Average & Statistics Calculator

Mean, median, mode, range and standard deviation from any list.

Mean (average)
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Median
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Mode
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Standard deviation
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Range
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Sum
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How many
Sorted values
How this works
Mean = sum ÷ count Median = middle value once sorted Mode = the value that appears most often SD = √( Σ(x − mean)² ÷ n ) population = √( Σ(x − mean)² ÷ (n−1) ) sample
MeasureUse it when
MeanValues are evenly spread with no extremes
MedianA few very large or small values would distort the mean
ModeYou need the most common value, including for text-like data
RangeA quick sense of spread
Standard deviationYou need how tightly values cluster around the mean
  • Salaries are usually reported as a median — one very high earner drags the mean up and misrepresents the typical figure.
  • Use the sample basis (n − 1) when your numbers are a sample of something larger, which is most of the time.
  • In a normal distribution about 68% of values fall within one standard deviation of the mean, and 95% within two.
What is the difference between mean and median?

The mean is the total divided by the count. The median is the middle value once sorted, so it is not pulled by a few extreme values — which is why incomes are quoted as medians.

Should I use sample or population standard deviation?

Use sample (n − 1) if your numbers are a subset of a bigger group, which is the usual case. Use population (n) only when you have every member of the set.

What if no number repeats?

There is no mode. If several values tie for most frequent, the set is multimodal and all of them are shown.

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