Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 36 / 3 / a / Solution

At several doses the three replicate plates differ much more than the square-root-of-mean scale expected from a Poisson distribution. For example the group at dose $100$ has sample mean about $42.67$ and sample variance about $274.33$, rather than variance near $42.67$. Its counts span a range of $33$, compared with a Poisson standard deviation about $6.53$. The dose-$33$ and dose-$1000$ groups likewise have variances above their means. Thus extra plate-to-plate variation is plausible. With only three replicates per dose this is evidence suggesting overdispersion, rather than a precise determination of it; not every group has excess sample variance.