Statistics Calculator
Mean, median, mode, and standard deviation.
Mean, median, mode and standard deviation
Paste a list of numbers and this statistics calculator returns the four measures that describe almost any dataset: the mean, the median, the mode and the standard deviation. The first three tell you where the centre of the data sits — and they disagree in revealing ways when the data is skewed. The fourth tells you how spread out it is.
How to use the Statistics Calculator
- Paste your Numbers, separated by commas or spaces.
- All four statistics appear at once.
- Compare the mean with the median — a large gap signals skew or outliers.
- Read the standard deviation as the typical distance from the mean.
Formula and a worked example
Mean = Σx ÷ n
Median = middle value when sorted
Standard deviation = √(Σ(x − mean)² ÷ n)
The mean is pulled by extreme values; the median is not. That is why average income is usually quoted as a median — a handful of very high earners drags the mean far above what most people actually earn.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: the mean is 5, the median is 4.5, the mode is 4 and the standard deviation is about 2.0. Replace the 9 with 90 and the mean jumps to 15.1 while the median barely moves to 4.5.
Frequently asked questions
When should I use the median instead of the mean?
Whenever the data is skewed or contains outliers — incomes, house prices, response times. The median describes the typical case far better.
What does standard deviation actually tell me?
The typical distance of a value from the mean. In roughly bell-shaped data, about 68% of values fall within one standard deviation and 95% within two.
What if there is no repeated value?
Then there is no mode. If several values tie for most frequent, the dataset is multimodal.
Is this population or sample standard deviation?
Population — it divides by n. For a sample estimate, divide by n − 1 instead; the difference is negligible for large datasets.
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