 15.13
The trimmed mean drops the top and bottom 10% of the sorted values before averaging, so it sits between the mean and the median when one end has extreme values.
Skew and outliers
- Skewness G₁
- 2.1 · highly skewed right
- Tukey fences (1.5 × IQR)
- 2.63 to 29.63
- Outliers
- 41 (1 far out)
Skewness under 0.5 either way is roughly symmetric, 0.5 to 1 is moderate and over 1 is high (Bulmer, Principles of Statistics, 1979). Values beyond the fences are outliers by Tukey's rule, and beyond 3 × IQR they are far out (NIST e-Handbook, section 7.1.6).
How often each value appears
| Cumulative | |||
|---|---|---|---|
| 9 | 1 | 10% | 10% |
| 11 | 1 | 10% | 20% |
| 12 | 1 | 10% | 30% |
| 15 | 3 | 30% | 60% |
| 18 | 1 | 10% | 70% |
How it's worked out
Each of the three measures answers "what is a typical value?" in its own way. The tool works them out the same way you would on paper.
- Mean. Add every value and divide by how many there are, .
- Median. Sort the values. With an odd count, take the middle one. With an even count, take the two middle values and average them.
- Mode. Count how often each value appears. The value with the highest count is the mode. If two values tie, both are modes. If nothing repeats, there is no mode.
For 3, 8 and 5 the sorted list is 3, 5, 8, so the median is the second value, 5. Add a 10 and there is no single middle value: the median is the average of 5 and 8, which is 6.5. A median can be a number that is not in your list.
The mean uses the size of every value, so one very large or very small value moves it. The median only cares about order, so it barely moves. That difference is the reason to look at both. The range, largest minus smallest, tells you how wide the list is. The skewness figure, , measures how lopsided it is; it is the same formula as SKEW in Excel and Google Sheets.
Worked examples
Ten waits at a walk-in clinic
A clinic manager logs ten waits in minutes: 12, 15, 9, 22, 15, 18, 41, 15, 11, 20. They add up to 178, so the mean is 17.8 minutes. Sorted, the two middle values are 15 and 15, so median = 15. The mode is 15, which appears 3 times. One patient waited 41 minutes, beyond Tukey's upper fence of 29.63. That one wait pulls the mean well above the median. For a notice on the wall, the median tells patients more about their own likely wait.
House prices with one mansion
Nine homes on a street sold for $210k to $310k. Their mean is $256.11k and their median is $250k. Add one $1,250k house and the mean jumps to $355.5k, while the median only moves to $255k. No price repeats, so there is no mode. This is why housing reports quote the median sale price.
Shoe sizes sold in one day
A shoe store sells twelve pairs: 9, 10, 8.5, 9, 11, 9.5, 9, 10, 10.5, 9, 8, 10. The mean size is 9.46, which is not a size anyone wears, and the median is 9.25. The mode, size 9, sold 4 pairs. For restocking, the mode is the figure that matters. The skewness is 0.15, so the sizes are spread fairly evenly around the middle.
Reading your result
When the mean and the median are close, your data are roughly balanced, and the mean is a fair summary. When the mean is well above the median, a few large values are stretching the right tail. Incomes, waiting times and home prices usually look like this. When the mean is below the median, a few small values stretch the left tail, as with test scores where most people do well.
The skewness rating uses a common rule of thumb from Bulmer's Principles of Statistics (1979). A value of between −0.5 and 0.5 is roughly symmetric. Between 0.5 and 1 either way is moderately skewed. Beyond 1 is highly skewed. The clinic waits score 2.1, which is high, and the recommendation switches to the median.
Outliers are flagged with Tukey's fences, as in the NIST e-Handbook: a value more than 1.5 times the interquartile range beyond the first or third quartile. An outlier is a reason to check a reading, not to delete it. The trimmed mean in the tool drops the top and bottom 10% of values; for the clinic it is 16 minutes, between the mean and the median.
Two modes far apart usually mean two groups are mixed in one list, such as the times of beginners and experts. No single center describes that well. Split the list and work out each group separately.
Common mistakes
- Finding the median without sorting. The middle of the list as typed means nothing. In the clinic list, the fifth and sixth values as typed are 15 and 18, but the true median is 15.
- Forgetting to average the middle pair. With an even count there are two middle values. For 3, 5, 8 and 10, the median is 6.5, not 5 or 8.
- Calling every value a mode. If each value appears once, there is no mode. Listing them all is a common homework slip.
- Dropping a zero. A zero is a real value. Leaving out a day with no sales raises the mean and shifts the median.
- Quoting the mean for skewed data. A mean of $355.5k describes none of the ten houses on that street. Report the median, or report both.
Questions people ask
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.1, Measures of location
- NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.11, Measures of skewness and kurtosis
- Tukey, J. W., Exploratory Data Analysis (1977), chapter 2 (fences for outliers)
- Microsoft Support, AVERAGE, MEDIAN, VAR.S and SKEW functions (Excel)
Maintained by Anil ShahUpdated October 28, 2026Checked against 6 reference values