Statistics Calculator
0 mean (average)
| # | Value | Deviation from Mean | Squared Deviation |
|---|
How Each Statistic Is Calculated
Enter any list of numbers and this calculator instantly returns the full descriptive-statistics summary. The mean is the sum of all values divided by the count. The median is the middle value once the data is sorted (or the average of the two middle values for an even-sized data set). The mode is the value or values that occur most often — if every value appears exactly once, there is no mode. The range is simply the maximum value minus the minimum value.
Sample vs. Population Standard Deviation
This calculator reports both conventions because the correct one depends on your data. Use population standard deviation (dividing the sum of squared deviations by n) when your list is the entire group you care about. Use sample standard deviation (dividing by n−1, known as Bessel's correction) when your list is a sample drawn from a larger population you're trying to estimate — this correction produces a slightly larger, less biased estimate. Variance is just the standard deviation before the square root is taken. For a deeper look at the standard deviation formula and step-by-step deviation table, see the standard deviation calculator.
When You Only Need the Mean
If all you need is a quick mean, median, and mode without the full variance breakdown, the average calculator is a faster, simpler tool. This statistics calculator is meant for when you need the complete picture — spread, variance, and both standard deviation conventions — from a single data set.
Frequently Asked Questions
Should I use sample or population standard deviation?
Use population standard deviation when your numbers represent the entire group you're interested in (dividing by n). Use sample standard deviation when your numbers are a sample drawn from a larger population you're trying to estimate (dividing by n-1, called Bessel's correction) - this calculator shows both so you can pick the right one for your situation.
What does it mean if there is no mode?
The mode is the most frequently occurring value in your data set. If every number you enter appears exactly once, no value repeats more often than any other, so the calculator reports 'None (no repeated value)' rather than picking one arbitrarily.