Six Sigma Black Belt Certified Practice Exam

In a Poisson distribution, what can be inferred about the relationship between the mean and standard deviation?

1. The mean is always less than the standard deviation

2. The mean equals the standard deviation

3. The mean is double the standard deviation

4. The standard deviation is irrelevant

The correct answer is: The mean equals the standard deviation

In a Poisson distribution, a fundamental characteristic is that the mean and the standard deviation are equal. This distinct feature stems from the definition of the Poisson distribution, which is often used to model the number of events that occur in a fixed interval of time or space, where these events happen with a known constant mean rate and independently of the time since the last event. The relationship between the mean (λ) and the standard deviation (σ) in a Poisson distribution can be mathematically expressed as follows: both the mean and the standard deviation are equal to the square root of the mean. Specifically, the standard deviation is the square root of λ, and because mean is also λ in this distribution, it leads to the conclusion that the mean equals the standard deviation. This property of the Poisson distribution is crucial for calculations and modeling, especially in scenarios where events are rare or independent. Understanding this relationship aids practitioners in assessing the variability of their data in relation to the expected number of occurrences.