Mean, Median, Mode Calculator
Compute the mean, median, mode, range, sample variance, and sample standard deviation of any list of numbers.
Mean, Median, Mode Calculator — input your values
What does this math calculator do?
This statistics calculator computes the three classic measures of central tendency — mean, median, and mode — plus the range, the sample variance, and the sample standard deviation, for any list of numbers you paste or type.
The mean balances the data, the median sits in the middle of the sorted values, and the mode is the most frequent value. Variance and standard deviation measure how spread out the numbers are; the standard deviation is reported in the same units as the data, which makes it easier to interpret. The sample versions divide by n − 1, the convention for a sample drawn from a larger population.
Formula and variables
Variance and standard deviation use the sample convention (divide by n − 1) as is standard for data sampled from a population.
| Symbol | Meaning |
|---|---|
| x | Each value in the list |
| n | Number of values |
| s² | Sample variance = Σ(x − mean)² ÷ (n − 1) |
| s | Sample standard deviation |
Worked example
Five employees earn $40k, $45k, $45k, $50k, and $120k. What are the mean, median, and mode?
- Mean = (40 + 45 + 45 + 50 + 120) ÷ 5 = 300 ÷ 5 = 60, so $60k.
- Sorted: 40, 45, 45, 50, 120 — the middle value is 45, so the median is $45k.
- 45 appears twice, so the mode is $45k.
Answer: Mean $60k, median $45k, mode $45k — the mean is inflated by the $120k outlier.
Tips and common mistakes
Tips
- Use the median instead of the mean when your data contains outliers, like a single huge salary or house price.
- A data set can have two modes (bimodal), several modes, or no mode at all — this calculator reports all of them.
- Standard deviation is most useful for comparing spread between data sets with similar means.
- For a quick sanity check: the mean of a sample always lies between the smallest and largest values.
Common mistakes to avoid
- Forgetting to sort the data before finding the median.
- Using the population variance (divide by n) when your data is a sample — this calculator uses n − 1.
- Reporting a mode when every value occurs exactly once; in that case there is no mode.
Mean, Median, Mode Calculator — frequently asked questions
What is the difference between mean, median, and mode?
The mean is the sum divided by the count, the median is the middle value of the sorted data, and the mode is the most frequently occurring value. They each summarize the center differently.
Why is sample variance divided by n − 1?
Because the sample mean slightly underestimates the population mean. Dividing by n − 1 (Bessel's correction) gives an unbiased estimate of the population variance.
What does standard deviation tell me?
It measures how spread out the values are around the mean, in the same units as the data. Around 95% of values typically fall within two standard deviations of the mean.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, the set is bimodal or multimodal, and this calculator lists every mode.
What if all my values are identical?
Then the mean, median, and mode are all that value, the range is zero, and the variance and standard deviation are zero.
Why is the range not a very robust measure?
Because it only depends on the two extreme values. A single outlier can stretch the range enormously even if the rest of the data is tightly packed.