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Worked Examples · Example 42

Q.Suppose your class teacher conducted a 20 marks unit test. You scored 12 marks and others obtained 20, 10, 18, 15, 6, 8, 2, 3, 5, 17, 19, 20. Find out your percentile rank of your score.

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✓ Free question

Including your own score, the class has 1313 scores in total; your score of 1212 marks corresponds to the 50th50^{th} percentile.

Percentile rank of an individual raw score: PR=B+0.5EN×100PR=\dfrac{B+0.5E}{N}\times100, where BB = number of scores strictly below XX, EE = number of scores equal to XX, and NN = total number of scores.

  1. List all scores (yours + the others): 12,20,10,18,15,6,8,2,3,5,17,19,2012,20,10,18,15,6,8,2,3,5,17,19,20. Total N=1+12=13N=1+12=13.
  2. Sort ascending: 2,3,5,6,8,10,12,15,17,18,19,20,202,3,5,6,8,10,12,15,17,18,19,20,20.
  3. Your score X=12X=12. Count scores strictly below 1212: 2,3,5,6,8,10⇒B=62,3,5,6,8,10\Rightarrow B=6. Count scores equal to 1212: only your own ⇒E=1\Rightarrow E=1.
  4. PR=6+0.5(1)13×100=6.513×100=50PR=\dfrac{6+0.5(1)}{13}\times100=\dfrac{6.5}{13}\times100=50.
  5. Self-check: 6.5/13=0.56.5/13=0.5 exactly, so PR=50PR=50 — meaning your score is right at the middle of the class (higher than half the students, lower than the other half). ✓
✓Final answer

Your percentile rank =50=50 (you scored higher than 50%50\% of the class of 1313)

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