A private college advertised that last year their freshman students, on average,

Question

A private college advertised that last year their freshman students, on average, had a score of

1200

on the college entrance exam. Assuming that average refers to the mean, which of the following claims must be true based on this information?

Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.

Last year some of their freshman students had a score of less than 1400 on the exam. Last year, the number of their freshman students who had a score of 1200 or below on the exam was equal to the number of their freshman students who had a score of 1200 or above on the exam Next year at least one of their freshman students will have a score of at least 1200 on the exam. Last year all of their freshman students had a score of 1200 or above on the exam Last year some of their freshman students had a score of exactly 1200 on the exam. None of the above statements is true.

Explanation / Answer

Since mean provide the average of all values and it is in the middle if the distribution is symmetric. But in the given case it is not given that the distribution is symmetric, so we cannot assume that mean is in the middle. So none of the given statement is true. Hence, last option is correct.

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