A student took two exams and achieved the 7th highest grade on each of them. Forty three students took one of the tests(Math) and 197 students took the other test(Geography). Compare his performance on the two tests in terms of percentile ranks. In which exam did he do better? Please show computations and explain.
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If you rank all the scores, you'll note the following
<br>Math: 6 persons scored higher and 36 persons scored lower than the test subject. I arrived at the 36 by subtracting the 7 highest scores (which includes the test subject) from the total number of candidates sitting for the exam (43 for math). Thus, 37 persons had a score lower than or equal to our test subject. Note the condition "lower than or equal to" and hence 37. Overall, 86.05 % (37/43)of the candidates taking the exam had a score equal to lower than our test subject. Thus the percentile ranking is 86.05.
<br>Geography: Once again 6 persons scored higher and 190 (197 less 7 highest) scored lower. Thus, 191 candidates scored lower than or equal to our test subject. Or in other words, 96.95 % or the scores were equal to or lower than our test subject.
<br>Overall, our test subject fared better in Geography than in Math. He/She managed to beat out 96.95 % of the candidates versus only 86.05 % of the candidates in the math sitting.
<br>Note that the percentile rank does not distinguish between the dispersion or absolute values in the scores. In order words, the 7th highest score in math could be 90 % and 58 % for geography. Also, the difference between the 7th highest and 8th highest scores may be different.
<br>Look at the excel spreadsheet to get a visualization of the ranking.