Edited to 8 testers (not 9)
I feel like this is probably an extremely easy question but I am unable to articulate my question to google to find an answer.
Basically, referring to the image below, there are 5 tests and 8 testers, each test has a percentage success rate. What I want to know is why the overall percentage success rate, 83% (417%/500%) differs from the individual counted success rate, 75%. The individual counted success rate is the sum the individual successes (6) over overall testers (8).
Your help is much appreciated.
Because the $67$% (well, actually $\frac{200}{3}$) and $50$% data is from $3$ and $2$ testers as opposed to the $100$%s which are only from $1$. In other words, the lower data counts for more of the data.
You should multiply the % by the corresponding number of testers when doing your calculation, so:
$$\frac{(50\% \cdot 2)+(\frac{200}{3}\%\cdot3)+3(100\%\cdot 1)}{2+3+3}=\frac{600}{8}=75\%$$