# Poisson distribution having variation coefficient = .5?

• B
In summary, the Poisson distribution is a probability distribution used to model the number of occurrences of an event over time or space. The variation coefficient, which measures the relative variability of a distribution, can be calculated for a Poisson distribution by dividing the standard deviation by the mean and multiplying by 100. In a Poisson distribution, the mean and variation coefficient are directly related, with an increase in mean resulting in an increase in the variation coefficient. The variation coefficient in a Poisson distribution can exceed 1, indicating a high level of variability in the distribution.
TL;DR Summary
How is it possible for a variation coefficient of poisson distribution to be anything other than 1?
Variation coefficient is calculated by

And the very definition of poisson distribution is that
$$\mu = \sigma$$

So how would any other value but 1 be a possible?

μ = σ2

gleem said:
μ = σ2
Then its no longer a poisson distribution because the very definition of a poisson distribution is that
μ = σ, not μ = σ2

pbuk
For a Poisson distribution, the mean is equal to the variance. Check your source.

I see what I did wrong. I mixed up variance and standard deviation.

## 1. What is the Poisson distribution?

The Poisson distribution is a probability distribution that is used to model the number of times an event occurs in a fixed interval of time or space. It is often used in situations where the probability of an event occurring is small, but the number of opportunities for the event to occur is large.

## 2. What does it mean for the variation coefficient to be .5 in a Poisson distribution?

The variation coefficient, also known as the coefficient of variation, is a measure of the relative variability of a dataset. In a Poisson distribution, a variation coefficient of .5 means that the standard deviation is half of the mean, indicating a moderate level of variation in the data.

## 3. How is the variation coefficient calculated in a Poisson distribution?

The variation coefficient in a Poisson distribution is calculated by dividing the standard deviation by the mean. This gives a measure of the relative variability of the data, allowing for comparison between datasets with different means and standard deviations.

## 4. Can a Poisson distribution have a variation coefficient greater than 1?

Yes, a Poisson distribution can have a variation coefficient greater than 1. This indicates a high level of variability in the data, with the standard deviation being larger than the mean. In these cases, the Poisson distribution may not be the best fit for the data and alternative distributions should be considered.

## 5. How does the variation coefficient affect the shape of a Poisson distribution?

The variation coefficient can affect the shape of a Poisson distribution in that a higher variation coefficient will result in a wider and flatter distribution, while a lower variation coefficient will result in a narrower and taller distribution. This is because a higher variation coefficient indicates a higher level of variability in the data, resulting in a wider spread of values around the mean.

• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
6
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
8
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
3
Views
927
• Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
14
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
12
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
3
Views
3K