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. Number of events (n) is 100. See calculation below for the mean and standard deviation of the number of heads (x) if we repeat it 100 times.

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:

$$ σ_{x} = \sqrt{n*p*(1−p)} $$

$$ σ_{x} = \sqrt{100*0.5*(1−0.5)} $$

Here n is the sample size and p is the population proportion of success.

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

Population proportion (p) Sample size (n)

Solution

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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