1. ## Percentile Rank

I just got an exam back and had this question wrong but the prof didn't explain how to do it properly:
" Of the 1000 students who took an exam, 480 scored below you, 100 had the same score as you and 420 scored above you. Find the percentile rank of your score."

Can someone explain how I should've done this?

4. ## Re: Percentile Rank

Think of this problem as a cumulative histogram with score in the exam along the x axis and the percentage of people (from 0 to 100) along the y axis. The percentile is calculated by ranking everyone's scores along the x-axis. As you do this, you get an increasing number on the y-axis corresponding to the score on the x-axis. When the scores are tied the percentile jumps at that point and then flattens for as many people as got the tied score as you all get awarded the same percentile. It then starts to rise again as the next highest score comes along.

You don't quite have all the information but you have enough information to calculate the percentile if you sketch it as a histogram and work out the percentages correctly.

The way I've suggested you construct the percentiles means that the 90th percentile is better than the 10th centile, but I did study somewhere whey they did it the other way round for some reason. I'm not sure if there's a 'right' or 'wrong' way to do it.

5. ## Re: Percentile Rank

What would the median of the distribution be in this case?

6. ## Re: Percentile Rank

So my guess would be (480 + 100) / 1000 = 58th percentile

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