What next?
A mean is one summary. These are the others and their uses.
How to use this calculator
- Enter your numbers separated by commas, spaces or new lines.
- The tool reads them instantly.
- Read the mean, median, mode, range and total.
What your result means
The mean adds every value and divides by the count, so it gets pulled around by outliers. The median — the middle value — is often a fairer ‘typical’ figure when a few numbers are extreme. Compare the two to see whether your data is skewed.
Why this one is different
Five figures sit beside the mean: median, mode, sum, smallest and largest, and the range between them. Read together they expose a single outlier — a mean well above the median means one large value is pulling it. Where nothing repeats, the mode row says so instead of naming whichever entry came first.
Mean, median and mode explained
The mean is what most people call the average: add every value and divide by how many there are. The median is the middle value when sorted — better than the mean when a few extreme numbers would otherwise skew the picture. The mode is the value that appears most often.
This tool reads any list of numbers — separated by commas, spaces or new lines — and reports all three averages plus the sum, count, smallest and largest values, and the range between them.
Formula
Median is the middle of the sorted list; the mode is the most frequent value; range is the largest value minus the smallest.
Example calculation
The values 4, 8, 15, 16, 23:
median (middle value) = 15
range = 23 − 4 = 19
Frequently asked questions
When should I use the median instead of the mean?＋
Use the median when your data has outliers — for example house prices or salaries, where a few very large values would pull the mean upward and misrepresent the typical value.
What if there is no repeated value?＋
Then there is no mode, and the tool shows "none". If several values tie for most frequent, all of them are listed.
What is the mode useful for?＋
Categorical or repeated data, where an average makes no sense. The most common shoe size sold or the most frequent delivery day are mode questions, not mean questions.
What does the range tell me?＋
How spread out the data is, from lowest to highest. It is easy to read but sensitive to a single outlier, which is why standard deviation is preferred for anything more serious.
How do I average percentages correctly?＋
Only average them directly if each percentage covers the same size group. Otherwise you need a weighted mean, using the group sizes as weights, or the answer will be wrong.
Can I average rates like speed?＋
Not with the arithmetic mean. Driving 60 km/h out and 30 km/h back averages 40 km/h, not 45, because you spend longer at the slower speed. That is the harmonic mean.
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Assumptions & limitations
Every figure here comes from a simplified model. Keep these limits in mind when reading your result:
- The mean, median and mode describe the numbers you typed and nothing more — they do not tell you whether the sample is representative of anything wider.
- The mean is pulled by outliers, so on skewed data such as salaries or house prices the median is usually the fairer ‘typical’ figure. Read both before quoting either.
- Every value is weighted equally. If some observations should count for more, that is a weighted average and needs a different calculation.
- The mode is only meaningful on repeated or grouped values. On continuous measurements every value tends to be unique, so the tool reports no mode.
- No dispersion measure is included beyond the range. Two sets can share a mean and be nothing alike, so treat the range as the crudest possible guide to spread.
Three averages, three different questions
The mean is the total shared equally and uses every value, which makes it the right summary for symmetric data and the wrong one when a few extreme values dominate. The median is the middle value once sorted and is unmoved by outliers, which is why incomes and house prices are reported as medians. The mode is the most frequent value and is the only one that works on categories rather than numbers. Reporting a single average without saying which one it is hides most of what the data was going to tell you.
Weighted means and the trap of averaging averages
When each value represents a different number of things, a plain mean is wrong. Averaging a class average of 70% from 30 students with 55% from 10 students gives 62.5%, but the true combined average is (70×30 + 55×10) ÷ 40 = 66.25%. The rule is that you can only average averages when the groups behind them are the same size; otherwise weight each by its group size. The same applies to rates and speeds, where the harmonic mean rather than the arithmetic one is often the correct tool.