The Hypergeometric distribution gives us the idea about whats the success numbers for a n draws without any replacement for a finite population. It is similar to binomial distribution but replacement is not there. Suppose there are 14 types of dresses out of which 7 are blue and 7 are red, you may have to choose 10 dresses out of it. Here the probability distribution of different combination of colors tells about hypergeometric distribution.

There are 3 parameters to determine it N,m and n where
  • N is the population size
  • m is the no of items having the desired characteristic in it (Success rate)
  • n is the no of trials taken
Hypergeometric Distribution Calculator is online tool to calculate the general statistical properties. you just have to enter the population size (N), number of successes (m) and number of trials (n) and get the all the statistical properties namely mean, standard deviation, variance, skewness, kurtosis, kurtosis excess, median, support, interquartile range, quartile deviation, momental skewness, characteristic function, moment generating function, factorial moment generating function and probability density function instantly.
Lets find statistical properties using the following steps:
If the population size (N), number of successes (m) and number of trials (n) is known then you can calculate statistical properties using some below formulas:
To calculate mean
Mean = $\frac{nm}{N}$
To calculate variance
Variance v = $\sigma^2$ = $\frac{nm (N-m)(N-n)}{N^2(N-1)}$
Standard deviation $\sigma$ is calculated by finding the square root of variance
To calculate skewness
Skewness = $\frac{(N - 2m)(N-1)^{\frac{1}{2}}(N - 2n)}{(nm(N-m)(N-n))^{\frac{1}{2}} (N - 2)}$
To calculate the probability distribution
P(x | N,m,n) = $\frac{\begin{pmatrix} m\\ x \end{pmatrix}\begin{pmatrix} N-m\\ n-x \end{pmatrix}}{\begin{pmatrix} N\\ n \end{pmatrix}}$
Substitute the values in above formula and get the answer.