Poisson Distributions
The Mean and Standard Deviation of Poisson Distributions
Learning Objectives
Calculate the mean and standard deviation of Poisson distributions.
Calculating the Mean
- The mean of a Poisson distribution is the mean that is stated in the problem:
- mean [latex]= \lambda[/latex]
Calculating the Standard Deviation
- We can also easily calculate the standard deviation of a Poisson distribution:
- standard deviation [latex]= \sigma = \sqrt{\lambda}[/latex]
Example 33.1
Problem Setup: There are, on average, 28,000 bankruptcies filed in Canada per year according to the Office of the Superintendent of Bankruptcy in Canada.
Question: What are the mean and standard deviation for this problem?
Solution: Click here to download the Excel solution. Also, see the solutions below:
- mean [latex]= \lambda = 28,000[/latex]
- standard deviation [latex]= \sigma = \sqrt{\lambda} = \sqrt{28,000} = 167.33201[/latex]