Statistics Calculator

How to calculate mean, median, mode and standard deviation

Descriptive statistics summarize a list of numbers in a few telling values: where the center is (mean, median, mode) and how spread out the data is (range, variance, standard deviation). Here's the recipe this calculator follows:

1. Paste your numbers above, separated by commas, spaces, or new lines. The results update as you type.
2. Read the center. The mean is the average (sum ÷ count); the median is the middle value when sorted; the mode is the most frequent value.
3. Compare mean and median. If the mean sits well above the median, a few large outliers are pulling the average up — the median is the more honest "typical" value.
4. Check the spread. The range is max − min; the standard deviation tells you the typical distance from the mean. Bigger means more scattered.

Population or sample: which standard deviation is this?

Every standard deviation calculator must pick one: population (divide by N — you have the whole group) or sample (divide by N − 1 — you're estimating a larger group). This calculator reports population statistics, which is what most homework problems mean by "variance" and "standard deviation."

Mean vs. median: which should you use?

Use the mean for symmetric data without extreme values — test scores in a tight class, for instance. Use the median when outliers exist: the median of house prices describes a neighborhood far better than a mean dragged up by one mansion. And when categories matter more than numbers (most common shirt size), the mode is your statistic.