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How do you avoid the issue of an item with a single 5-star rating getting a higher average rating than one with (99 5-star ratings and one 4-star rating)? How do you properly rank based on average star and frequency?

Sample name|No.of raters|star rating|average star rating
a          |10          |5          |5  
b          |100         |5,4        |4.8
c          |1000        |5,3        |4.5
d          |1500        |4          |4
e          |2000        |5,4,3      |4.2
ttnphns
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Cristiana214
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    While it's somewhat different in form, there's one suggested approach in [this answer](http://stats.stackexchange.com/questions/141540/ranking-batters-by-average-when-number-of-observations-innings-vary/141561#141561) – Glen_b Mar 16 '15 at 05:04

1 Answers1

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You can simply calculate average stars,

$$ \bar s = {\sum s_{i} \over n}, $$

but it's better to add a correction for total number of answers given. One way to correct is to add some "dummy" one star (e.g. $10$), so

$$ \bar s' = {\sum s_{i} + 10 \over n + 10}. $$

Items with a large number of votes see their modified average alter very little from their real average, but items with relatively few votes will see their modified average move considerably toward low values.

This is known as "Bayesian averaging". In effect, the items with many votes will rank higher than items with the same average but fewer votes.

Tomaso Neri
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