📊 Average Calculator
Paste any set of numbers, separated by commas, spaces or new lines, and get the mean, median, mode and range at once, along with the sum, the count and the sorted list.
Mean, median, mode and range: four answers to one question
"Average" is ambiguous. It usually means the mean, but median and mode are also averages, and they can be wildly different numbers for the same data. Choosing the wrong one is how a statistic becomes misleading without anyone technically lying.
The four measures
| Measure | Definition | Best for |
|---|---|---|
| Mean | Sum divided by count | Symmetric data with no extreme values |
| Median | Middle value when sorted | Skewed data: income, house prices, waiting times |
| Mode | Most frequent value | Categories, shoe sizes, anything non-numeric |
| Range | Maximum minus minimum | A quick sense of spread, though sensitive to outliers |
Why the mean and median diverge
The mean is pulled by every value, including extreme ones. The median only cares about position. Take the salaries in a small firm: 24,000, 26,000, 28,000, 30,000 and 420,000. The mean is 105,600, which describes nobody. The median is 28,000, which describes the typical employee exactly.
This is why income, wealth and house price statistics are nearly always reported as medians. When a report gives you a mean for data you know is skewed, it is worth asking why.
A quick diagnostic: if the mean is noticeably above the median, the data has a long right tail. If it is below, a long left tail. If they are close, the distribution is roughly symmetric and the mean is safe to use.
The mode, and when there is not one
The mode is the most frequent value. A data set can have no mode, if nothing repeats; one mode; or several, when values tie. It is the only average that works for categorical data: you cannot take the mean of a list of colours, but you can find the most common one. For continuous measurements, the mode is often meaningless without grouping the data into bins first.
Weighted means
A plain mean treats every value as equally important, which is often wrong. If 90% of 10 students pass one class and 50% of 90 pass another, the overall pass rate is not 70%. It is (9 + 45) / 100 = 54%. The correct calculation weights each group by its size:
weighted mean = Σ(value × weight) / Σ(weight)
This is the same arithmetic behind a GPA, where credit hours are the weights, and behind a course grade, where assessment percentages are. It is also the single most common error in casually reported statistics.
Quartiles and the interquartile range
Quartiles split sorted data into four parts. Q1 is the value a quarter of the way through, Q3 three quarters. The interquartile range, Q3 minus Q1, covers the middle half of the data and ignores the extremes entirely, which makes it a far more robust measure of spread than the range. A common outlier rule flags anything more than 1.5 times the IQR beyond Q1 or Q3.
A worked example
The data set 12, 15, 18, 20, 25, 18, 31, 14. Sorted: 12, 14, 15, 18, 18, 20, 25, 31. The sum is 153 over 8 values, so the mean is 19.125. With an even count, the median is the average of the two middle values, (18 + 18) / 2 = 18. The mode is 18, appearing twice. The range is 31 − 12 = 19, Q1 is 14.75, Q3 is 21.25 and the IQR is 6.5. The mean sitting above the median tells you the 31 is pulling it rightwards.
Frequently Asked Questions (FAQs)
Should I use the mean or the median?
Median when the data is skewed or has outliers, which covers income, house prices, response times and most real-world measurements with a floor at zero. Mean when the data is roughly symmetric, which covers heights, test scores and measurement errors.
How do I find the median of an even number of values?
Sort them and take the mean of the two middle values. For eight values, average the fourth and fifth. For an odd count, the median is simply the middle value with no arithmetic needed.
Can a data set have more than one mode?
Yes. Two values tying for most frequent makes it bimodal, three makes it trimodal. A bimodal distribution often means two different populations have been mixed together, which is usually more interesting than the average itself.
What is the difference between range and standard deviation?
Range uses only the two extreme values, so a single outlier dominates it. Standard deviation uses every value and measures typical distance from the mean. Range is quick; standard deviation is informative.
Why can I not average percentages directly?
Because percentages from different-sized groups carry different weight. A 90% rate in a group of 10 and a 50% rate in a group of 90 average to 54%, not 70%. Convert back to counts, add, and divide by the combined total.
What counts as an outlier?
A common rule flags any value more than 1.5 times the interquartile range beyond Q1 or Q3. It is a convention, not a law, and an outlier is not automatically an error. Investigate before deleting: outliers are sometimes the most important data points you have.