Math calculator
Discrete Variance Calculator
Measure probability-weighted squared spread around a discrete mean. Formula and variance and deviation remain visible in one place for independent verification.
Discrete Variance inputs
Calculation inputs
Recognizing a Discrete Variance problem
Variance distinguishes distributions with the same mean but different uncertainty, risk, or concentration.
The core relation in Discrete Variance
Discrete variance is Σ(x−μ)²P(x), where μ is expected value. Standard deviation is its nonnegative square root.
For values 0,1,2 with probabilities .25,.5,.25, μ=1, variance=.5, and standard deviation≈.7071. This Discrete Variance example can be compared with distribution center.
Hand-checking the Discrete Variance result
Check Discrete Variance from Possible values, then verify Corresponding probabilities. Estimate the Discrete Variance Variance and deviation before computing it again. If Corresponding probabilities changes during Discrete Variance, keep Corresponding probabilities fixed. That Discrete Variance comparison shows whether Variance and deviation moves as expected.
Find expected value, square every deviation from it, weight those squares, and add.
Using the Discrete Variance result
Probabilities must align and sum to one. Variance has squared units, so standard deviation is easier to compare on the original scale.
Reproducing Discrete Variance
A reproducible Discrete Variance record contains Possible values, Corresponding probabilities, the selected calculation mode, and the final rounding rule. Keep decimals on the zero-to-one scale during probability arithmetic and label any percentage conversion separately. Exact counting results should remain integers even when they are very large.
For Discrete Variance, for an independent check, simplify the setup by removing one stage or fixing one object. The smaller result should relate to the original through a known factor, coefficient, or complement rather than through coincidence.
Confirming the Discrete Variance setup
Classify Possible values before using Discrete Variance. Confirm that Corresponding probabilities fits the allowable Discrete Variance range.
Test a zero or certain-event Discrete Variance boundary. Compare that simple Discrete Variance case with Corresponding probabilities.
Cross-checking Discrete Variance
Check the direction of Variance and deviation by changing Possible values slightly. Hold Corresponding probabilities steady during this Discrete Variance trial. The new Variance and deviation should move as the Discrete Variance relationship predicts unless the calculation crosses a stated boundary.
Validating Discrete Variance
A simple Possible values supplies a benchmark for Discrete Variance. Retain Corresponding probabilities and predict Variance and deviation. The benchmark helps distinguish an unlikely Discrete Variance magnitude from ordinary rounding in Variance and deviation.
Questions about Discrete Variance
Can variance be negative?
No.
What does zero variance mean?
All probability is at one value.
Why square deviations?
To prevent cancellation.
What units does deviation use?
The original value units.