Statistics Calculator
Paste or type a list of numbers and get the mean, median, mode, spread, quartiles and outliers at once — updated as you type.
How it's calculated
The mean is the sum divided by the count. The median is the middle value of the sorted list. The mode is the most repeated value. Variance is the average squared distance from the mean — divided by n − 1 for a sample or n for a whole population — and the standard deviation is its square root.
Worked example
Data: 2, 4, 4, 6. Mean: 16 ÷ 4 = 4. Squared distances from the mean: 4 + 0 + 0 + 4 = 8. Population variance: 8 ÷ 4 = 2, so the standard deviation is √2 ≈ 1.414. Sample variance: 8 ÷ 3 ≈ 2.667, standard deviation ≈ 1.633. Median: (4 + 4) ÷ 2 = 4. Mode: 4.
Frequently asked
When should I use sample vs population standard deviation?
Use population when your numbers are the entire group you care about (every student in one class, every sale this month). Use sample when they are a subset used to estimate a larger group. Sample divides by n − 1 instead of n, which corrects the tendency of small samples to understate spread.
How is the median calculated for an even number of values?
The values are sorted and the two middle ones are averaged. For 2, 4, 6, 8 the median is (4 + 6) ÷ 2 = 5.
How are quartiles and outliers worked out?
Quartiles use linear interpolation between sorted values, the same method as Excel's QUARTILE.INC. A value is flagged as an outlier if it lies more than 1.5 × IQR below Q1 or above Q3.
Can there be more than one mode?
Yes. If several values tie for the most repeats, all are listed. If no value repeats, there is no mode.