Mean and Standard Deviation of Binomial Distribution Calculator

Binomial Distribution can be defined as the probability distribution of number of successes in an experiment which is run multiple times. For example a coin is flipped 100 times. Here probability of getting head (p) is 0.5. Sample size (n) is 100.

The mean of the binomial distribution is calculated as:

$$ μ_{x} = n*p $$

$$ μ_{x} = 100*0.5 $$

The standard deviation of the binomial distribution is calculated as:

$$ σ_{x} = \sqrt{n*p*(1−p)} $$

$$ σ_{x} = \sqrt{100*0.5*(1−0.5)} $$

Enter values of sample size and population proportion of success in the calculator below for calculating mean and standard deviation for binomial distribution.


Step by Step Calculation

$$ μ_{x} = n*p $$

$$ σ_{x} = \sqrt{n*p*(1−p)} $$

Sample size (n) can't be less than or equal to 0. It must be a whole number. Population proportion (p) must lie between 0 and 1.
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