The POISSON function in Excel is a statistical function used to model the probability of a given number of events occurring within a fixed interval, based on a known average rate of occurrence. This function is particularly useful in fields such as finance, healthcare, and operations management, where events happen independently over time.

Syntax

POISSON(x, mean, cumulative)

• x: The number of events for which you want to calculate the probability.
• mean: The expected average number of events (lambda).
• cumulative: A logical value that determines the form of the function. If TRUE, it returns the cumulative probability; if FALSE, it returns the probability mass function.

Example #1

=POISSON(3, 2.5, FALSE)

This function calculates the probability of observing exactly 3 occurrences when the average is 2.5 events. The result could be approximately 0.2136.

Example #2

=POISSON(3, 2.5, TRUE)

This version computes the cumulative probability of observing 3 or fewer events when the average number is 2.5. The result might be around 0.6832.

Example #3

=POISSON(0, 1, FALSE)

This function evaluates the probability of no events occurring with a mean of 1. The resulting probability would be about 0.3679.

Error handling

• VALUE!: Occurs if any of the arguments are of the wrong type, such as non-numeric values.
• NUM!: Indicates that the ‘x’ value is negative or that the ‘mean’ is less than 0.

Conclusion

The POISSON function is an essential tool for statistical analysis in Excel, particularly for analyzing events that occur randomly over time. By understanding its syntax and functionalities, users can effectively harness its power for their data-driven decision-making.