Probability Distribution Standard Deviation Calculator
Calculate expected value, variance, standard deviation, coefficient of variation, and probability checks from a discrete x-and-probability distribution table.
Probability Distribution Standard Deviation Calculator inputs
Change the calculator-specific fields below. The result, checks, and visual update from this calculator’s own formula engine.
Probability Distribution Standard Deviation Calculator results
How the standard deviation calculator for probability distribution works
This page is built for the exact search intent represented by standard deviation calculator for probability distribution. It exposes the governing assumptions and supporting quantities instead of returning an unexplained headline number.
Weighted, not raw-data, standard deviation
A discrete probability distribution lists possible values and the probability assigned to each value. The mean is Σxp and the variance is Σx²p − μ². This differs from a sample standard deviation calculated from observed raw data.
Probability validation and normalization
In probability mode, probabilities must sum to one within a small numerical tolerance. Normalization mode treats entered positive numbers as weights and divides each by the total. The result explicitly reports the final probability sum so a mistaken table cannot pass unnoticed.
Interpretation
Standard deviation is measured in the same units as X and describes spread around expected value. Variance is in squared units. The coefficient of variation can aid relative comparison when the mean is nonzero, while entropy describes probability uncertainty rather than numeric distance between outcomes.
Reliable-use checklist
Confirm that the selected mode, units, signs, dates, rates, and definitions match the original problem. Retain the detailed output and supporting cards so the answer can be reproduced. Test a known example before relying on a custom case, and use current official or professional guidance when taxes, benefits, safety, contracts, or regulated decisions are involved.
The standard deviation calculator for probability distribution runs locally in the browser. It does not transmit entered values, create an account, or retain a calculation history. Full internal precision is kept during calculation and display rounding is applied only to readable outputs.
Probability Distribution Standard Deviation Calculator questions
Can x values be negative?
Yes. Outcomes may be any finite real numbers.
Should I use sample or population division?
Neither. A fully specified probability distribution uses probability-weighted moments.
What if probabilities are percentages?
Enter decimals such as 0.25, or enter 25 and use normalization mode for all rows consistently.