How to use the HYPGEOM.DIST function
Author: Oscar Cronquist Article last updated on February 28, 2023
The HYPGEOM.DIST calculates the hypergeometric distribution.
A hypergeometric distribution is a probability distribution that describes the number of successes in a fixed-size sample drawn from a finite population without replacement. It is similar to the binomial distribution (BINOM.DIST function) which describes the number of successes in a fixed-size sample drawn from a finite population with replacement.
In the hypergeometric distribution, each draw is dependent on the previous draw, as the sample size decreases with each draw. The geometric distribution becomes increasingly similar to the binomial distribution if the population size grows larger.
Table of Contents
1. HYPGEOM.DIST Function Syntax
HYPGEOM.DIST(sample_s, number_sample, population_s, number_pop, cumulative)
2. HYPGEOM.DIST Function Arguments
| sample_s | Required. A number representing how many successes in the sample. |
| number_sample | Required. The sample size. |
| population_s | Required. The total number of successes in the entire population. |
| number_pop | Required. The population size. |
| cumulative | Required. A logical value that determines the form of the function. TRUE - HYPGEOM.DIST returns the cumulative distribution function. FALSE - HYPGEOM.DIST returns the probability mass function. |
3. HYPGEOM.DIST Function example
This example uses the HYPGEOM.DIST function to calculate the probability of getting a spade from a deck of cards (standard 52 cards). The distribution chart, and the table next to it, show the probability of getting 1 spade, 2 spades, 3 spades, ... and up to 13 spades based on 13 cards out of 52 cards.
sample_s - 3
number_sample - 13
population_s - 13
numbeer_pop - 52
cumulative - FALSE
Formula in cell C18:
=HYPGEOM.DIST($B18,$C$3,$C$4,$C$5,C$13)
For example, you get 13 cards out of 52 cards. What is the chance that you get exactly 3 spades and the remaining cards are anything else (clubs, diamonds, and hearts)?
The table in B15:D27 shows that if the sample_s is 3 HYPGEOM.DIST returns approx 0.286 in cell C17, the probability is 28.6%.
What is the probability of getting up to 3 spades?
Valid outcomes are 0, 1, 2, and 3 but not more than 3 spades. The cumulative values are calculated in column TRUE, sample_s is 3 and the corresponding cumulative value is approx 0.585 or 58.5%
The cumulative value is calculated like this: 0.013 + 0.08 + 0.206 + 0.286 equals approx 0.585
Functions in this article
Functions in 'Statistical' category
The HYPGEOM.DIST function function is one of many functions in the 'Statistical' category.
Calculates the average of the absolute deviations of data points from their mean.
Calculates the average of numbers in a cell range.
Returns the average of a group of values. Text and boolean value FALSE evaluates to 0. TRUE to 1.
Returns the average of cell values that are valid for a given condition.
Returns the average of cell values that evaluates to TRUE for multiple criteria.
Calculates the beta distribution.
Calculates the inverse of the cumulative beta distribution.
Calculates the individual term binomial distribution probability.
Calculates the minimum value for which the binomial distribution is equal to or greater than a given threshold value.
Calculates the probability of the chi-squared distribution, cumulative distribution or probability density.
Calculates the right-tailed probability of the chi-squared distribution.
Calculates the inverse of the left-tailed probability of the chi-squared distribution.
Calculates the inverse of the right-tailed probability of the chi-squared distribution.
Calculates the test for independence, the value returned from the chi-squared statistical distribution and the correct degrees of freedom. Use this function to check if hypothesized results are valid.
Calculates the confidence interval for a population mean.
Calculates the confidence range for a population mean using a Student's t distribution.
Calculates the correlation between two groups of numbers.
Counts all numerical values in an argument.
Counts the non-empty or non-blank cells in a cell range.
Counts empty or blank cells in a range.
Calculates the number of cells that is equal to a condition.
Calculates the number of cells across multiple ranges that equals all given conditions.
Calculates the covariance meaning the average of the products of deviations for each pair in two different datasets.
Calculates the sample covariance meaning the average of the products of deviations for each pair in two different datasets.
Calculates the exponential distribution representing an outcome in the form of probability.
Calculates the F probability for two tests.
Calculates the right-tailed F probability for two tests.
Calculates the two-tailed probability from an F-test
Calculates a value based on existing x and y values using linear regression.
Calculates how often values occur within a range of values and then returns a vertical array of numbers.
Calculates the GAMMA value.
Calculates the gamma often used in queuing analysis (probability statistics) that may have a skewed distribution.
Calculates the geometric mean.
Returns estimated exponential growth based on given data.
Returns a value representing the y-value where a line intersects the y-axis.
Calculates the k-th largest value from an array of numbers.
Returns an array of values representing the parameters of a straight line based on the "least squares" method.
Returns an array of values representing the parameters of an exponential curve that fits your data, based on the "least squares" method.
Calculates the lognormal distribution of argument x, based on a normally distributed ln(x) with the arguments of mean and standard_dev.
