What is the standard deviation of a binomial distribution?

For a binomial distribution with n trials and probability of success p on each trial, the standard deviation (sigma or σ) is defined as: σ = √np(1 - p). The standard deviation is a measure of the amount of variation from the mean, denoted in statistics as "μ" the Greek letter mu.

As an example, imagine a coin that is flipped 100 times, with a binomial distribution defined by the number of heads. In this case:

n = 100

p = 0.5

μ = np = 100 x 0.5 = 50

σ = √100 x 0.5(1 - 0.5) = √25 = 5

In other words, out of 100 coin flips, one can expect the number of heads on average to fall between 50 +/- 5, or between 45 and 55.