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>Life expectancy is a weighted average

Sure, if all the weights are 1. Where i come from, we just call that an average.

>People who die early drag the average down much more than people who live close to the mean life expectancy.

This is true of all averages where all weights are the same.

I should probably have said the change in life expectancy is a weighted average, weighted by how far you are from the average. If average life expectancy is 80, removing a data point where somebody died at 40 has 8x the effect of removing a data point where somebody died at 75.

Ok, that makes a lot more sense in light of your argument!

In case anyone else is curious about the specific term for the concept you are describing, it's https://en.wikipedia.org/wiki/Leverage_(statistics)

(To reproduce exactly the scenario being discussed, you fit a constant-only model to the data using least squares: that gives the average as the best fit. Then, you measure the leverage of each point of interest.)

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