Calculate the largest number in a cell range.
Calculates the highest value based on a condition or criteria.
Calculates the median based on a group of numbers. The median is the middle number of a group of numbers.
Returns the smallest number in a cell range.
Returns the smallest number. Text values and blanks are ignored, boolean value TRUE evaluates to 1 and FALSE to 0 (zero).
Calculates the smallest value based on a given set of criteria.
Returns the most frequent number in a cell range. It will return multiple numbers if they are equally frequent.
Calculates the most frequent value in an array or range of data.
Calculates the normal distribution for a given mean and standard deviation.
Calculates the inverse of the normal cumulative distribution for a given mean and standard deviation.
Calculates the percent rank of a given number in a data set.
Calculates the percent rank of a given number compared to the whole data set.
Returns the number of permutations for a set of elements that can be selected from a larger number of elements.
Returns the number of permutations for a specific number of elements that can be selected from a larger group of elements.
Calculates a number of the density function for a standard normal distribution.
Calculates the probability that values in a range are between a given lower and upper limit.
Returns the quartile of a data set.
Returns the quartile of a data set, based on percentile values from 0..1, inclusive.
Returns the rank of a number out of a list of numbers.
Calculates the rank of a number in a list of numbers, based on its position if the list were sorted.
Calculates the skewness of a group of values.
Calculates the slope of the linear regression line through coordinates.
Returns the k-th smallest value from a group of numbers.
Calculates a normalized value from a distribution characterized by mean and standard_dev.
Returns standard deviation based on the entire population.
Returns standard deviation based on a sample of the entire population.
Estimates the standard deviation from a sample of values.
Returns the standard deviation based on the entire population, including text and logical values.
Calculates values along a linear trend.
Calculates the mean of the interior of a data set.
Returns the variance based on the entire population. The function ignores logical and text values.
The VAR.S function tries to estimate the variance based on a sample of the population. The function ignores logical and text values.
Excel function categories
Excel functions that let you resize, combine, and shape arrays.
Functions for backward compatibility with earlier Excel versions. Compatibility functions are replaced with newer functions with improved accuracy. Use the new functions if compatibility isn't required.
Perform basic operations to a database-like structure.
Functions that let you perform calculations to Excel date and time values.
Let's you manipulate binary numbers, convert values between different numeral systems, and calculate imaginary numbers.
Calculate present value, interest, accumulated interest, principal, accumulated principal, depreciation, payment, price, growth, yield for securities, and other financial calculations.
Functions that let you get information from a cell, formatting, formula, worksheet, workbook, filepath, and other entitites.
Functions that let you return and manipulate logical values, and also control formula calculations based on logical expressions.
These functions let you sort, lookup, get external data like stock quotes, filter values based a condition or criteria, and get the relative position of a given value in a specific cell range. They also let you calculate row, column, and other properties of cell references.
You will find functions in this category that calculates random values, round numerical values, create sequential numbers, trigonometry, and more.
Calculate distributions, binomial distributions, exponential distribution, probabilities, variance, covariance, confidence interval, frequency, geometric mean, standard deviation, average, median, and other statistical metrics.
Functions that let you manipulate text values, substitute strings, find string in value, extract a substring in a string, convert characters to ANSI code among other functions.
Get data from the internet, extract data from an XML string and more.
Excel categories
Latest updated articles.
More than 300 Excel functions with detailed information including syntax, arguments, return values, and examples for most of the functions used in Excel formulas.
More than 1300 formulas organized in subcategories.
Excel Tables simplifies your work with data, adding or removing data, filtering, totals, sorting, enhance readability using cell formatting, cell references, formulas, and more.
Allows you to filter data based on selected value , a given text, or other criteria. It also lets you filter existing data or move filtered values to a new location.
Lets you control what a user can type into a cell. It allows you to specifiy conditions and show a custom message if entered data is not valid.
Lets the user work more efficiently by showing a list that the user can select a value from. This lets you control what is shown in the list and is faster than typing into a cell.
Lets you name one or more cells, this makes it easier to find cells using the Name box, read and understand formulas containing names instead of cell references.
The Excel Solver is a free add-in that uses objective cells, constraints based on formulas on a worksheet to perform what-if analysis and other decision problems like permutations and combinations.
An Excel feature that lets you visualize data in a graph.
Format cells or cell values based a condition or criteria, there a multiple built-in Conditional Formatting tools you can use or use a custom-made conditional formatting formula.
Lets you quickly summarize vast amounts of data in a very user-friendly way. This powerful Excel feature lets you then analyze, organize and categorize important data efficiently.
VBA stands for Visual Basic for Applications and is a computer programming language developed by Microsoft, it allows you to automate time-consuming tasks and create custom functions.
A program or subroutine built in VBA that anyone can create. Use the macro-recorder to quickly create your own VBA macros.
UDF stands for User Defined Functions and is custom built functions anyone can create.
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