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The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?Group of answer choices75% of the students sampled had textbook costs that exceeded $500.The average of the 500 textbook costs was $500.25% of the students sampled had textbook costs that exceeded $500.75% of the students sampled had textbook costs equal to $500.

Question

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value 500.Whichofthefollowinginterpretationsofthe75thpercentileiscorrect?Groupofanswerchoices75500. Which of the following interpretations of the 75th percentile is correct?Group of answer choices75% of the students sampled had textbook costs that exceeded 500.The average of the 500 textbook costs was 500.25500.25% of the students sampled had textbook costs that exceeded 500.75% of the students sampled had textbook costs equal to $500.

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Solution

The correct interpretation of the 75th percentile being 500isthat75500 is that 75% of the students sampled had textbook costs that did not exceed 500. This means that the majority of students spent 500orlessontextbooksforthefallterm.The75thpercentile,alsoknownasthethirdquartile,isameasureofstatisticaldistribution,notanaverageoratotal.Therefore,itdoesnotmeanthattheaveragecostoftextbookswas500 or less on textbooks for the fall term. The 75th percentile, also known as the third quartile, is a measure of statistical distribution, not an average or a total. Therefore, it does not mean that the average cost of textbooks was 500, nor does it mean that 75% of students spent exactly 500.Italsodoesnotmeanthat25500. It also does not mean that 25% of students spent more than 500. Rather, it indicates that 25% of students spent more than $500 on textbooks.

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