How do I properly average these percentages?

Question

I have attendance records for an annual event:

person 1: $4$ of $8$ attended $= 50.00$%, or every $2$ years

person 2: $1$ of $4$ attended $= 25.00$%, or every $4$ years

person 3: $4$ of $5$ attended $= 80.00$%, or every $1.25$ years

I want to show the percentage of events attended by the average person, so I aggregate the data, weighing each person equally:

Avg attended $= 52$%

Avg time interval = every $2.4 y$

The odd thing is this: $52$% attendance to an annual event does not correlate to attending every $2.4$ years. It correlates to every $1.9$ years.

So which is true of the above data? The average person comes $52$% of the time OR the average person comes every $2.4$ years? They can't both be true. Where have I gone wrong?

Thank you very much for the help.

Answer 1

In certain situations, especially many situations involving rates and ratios, the harmonic mean provides the truest average.

https://en.wikipedia.org/wiki/Harmonic_mean

Answer 2

So, it turns out the answer is fairly simple. Lets take some intervals, as we did above:

person 1: every $1$ year

person 2: every $2$ years

person 3: every $5$ years

Average those together and you get a value of :

average person: every $2.67$ years

This is wrong. Imagine a 10 year interval and ask how many events each person attended:

In $10$ years each person would attend:

person 1: attends $10$ events

person 2: attends $5$ events

person 3: attends $2$ events

Average those together:

average person: attends $5.67$ events in $10$ years OR $.567$ events per year OR every $1.76$ years, which is the correct answer

Arithmetic Average of the intervals is meaningless. So, how do you average $(1,2,5)$ together and arrive at an answer of $1.76$?

Harmonic Mean, just as CAGT mentions above. Thanks everyone for the help!