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
127.69cm2
23.136kg2
Can we say that the weights show greater variation that the heights ?
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Solution
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