The average of one murder per murderer I'd generally agree with, but one of the Eton murderers killed 9 before committing suicide. So you are right to have qualms. But it is an upper bound and so still useful.
That said, one correction. El Salvador had a murder rate in 2017 of 61.7/100,000. This is comparable to Eton.
Let's take your analysis a step farther. If we have 230 * 30 people, each of whom has 1.1 chances in 100,000 of committing murder, the number of expected murderers is 0.0759. And the distribution of number of murders is a Poisson distribution. That means that the probability of k murders is λ^k e^(-λ) / k!.
Add those up and the expected probability of 4 or more murderers is only 1.3014245782150269e-06.
Therefore, even with a small absolute number, we can be very sure that the true murder rate for graduates of Eton are significantly higher than the UK population.
However Eton does attract people internationally. And the international murder rate in 2017 was 6.1/100,000 per https://worldpopulationreview.com/country-rankings/murder-ra.... Using that as a murderer rate, the odds against Eton producing 4 murderers in 30 years improve...to about 1/1000. Which means that Eton's murders are still likely to not be chance.
the true murder rate should be higher than the general population because its a boys school and men are carrying out more murders than women. but I assume its still higher once you account for that.
But looking at https://data.worldbank.org/indicator/VC.IHR.PSRC.P5?location... it looks like the homicide rate already was single gender. Even the peak rate in 2002 (probably skewed upwards by Harold Shipman) is well below the current world average. And UK rates have been low for many decades. 2002 is the peak of a rise in homicides starting around 1960, and it had been low since at least the 1800s.
I dug in a bit farther. Only about 5% of Eton's students are international. So let's lose them, and also lose the older murderer and the international murderer. Even using the highest murder rate from 2002, there is less than a 1% chance that they'd have had 2 or more murderers in a 30 year period.
That said, one correction. El Salvador had a murder rate in 2017 of 61.7/100,000. This is comparable to Eton.
Let's take your analysis a step farther. If we have 230 * 30 people, each of whom has 1.1 chances in 100,000 of committing murder, the number of expected murderers is 0.0759. And the distribution of number of murders is a Poisson distribution. That means that the probability of k murders is λ^k e^(-λ) / k!.
Therefore our estimates are:
Add those up and the expected probability of 4 or more murderers is only 1.3014245782150269e-06.Therefore, even with a small absolute number, we can be very sure that the true murder rate for graduates of Eton are significantly higher than the UK population.
However Eton does attract people internationally. And the international murder rate in 2017 was 6.1/100,000 per https://worldpopulationreview.com/country-rankings/murder-ra.... Using that as a murderer rate, the odds against Eton producing 4 murderers in 30 years improve...to about 1/1000. Which means that Eton's murders are still likely to not be chance.