I just took an online test and I was notified that the average score for the test was 45% (out of 100%) and I received a 72%.

Using these 2 pieces of information would it be possible to calculate under what percentile I fall for test scores?


No, that would not be possible without further information about the distribution.
Consider for example a situation where there were only 2 students, you got 72 and the other person got 18. In that case you did the best. Consider another alternative where two people got 0, you got 72, and 2 people got 73. In that case, you were right in the middle of the pack.


This is clearly impossible. To appreciate this just consider two possible scenarios of 100 people having taken the test so far.

  • 100 scored 45%
  • 45 scored 100%, 55 scored 0%

In the first case you are the best, in the second a bit above average.


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