What would cause the mean to be less than the median

Question

What would cause the mean to be less than the median, and under what conditions would the mean and the median be close to one another?

Answer 1

Imagine a data set that is spread out totally evenly: {1,2,3,4,5,6,7}

 

If we calculate the mean  sum/# of values, we get 28/7 = 4

Likewise, we can see that the middle value (median) when the data points are laid out in order is also 4.

 

This answers your second question:  If the data are spread out evenly OR are bunched evenly on either side of the mean, then the mean and median will be about the same.  Think about this example: {3,3,3,4,5,5,5}.  These data point are grouped evenly on either side of them mean, so the mean and median will also be the same.

 

HOWEVER, if we bunch data near the bottom, things change: {1,1,1,4,4,4,4}

By observation, we can see that the median is 4, but the individual values are skewed toward the low end, so the mean will be lower.  19/7 = 2.71 (rounded). 

 

So, we can conclude that if the data are bunched up at one end (but there are still plenty of middle values), then the mean will move toward that end, and the median will remain the same.