The POISSON function in Excel is used to calculate the Poisson probability of a given number of events occurring within a specified period. This function is part of Excel’s statistical functions and is useful for predicting the probability of a certain number of events happening within a fixed interval, given the average number of times the event occurs over that interval.
Syntax
POISSON(x, mean, cumulative)
- x: The number of events for which you want to calculate the probability.
- mean: The expected number of events that occur (average rate of occurrence).
- cumulative: A logical value that determines the form of the function. If TRUE, POISSON returns the cumulative distribution function, which is the probability that the number of random events occurring will be between zero and x inclusive. If FALSE, it returns the probability mass function, which gives the probability of exactly x events occurring.
Steps to Use
=POISSON(3, 2.5, FALSE)
=POISSON(3, 2.5, TRUE)
- Open your Excel spreadsheet where you want to perform the calculation.
- Select the cell where you want the result to appear.
- Enter the POISSON function using the syntax mentioned above. For example:
- To find the probability of exactly 3 events occurring when the average rate is 2.5, you would enter:
- To find the cumulative probability of up to 3 events occurring, you would enter:
Example
Suppose you have a scenario where a call center receives an average of 6 calls per hour, and you want to calculate the probability of receiving exactly 4 calls in an hour:
=POISSON(4, 6, FALSE)
- Click on the cell where you want the result.
- Type the formula:
- Press Enter. The cell will display the probability of receiving exactly 4 calls in one hour.
Important Notes
- The function assumes that events are independent, and the average rate (mean) is constant.
- The cumulative form (when `cumulative` is TRUE) can be useful for calculating probabilities over a range of values.
- The POISSON function was replaced in Excel 2010 and later by the more sophisticated POISSON.DIST function, which provides the same functionality.
This function is particularly applicable in fields such as quality control, telecommunications, traffic flow, and natural event prediction, where events occur sporadically and independently.
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