Statistics calculator

Formula

How it works

The mean adds the values and divides by how many there are. The median and quartiles come from sorting the values and finding the middle positions (linear interpolation between the two nearest ranks). Variance here is the sample variance, dividing by n − 1 rather than n, which is the usual choice when the values are a sample rather than an entire population.

Worked example

The same calculation with the default values:

• How many values (2–8) 6
• Value 1 4
• Value 2 8
• Value 3 6
• Value 4 5
• Value 5 3
• Value 6 9
• Value 7 0
• Value 8 0

1. sum = 35
2. mean = 35 ÷ 6 = 5.833333
3. variance = Σ(x − mean)² ÷ (6 − 1) = 5.366667
4. standard deviation = √5.366667 = 2.316607

Result: Count: 6 · Sum: 35 · Mean: 5.83333333

Common mistakes

• Using the population variance formula (dividing by n) when the data is a sample, or vice versa - this calculator divides by (n−1) for sample variance (Bessel's correction), which is appropriate when the data is a sample of a larger population, not the whole population itself.
• Assuming the mean represents a "typical" value when the data has extreme outliers - a single very large or very small value can pull the mean far from where most of the data actually sits.
• Interpreting a large standard deviation as always "bad" - it simply measures spread; whether that spread is good or bad depends entirely on what's being measured.