To give an overview of a set of number, we can use mean or median. When to use mean and when to use median?

We can get the sum of numbers from mean, but not median. If we need the total value, mean is a good choice. If you want to eliminate the effect of some extrem value, we may use median. If we only care the overview of a set of number, median is also a good choice.

Examples

How much milk we should buy?

In this question, we care the total amount of milk consumed. Average consumption of milk per member is more useful than median of the milk consumption.

Should a student care mean or median of exam score?

Median if the student want to know his/her rank. There 50% of student have score higher and 50% of them have lower than median. Student can know he/she is in the upper half or lower half.

Truncated mean

Truncated mean is a mean value of a set of number with some maximum and minimum number removed. It strive a balance between mean and median.

This method is used in scoring method of some sport. If judges gives extremely high or low score, their score will be removed. It lowers the effect of bias of some judges.