Question

How can a median be greater than the mean?

Answer 1

Hint: We first explain the concept of median and mean. We draw the events where the median value is greater than the mean. We explain the skewness and big difference between numbers which allows the median to be greater.

Complete step-by-step solution:
The mean will be lower than the median in any distribution where the values decrease from the middle value faster than they increase from the middle value.
The median of a set of numbers is the value that is in the middle. In a set with an odd number of values, it's the middle value. In a set with an even number of values, it's the mean of the two middle values. The mean is generally understood as average, where the sum of the values is divided by the number of values.
We can do it by taking a set of numbers and skewing the values to be very low below the median and just above the median. For instance, if we take a set of five numbers and set the middle value as 10, we can place the two lower values at 1 and 2 and the higher values at 11.
We take the distinct values of 1, 2, 10, 11, 11.
We take the mean as \[\dfrac{1+2+10+11+11}{5}=7\] and the median value is 10. We can see that the median value is greater than the mean.

Note: We also have another point of view about such cases. The data are skewed to the left, with a long tail of low scores pulling the mean down more than the median. There is one definition of Pearson's skewness. However, skewness is also, perhaps more often, defined in terms of the third moment, and with this definition, it need not be true.