Distribution Variance Calculator

How it is calculated

Enter the possible values of the random variable and their probabilities as two comma-separated lists of equal length, in the same order. Use a dot for decimals, because the comma separates the items. The tool computes the mean μ = Σ p·x, the variance σ² = Σ p·(x − μ)² straight from the definition, and the standard deviation σ = √σ², all shown to four decimals.

Inputs it rejects, showing no result: lists of different length, entries that are not numbers, any probability below 0 or above 1, and probabilities whose sum is not within 0.001 of 1. The tolerance lets rounded values like 0.3333, 0.3333, 0.3333 through, but they are used as typed, not rescaled, so the mean comes out as 0.9999 rather than 1. Values themselves can be any real numbers.

Common mistakes

• Giving counts or percentages as probabilities. Counts like 10, 30, 40, 20 or percentages like 50, 50 are above 1 and the tool returns nothing; divide by the total first (0.1, 0.3, 0.4, 0.2).
• Using a decimal comma, as in 0,3. The comma is the separator, so write 0.3. Separating items with spaces or semicolons instead of commas gives no result either.
• Lists of different lengths, such as five values and four probabilities, or a missing probability for one outcome.
• Confusing this with sample variance. The values here are the whole distribution with its probabilities, so there is no n − 1 correction, and it is not calculated from a list of observed data points.
• Rounding probabilities so they no longer add up. 0.33, 0.33, 0.33 sum to 0.99, which is outside the 0.001 tolerance and gives no result; use 0.3333 or fractions that really sum to 1.