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:
(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.