How do I properly average these percentages? 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.
 A: In certain situations, especially many situations involving rates and ratios, the harmonic mean provides the truest average.
https://en.wikipedia.org/wiki/Harmonic_mean
A: 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!
