Question

90% of scores are better than average

On a certain statistics test, the professor said that 90% of the students scored better than average. Discuss whether or not this is possible.

Answer 1

Answer 2

This statement appears to be logically contradictory, as it suggests that 90% of scores are better than the average. However, by definition, the average represents the midpoint of all scores, meaning that exactly 50% of scores are better than the average and 50% are worse than the average.

If 90% of students scored better than the average, it implies that the average score is higher than the majority of scores, which is not possible if the average is indeed calculated correctly. This discrepancy might arise due to a misunderstanding or miscommunication of the professor's statement.

It is essential to note that an average can take different forms, such as the mean, median, or mode. If the professor meant that 90% of students scored better than the median or mode, it would be feasible, as these measures are not necessarily representative of the midpoint in skewed distributions. However, the mean, which is commonly referred to as the average, should always have 50% of scores above and below it.

In conclusion, the statement that 90% of scores are better than the average is not possible when considering the mean as the average, but it could be possible with other measures like the median or mode, depending on the distribution of scores. Clarification from the professor would be necessary to understand the intended meaning accurately.