The coefficient of variation for a Poisson distribution with λ(mean) = 5 is ______.

The correct answer is 44.7 percent.

Key PointsPoisson distribution- 

• The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.
• It is named after French mathematician Siméon Denis Poisson.

Important Points

• The coefficient of variation (CV) is a measure of the relative variability of a distribution.
• It is calculated by dividing the standard deviation by the mean.
• For a Poisson distribution, the standard deviation is equal to the square root of the mean.
• So, the CV for a Poisson distribution is calculated as follows -
  • CV = 1/√λ
  • For a Poisson distribution with mean = 5, the CV is therefore:
  • CV = 1/√λ = 0.4472
  • This is equal to 44.72 percent, rounded to two decimal places.
  • In other words, the coefficient of variation tells us that the standard deviation is 44.72% of the mean.
• This means that the distribution is relatively spread out, with a significant number of values that are above and below the mean.
• The coefficient of variation is a useful measure of variability because it is independent of the scale of the distribution.
• This means that it can be used to compare the variability of distributions with different means.