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Statistics Calculator
Paste in any list of numbers to instantly get the mean, median, mode, range, variance and standard deviation.
Mean, median, mode and range
The mean is found by adding up all the values and dividing by how many there are — it's pulled around by outliers. The median is the middle value once the data is sorted, and it holds up better against outliers. The mode is the most frequently occurring value, and a data set may have no mode, one mode, or several. The range is simply the difference between the largest and smallest values.
Variance and standard deviation, with an example
Variance measures how spread out the data is around the mean. For the set 4, 8, 15, 16, 23, 42, the mean is 18. The population variance is the average of the squared differences from the mean (910 ÷ 6 ≈ 151.67), and the population standard deviation is its square root (≈ 12.32). If this data is just a sample from a larger population, the sample variance instead divides by 5 (that is, n−1): 910 ÷ 5 = 182, giving a sample standard deviation of ≈ 13.49.
Frequently asked questions
What's the difference between mean, median and mode?
The mean is the sum of all values divided by their count, and it's sensitive to outliers. The median is the middle value once the data is sorted, and it resists outliers better. The mode is the most frequent value — a data set can have no mode, one mode, or several.
What is standard deviation?
Standard deviation measures how spread out the data is around the mean. It's the square root of the variance — the average of the squared differences between each value and the mean.
What's the difference between population and sample standard deviation?
Population statistics divide by n (the full count) and are used when your data is the entire group you care about. Sample statistics divide by n − 1, which corrects for the bias of estimating a population's spread from just a sample of it.
How is the range calculated?
The range is simply the largest value minus the smallest value in the data set — a quick, rough measure of spread.