suppose that your younger sister is applying for entrance to college and has tak
ID: 3044728 • Letter: S
Question
suppose that your younger sister is applying for entrance to college and has taken the SATs. She scored at the 78th percentile on the verbal section of the test and at the 93rd percentile on the math section of the test. Because you have been studying statistics, she asks you for an interpretation of these values. What would you tell her?
Response: I would tell her that out of all the people who took the verbal section, _________ % scored higher than she did and _____ % scored at or below her score. For the math section, ______% of those who took the exam scored at or below her score and __________% scored higher than she did.
Explanation / Answer
The most common definition of a percentile is a number where a certain percentage of scores fall below that percentile. You might know that you scored 67 out of 90 on a test. But that figure has no real meaning unless you know what percentile you fall into. If you know that your score is in the 90th percentile, that means you scored better than 90% of people who took the test. Suppose your exam score is better than 90% of the rest of the class. That means your exam score is at the 90th percentile (so k = 90), which hopefully gets you an A. Conversely, if your score is at the 10th percentile, then k = 10; that means only 10% of the other scores are below yours, and 90% of them are above yours; in this case an A is not in your future.Hence in this case
Response: I would tell her that out of all the people who took the verbal section, 22% scored higher than she did and 78% scored at or below her score. For the math section, 93% of those who took the exam scored at or below her score and 7% scored higher than she did.
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