Calculating a weighted avearge

Question

In a competition:

Play 1 has 25 people attend who give an average score of 24

Play 2 has 29 people attend who give an average score of 22

Play 3 has 34 people attend who give an average score of 27

Which play wins ?  How do I calculate a like for like result ?

Answer 1

The purpose of the mean, or average score, is to give a scaled figure so that direct comparisons can be made between different sized samples. In other words, the mean is a like-for-like statistic. Therefore Play 3 wins because it has the highest average.

When you have a mean value and a sample size, the sum of the data in the sample=mn, where m is the mean and n is the size. For example, Play 1 has a total score of 24×25=600, so dividing by 25 gives the mean score 24.

The weighted mean would be the total sum of the data divided by the sum of the sample sizes. Therefore:

(24×25+22×29+27×34)/(25+29+34)=

(600+638+918)/88=49/2=24.5 is the weighted mean. Note that the average score for Play 3 is the only score above the weighted average.