Question

A student went around the math department and asked the professors how many tattoos they have when taken as a fraction of the total body surface area, (for instance a full back tattoo would be 1/4 body coverage) the student found that the median for the tattoo coverage was 3/10 but the mean was 3/5. What could explain this difference.

Answer 1

Median is low and mean is large. This means the distribution is right skewed (positive skew). Positive skewness indicates that the values less than the median lies closer to the median whereas the values greater than the median are more spread out. The positive skewness indicates the presence of large outliers too. In this case, the outliers can be one or two professors who have full body tattoos. That is coverage around 9/10. This value(s) causes the mean to increase but the median is not affected by the presence of an outlier.

Therefore, a possible explanation is that one or two professors will have very high tattoo coverage compared to the rest of the group.