The profile of the expected and observed distributions
We could explain the expected profile as the right two peaks are
the adult male weights, the preceding peaks are due to adolescent
males. To see better, we would need to superimpose a male weight
profile on top of a female weight profile.
To make a $\chi$-squared test pass we want to group data which
reduces the overall statistic. To do this we would try to group a
class which is an over-estimate with a class which is an
To make it fail, we would want to increase the statistic. To do
this we would group together classes which are over-estimates and
group together classes which are under-estimates.
Obviously, we would want to group classes in ways which look
We looked at these ways to group the data: