Mean, Median & Standard Deviation Calculator
Paste a list of numbers to instantly get the mean, median, mode, range, and standard deviation.
What each measure tells you
- Mean — the arithmetic average (sum ÷ count)
- Median — the middle value once sorted (average of the two middle values if the count is even)
- Mode — the most frequently occurring value(s)
- Standard deviation — how spread out the values are from the mean
Population vs sample standard deviation
Population standard deviation divides by the total count (n) and is used when your numbers represent an entire population. Sample standard deviation divides by (n − 1) instead — a small correction that gives a better estimate when your numbers are only a sample drawn from a larger population.
Worked example
For the set 4, 8, 6, 5, 3, 7: the mean is 5.5, the median is 5.5, there's no repeated value (no mode), the range is 5, and the population standard deviation is about 1.708.
Frequently asked questions
What if two or more values tie for the most frequent?
The calculator lists every value that shares the highest frequency — a data set can have more than one mode (bimodal or multimodal).
Which standard deviation should I use?
Use population standard deviation if your numbers are the entire group you care about. Use sample standard deviation if your numbers are a sample used to estimate a larger, unmeasured population.