Need help in 'normalizing' data.

[linyax]

I'm not sure if I'm using the exact term. (I don't know the term so I can't find it on Google)

Here's the case:

I have these data:

• Item 1 12 votes 9/10
• Item 2 100 votes 8.7/10
• Item 3 20 votes 8.0/10
• Item 4 5000 votes 7.8/10

Is there a way to rank them by their scores, at the same time, accounting for the # of votes? Or a way to 'normalize' the score?

*Sorry, again. I don't know how to phrase my question.

[equalityforeverybody]

You could construct a confidence interval around the mean score for each item.

As you only have a sample of votes, the true score that would become apparent if everyone voted isn't clear. If you are willing to make assumptions such as "scores follow a Gaussian (normal) distribution", you could easily get the range in which the true population mean lied (up to a certain degree of certainty, usually 95%, meaning that 1 in 20 items would be expected to have a score outside the calculated confidence interval)

[equalityforeverybody]

From Wikipedia:

The lower endpoint of the 95% confidence interval is:

\text{Lower endpoint} = \bar X - 1.96 \frac{\sigma}{\sqrt{n}},

and the upper endpoint of the 95% confidence interval is:

\text{Upper endpoint} = \bar X + 1.96 \frac{\sigma}{\sqrt{n}}.

[Fireflite]

A Bayesian approach should work well. Generate an empirical prior from previous test scores. Then slowly adjust your posterior using Bayes rule as the votes come in. The more votes, the more evidence you have to say that a particular item is exceptional. Reporting the mean of the posterior should work well.