Thread: real world problem with 'average'

hi,

i have a real world maths problem to do with a voting system and the 'average'.

i have an online voting competition in our company for a childrens xmas art. there is a star rating (scale between 1-5) and you can vote on any or all pictures. both the 'average' of the star no. and the number of people who have voted is shown beside each picture.

i now see that some pictures have say 30 people voting on them while others mught have 4 people. however the more popular picture could have a lower average than the less popular one but the popular one may have received more '5' star votes. i was going to pick the winner based on the highest average.

is there some formula that would make this fairer i.e. using the no. of votes and the average.

thanks for any help...

Originally Posted by kieran5405

hi,

i have a real world maths problem to do with a voting system and the 'average'.

i have an online voting competition in our company for a childrens xmas art. there is a star rating (scale between 1-5) and you can vote on any or all pictures. both the 'average' of the star no. and the number of people who have voted is shown beside each picture.

i now see that some pictures have say 30 people voting on them while others mught have 4 people. however the more popular picture could have a lower average than the less popular one but the popular one may have received more '5' star votes. i was going to pick the winner based on the highest average.

is there some formula that would make this fairer i.e. using the no. of votes and the average.

thanks for any help...

There is no right answer for such problems, as I see it you want to discount the votes of people who actively dislike a picture in favour of those who like a picture.

One approach that you will probably not like is to determine the total number of different voter (if you can) and assume all have viewed all the pictures and those that have not voted for a picture would have given it a 3. Then use the average score over all viewers whether they voted or not.

I bet you have not recorded the IP addresses of the voters, have you?

This is a missing data/data imputation (a statistical term meaning to make up data) problem.

CB

i have recorded their ntusername for each vote they submitted...as they were only allowed to vote for each picture 1 time...so i could figure out the total number of individual voters who have voted.

so u think i should get this figure...and then subtract the figure from the no of voters each picture got...and then multiple this figure by 3. then add this figure to the picture's average.

this would be a fairer way of getting a winner???

Originally Posted by kieran5405

i have recorded their ntusername for each vote they submitted...as they were only allowed to vote for each picture 1 time...so i could figure out the total number of individual voters who have voted.

so u think i should get this figure...and then subtract the figure from the no of voters each picture got...and then multiple this figure by 3. then add this figure to the picture's average.

this would be a fairer way of getting a winner???

I would try it and see if you like the answer, there is no objectivly fair way to do this (possibly because you have no definition of fair).

There is an underlying assumption that every one who voted could have voted for all the pictures (either favourably or otherwise). If they did not vote for a picture they were indifferent to it so you impute a indifferent response for such a picture.

CB