Past exam of the options I course of the University of Oxford / 2006 / O / O1 / iii / Solution

The expected counts in the final two separate classes are too small for a reliable chi-squared asymptotic approximation. Pooling the last three classes gives the tail class $\ge 7$, with observed frequency $8+3+1=12$ and expected frequency $5.464+1.473+0.447=7.384$. This exceeds the usual expected-count guideline of 5. Pooling only the last two would leave an expected count of $1.920$, still too small. Pooling requires recomputing the contribution from the pooled totals, rather than adding the old separate contributions.