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 $=  \lambda$

Calculating the Standard Deviation

• We can also easily calculate the standard deviation of a Poisson distribution:
• standard deviation $= \sigma = \sqrt{\lambda}$

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 $= \lambda = 28,000$
• standard deviation $= \sigma = \sqrt{\lambda} = \sqrt{28,000} = 167.33201$