POISSON Function

The Excel POISSON function retrieves the Poisson distribution. This distribution is commonly used to predict the countable events over a certain period of time. It is used in various real-time scenarios to identify the likelihood of crimes in metropolitan cities, predict the occurrence of floods in remote areas over a specific period, determine the number of errors occurring in specific software, determine hospitals where the number of critical cases arrived during night hours, and more.

The POISSON function interchanges the POISSON.DIST function in Excel 2010.

Compatibility

This advanced excel function is compatible with the following versions of MS-Excel −

Excel for Microsoft 365
Excel for Microsoft 365 for Mac
Excel for the web
Excel 2021
Excel 2021 for Mac
Excel 2019
Excel 2019 for Mac
Excel 2016

Syntax

The syntax of POISSON function is as follows −

POISSON(x,mean,cumulative)

Arguments

You can use the following arguments with the POISSON function −

Argument	Description	Required / Optional
X	It specifies the total number of events.	Required
Mean	It denotes the expected numeric value.	Required
Cumulative	It represents a logical value whose value is either TRUE or FALSE. If its value is TRUE, POISSON will retrieve the cumulative Poisson probability that the random events frequency resides between zero and x inclusive. If its value is FALSE, POISSON will retrieve the Poisson probability mass function that the events frequency will be the same as that of x.	Required

Argument

Description

Required / Optional

It specifies the total number of events.

Required

Mean

It denotes the expected numeric value.

Required

Cumulative

It represents a logical value whose value is either TRUE or FALSE.

If its value is TRUE, POISSON will retrieve the cumulative Poisson probability that the random events frequency resides between zero and x inclusive.

If its value is FALSE, POISSON will retrieve the Poisson probability mass function that the events frequency will be the same as that of x.

Required

Points to Remember

If the x value is in decimal form, its value gets truncated to become an integer.
If x is other than a numeric value, then the POISSON function will retrieve the #VALUE! error.
If the mean is non-numeric, the POISSON function will get the #VALUE! error.
The POISSON function will retrieve the #NUM! error value if the x is negative.
The POISSON function would get the #NUM! error if the mean value is negative.

Examples of POISSON Function

Practice the following examples to learn the use of the POISSON function in Excel.

Example 1

Assume the sample dataset where the X, Mean, and Cumulative values are specified in the range C2:C4 cells. You can enter the formula =POISSON(C3,C4,C5) in the C6 cell.

And then you may press the Enter key to get the result of 6.14421E-06

Example 2

If the x value is in decimal form, its value gets truncated to become an integer.

Solution

You can enter the formula =POISSON(43.8,14,FALSE) in the C8 cell. The value of X that is 43.8 truncated to 43 and then press the Enter tab.

Therefore, the Poisson function would retrieve the Poisson probability mass function whose value is 2.64385E-10.

Example 3

If x is other than a numeric value, then the POISSON function will retrieve the #VALUE! error.

Solution

Lets suppose that the x contains the text value Harry. Enter the expression =POISSON("Harry",14, FALSE) in the C8 cell.

Once you press the Enter tab, the function will obtain the #VALUE! error.

Example 4

If the mean is non-numeric, the POISSON function will get the #VALUE! error.

Solution

You may write the expression =POISSON(23,"len", FALSE) in the C8 cell. As you can see in this expression, the second argument (Mean) is a len in text form.

Therefore, the #VALUE! error is obtained once you press the Enter key.

Example 5

The POISSON function will retrieve the #NUM! error value if the x is negative.

Solution

You may set the value of X to -43 and enter the Poisson formula =POISSON(-43,15,FALSE) in the desired cell and press the Enter tab.

Therefore, the Poisson Distribution for this case will return the #NUM as the x is less than 0 which is strictly prohibited.

Example 6

The POISSON function would get the #NUM! error if the mean value is negative.

Solution

First, enter the expression =POISSON(67,-6,FALSE) in the C8 cell where the Mean value is less than zero.

When you press the Enter key, the Poisson function will obtain the #NUM! error.

Hence, providing the positive and numeric values for the X and Mean arguments is mandatory to yield correct results from the POISSON Distribution function.

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