Suppose you learn that in an exam in a large class a majorit

Suppose you learn that in an exam in a large class, a majority of the students scored above the mean. Then you would conclude:

Select one:

A. the distribution of scores is left skewed

B. the distribution is symmetric.

C. that whoever said this made a mistake. This is impossible.

D. the distribution of scores is right skewed

Solution

I\'m kind of astonished all of you answered this incorrectly. I really hope you all aren\'t purposely trying to sabotage the question asker. That would be pretty low. The correct answer is \"A. the distribution of scores is left skewed.\" Here\'s why:

50% of the data lies above the median and 50% lies below. That\'s just what median is. Knowing if the mean falls above the median or below tells us if the majority of the data lies above or below the mean. So, if the mean is above the median, we know that more than 50% of the data lies below the mean (that\'s the 50% below the median, plus whatever % is between the median and the mean). In the question, a majority (i.e. more than 50%) lies above the mean. This tells us that our median must greater than the mean. Median > mean is a fundamental characteristic of a unimodal LEFT SKEWED data set. Think about it... if your graph is skewed left, you use the median to describe a typical center value because the lower data is pulling the mean too far to the left. Since your median is to the right of the mean, you know that more than 50% of your data is above the mean (the 50% above the median plus the % between the mean and the median.

If you need more convincing, I just answered this exact question on my quiz and got it correct.