# How can I calculate a percentage with a third factor? (two schools voting separately)

#### checifaccioqui

##### New member
How can I calculate the percentage considering a third factor? Immagine that two schools have voted. In the first there are 330 candidates, the total votes are 1400 and the winner get 120 votes. In the second school there are 150 candidates, the total votes are 900 and the winner get 44 votes. How could you calculate the percentage of each winner considering not only the rate between votes of winner and Total votes but number of candidates too. Thanks in advance.

#### tkhunny

##### Moderator
Staff member
If only that were a well-defined problem statement...

Are the 150 candidates a subset of the 330 candidates?
Are the schools related?
What does "get's 120 votes" mean? Did the winner have 120 votes cast and this was the greatest amount of votes for a single candidate or do we have no idea how many votes were cast for the winner, but for the victory "120 votes" were awarded.

#### checifaccioqui

##### New member
If only that were a well-defined problem statement...

Are the 150 candidates a subset of the 330 candidates?
Are the schools related?
What does "get's 120 votes" mean? Did the winner have 120 votes cast and this was the greatest amount of votes for a single candidate or do we have no idea how many votes were cast for the winner, but for the victory "120 votes" were awarded.

Nope.. they are two different schools with two different votings.
In the first school the candidate won with 120 votes (so got the largest amount of votes), in the second school the largest amount of votes was 44.

In order to compare these two winners I need to consider not only the votes given to the winners on the total votes but the number of candidates too.

#### tkhunny

##### Moderator
Staff member
Nope.. they are two different schools with two different votings.
In the first school the candidate won with 120 votes (so got the largest amount of votes), in the second school the largest amount of votes was 44.

In order to compare these two winners I need to consider not only the votes given to the winners on the total votes but the number of candidates too.
Why isn't percentage of total vote good enough?

#### checifaccioqui

##### New member
Why isn't percentage of total vote good enough?
If you have to find which of the two winners has got the best result you should consider the number of candidates too.

#### Jomo

##### Elite Member
If you have to find which of the two winners has got the best result you should consider the number of candidates too.
Why??

#### tkhunny

##### Moderator
Staff member
How can I calculate the percentage considering a third factor? Immagine that two schools have voted. In the first there are 330 candidates, the total votes are 1400 and the winner get 120 votes. In the second school there are 150 candidates, the total votes are 900 and the winner get 44 votes. How could you calculate the percentage of each winner considering not only the rate between votes of winner and Total votes but number of candidates too. Thanks in advance.
If you have to find which of the two winners has got the best result you should consider the number of candidates too.
Okay...

"Expected" is the average number of votes per candidate if votes are distributed evenly (which is a silly assumption unless it's a blind vote).

(Observed - Expected) / Expected

(120 - (1400/330))/(1400/330) = (120 - 4.24)/4.24 = 27.30

(44 - (900/150))/(900/150) = (44 - 6)/6 = 6.33