# Question: In the Olympic Games when events require a subjective judgment

In the Olympic Games, when events require a subjective judgment of an athlete’s performance, the highest and lowest of the judges’ scores may be dropped. Consider a gymnast whose performance is judged by seven judges and the highest and the lowest of the seven scores are dropped.

a. Gymnast A’s scores in this event are 9.4, 9.7, 9.5, 9.5, 9.4, 9.6, and 9.5. Find this gymnast’s mean score after dropping the highest and the lowest scores.

b. The answer to part a is an example of (approximately) what percentage of trimmed mean?

c. Write another set of scores for a gymnast B so that gymnast A has a higher mean score than gymnast B based on the trimmed mean, but gymnast B would win if all seven scores were counted. Do not use any scores lower than 9.0.

a. Gymnast A’s scores in this event are 9.4, 9.7, 9.5, 9.5, 9.4, 9.6, and 9.5. Find this gymnast’s mean score after dropping the highest and the lowest scores.

b. The answer to part a is an example of (approximately) what percentage of trimmed mean?

c. Write another set of scores for a gymnast B so that gymnast A has a higher mean score than gymnast B based on the trimmed mean, but gymnast B would win if all seven scores were counted. Do not use any scores lower than 9.0.

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