Question

A private college advertised that last year their freshman students, on average, had a score of 1120 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.

A. Next year at least one of their freshman students will have a score of at least 1120 on the exam.
B. Last year some of their freshman students had a score of more than 950 on the exam.
C. Last year at least one of their freshman students had a score of 1120 or above on the exam.
D. Last year more than half of their freshman students had a score of at least 1120 on the exam.
E. Last year some of their freshman students had a score of exactly 1120 on the exam.
F.None of the above statements is true.

Answer 1

Answer: Option B and option C are both correct

Step-by-step explanation: In basic statistics, the mean or the average of a set of data simply refers to a value that is a good and acceptable representative of the whole data observed. By representation, this means not all in the class of observed data has the exact value that is given as the average, but the better majority of the observed data is very close to the value taken as average or mean.

If the college gave the average exam score as 1120, what this simply implies is that the college is very confident that the better majority of the students scored either slightly below 1120, or slightly above 1120. Having an exact score of 1120 is a little bit possible but having a little less than or a little more than 1120 is highly possible.

So the figure given as average doers not actually refer to the score of any particular student(s) but it actually represents a large majority of the test participants, such that if any one of them is chosen randomly, there is a very good chance that he would score either a little below 1120, or a little above 1120.

So option B (Last year some of their freshman students had a score of more than 950 on the exam) is correct and option C (Last year at least on of their freshman students had a score of 1120 or above on the exam) is equally correct.