Question

A private college advertised that last year their freshman students, on average, had a score of 1100 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 more than 1000.

Last year, the number of their freshman students who had a score of more than 1100 or was equal to the number of their freshman students who had a score of less than 1100.

Last year all of their freshman students had a score of at least 1100.

Next year at least one of their freshman students will have a score of at least 1100.

Last year some of their freshman students had a score of exactly 1100.

None of the above statements.

Answer 1

In the list provided, only one statement is always true. This statement is as follows:

Last year some of their freshman students had a score of more than 1000.

(Tick box corresponding to this statement only)

This statement is always true because if the scores of all students in less than 1000 than average cannot be 1100.

Reason why other statements are not always true:

Last year, the number of their freshman students who had a score of more than 1100 or was equal to the number of their freshman students who had a score of less than 1100. --> This statement is false because mean does not always divides the dataset into half. Median divides the dataset into two half.

Last year all of their freshman students had a score of at least 1100. --> This statement can only be true in one condition when all student scores equal marks that is 1100.

Next year at least one of their freshman students will have a score of at least 1100. --> This statement is prediction so it will not always be true.

Last year some of their freshman students had a score of exactly 1100. --> This statement is not always true as the mean doesn't have to be in the list of numbers.