Question

Show all your work. Indicate clearly the methods you use. As part of the President's Challenge, students can attempt to earn the Presidential Physical Fitness Award or the National Physical Fitness Award by meeting qualifying standards in five events: curl-ups, shuttle run, sit and reach, one-mile run, and pull-ups. The qualifying standards are based on the 1985 School Population Fitness Survey. For the Presidential Award, the standard for each event is the 85th percentile of the results for a specific age group and gender among students who participated in the 1985 survey. For the National Award, the standard is the 50th percentile. To win either award, a student must meet the qualifying standard for all five events. Jane, who is 9 years old, did 40 curl-ups in one minute. Matt, who is 12 years old, also did 40 curl-ups in one minute. The qualifying standard for the Presidential Award is 39 curl-ups for Jane and 50 curl-ups for Matt. For the National Award, the standards are 30 and 40, respectively. Compare Jane's and Matt's performances using percentiles. Explain in language simple enough for someone who knows little statistics to understand.

Answer 1

If your score is the 85th percentile this means that your score is above the 85% of the total population. If your score is in the 50th percentile this means that your score is above the 50% of the population.

The qualifying standard for the Presidential award is the 85th percentile. The 85th percentile is going to be different depending on the age and gernder. Jane was able to meet the standard but Matt wasn't. This means that the score (40 curlups) is above the 85% of the total number of scores for the population of 9 year old girls, but is is below the 85% if the total number of scores in the population of 12 year old boys. This means that the performance of Jane was better.

The standar for the National award for Matt is 40, which was his own score. This means that Matt's score corresponds to the 50th percentile. Again, it is evident that the performance of Jane was better because her score was above the 85th percentile.