Question

The following values are calculated in respect of heights and weights of the students of a section of class $XI$.

	Height	Weight
Mean	$162.6cm$	$52.36kg$
Variance	$127.69{cm}^2$	$23.136{kg}^2$

Can we say that the weights show greater variation that the heights ?

Answer 1

Definition: Variance Ratio

Variance ratio or co-efficient of dispersion is defined as the ratio of variance to mean. It is defined only for those models, where the mean is non zero. It is frequently used for exponential and Poisson distribution for count data etc.

If variance ration $=0$, the underlying distribution will be a constant random variable

If $0<$ variance ration $<1$, underlying distribution could be binomial

If variance ratio $=1$, underlying distribution is Poisson

If variance $>1$, over-dispersed negative binomial distribution.

Hence variance ratio of height $=127.69/162.6cm=0.79cm$

And variance ratio of weight $=23.136/52.36kg=0.44kg$