Compute the three measures of central tendency — mean, median, and mode — from any list of numbers. Along with count, sum, min, max, and range, these are the bare minimum single-variable summary most data analysis starts with.
The three central tendency measures
Mean — the arithmetic average. Sum all values, divide by count. Treats every data point equally; sensitive to outliers. Also called the “expected value” in probability contexts. The most common meaning of “average” in everyday speech.
Median — the middle value when the data is sorted. For an odd count, it’s the value exactly in the middle. For an even count, it’s the midpoint of the two middle values. Robust to outliers — adding an extreme value barely shifts the median. Used for anything where outliers would distort the answer (income distributions, response times, house prices).
Mode — the value that appears most frequently. For unimodal data, there’s a single mode. For multimodal data, there are multiple modes tied for maximum frequency — the tool reports all of them. For data where every value is unique, there’s no mode (every value appears exactly once, so nothing has a higher frequency than anything else).
Example: simple dataset
Enter 10, 20, 20, 30, 40, 50. You get:
- Count: 6, Sum: 170
- Mean: 170 / 6 ≈ 28.33
- Median: (20 + 30) / 2 = 25 (midpoint of the two middle values when sorted)
- Mode: 20 (appears twice, everything else once)
- Min: 10, Max: 50, Range: 40
Three different “centres” of the same data, each telling you something slightly different.
Example: the effect of an outlier
Enter 100, 200, 300, 400, 500. Mean = 300, median = 300 — both agree.
Now change one value: 100, 200, 300, 400, 50000. Mean jumps to 10,200; median stays at 300. A single outlier has enormous leverage on the mean but none on the median. This is why “median household income” is the standard summary — it’s not distorted by billionaires — while “mean GDP per capita” makes sense as a total-wealth indicator where every dollar should count.
Example: bimodal data
Enter 1, 1, 2, 3, 3. The mode is “1, 3 (×2)” — two values tied for maximum frequency. Bimodal data typically signals two underlying populations mixed together; the individual modes may each be meaningful.
Example: no mode
Enter 5, 10, 15, 20. Every value appears exactly once, so the mode is reported as “no mode (all unique)”. Some definitions would say “every value is a mode”; the tool takes the more informative approach of flagging the case explicitly.
When to use which
- Numeric, symmetric data (heights, IQ scores, measurement errors): all three usually agree closely. Any of them is a reasonable “typical value”.
- Skewed data (income, wealth, time-to-event): the median is usually the better summary — it’s what “typical” should mean for skewed distributions. Report the mean too if your audience expects it, but lead with the median.
- Categorical or repeated-value data (survey responses on a 1–5 scale, dice rolls, binary flags): the mode is the most informative — “which answer was picked most often?”
- Quick sanity check: all three at once reveals skew. Mean > median means positive skew (long right tail); mean < median means negative skew; mean ≈ median means roughly symmetric.
What this tool does not do
It doesn’t compute variance, standard deviation, or quartiles. Those are different aspects (measures of spread and position, not central tendency). For the full summary, use the descriptive statistics calculator in the same category.
It doesn’t handle grouped / frequency data. If you have “10 values of 5 and 15 values of 7”, expand that into a flat list first.
It doesn’t plot the distribution. Mean/median/mode are summary numbers; for visualisation, use a spreadsheet or a charting library.
It doesn’t compute confidence intervals, hypothesis tests, or any inferential statistics. For that, use R, SciPy, or a dedicated statistical package.
It doesn’t distinguish between sample and population. Mean, median, mode are the same value regardless of which you’re thinking about. (Variance and standard deviation are where that distinction matters.)