To remove the problem of small numbers, you could use a Poisson distribution to perform a statistical test on the number of murderer rate. The actual murderer count (4 murderers) as compared to the expected murderer rate (0.07 murderers) gives a p-value of about 1e-6.
That said, this doesn’t account for the look-elsewhere effect, so it probably should be scaled by the population size. However, even after scaling by the ~32k public schools in the UK, it still gives a p-value of 0.03, so it’s statistically unlikely that there would exist a single public school among all 32k that would have this high a rate of murderers.
That said, this doesn’t account for the look-elsewhere effect, so it probably should be scaled by the population size. However, even after scaling by the ~32k public schools in the UK, it still gives a p-value of 0.03, so it’s statistically unlikely that there would exist a single public school among all 32k that would have this high a rate of murderers.