Mathematics · Probability
Binomial Mean and Variance Calculator
Calculate expected successes, variance and standard deviation.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Mean=100×0.2=20.
- Variance=100×0.2×0.8=16.
Problem → model → reason → result
What problem does this model solve?
Calculate expected successes, variance and standard deviation.
Why does the model apply?
A binomial count adds n independent Bernoulli variables.
What assumptions does it make?
Outcomes and selection rules match the stated model; independence, equal likelihood and replacement are assumed only when the problem actually provides them.
Formula
μ=np; σ²=np(1−p)
Calculation and working
The calculator above substitutes your inputs into the model and leaves the calculation steps visible so the answer can be checked rather than merely accepted.
What does the result mean?
The result answers the stated problem in the units implied by your inputs. Read its sign, size and units together, then compare it with the original values before drawing a conclusion.
Worked example
n=100 and p=.2 gives mean 20 and variance 16.
Common mistake
These formulas assume independent identical trials.
When does this model not apply?
The numerical answer is only as valid as the assumed outcome space and dependence structure.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Binomial mean and variance do?
Calculate expected successes, variance and standard deviation.
How does the Binomial mean and variance work?
The calculator applies μ=np; σ²=np(1−p). A binomial count adds n independent Bernoulli variables.
What can I learn from the Binomial mean and variance?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.