What is the difference between median and average?

Answer 1

If I remember correctly, there are four types of averages:

mean: this is what most people think of as the "average" of a bunch of numbers. The mean of 2 and 8 is 5.

mode: this is the number that occurs most in a set of numbers. The mode of 2, 2, 2, 5. and 9 is 2.

median: this is the number that occurs in the middle of a set of number when they're arranged from lowest to highest. If there are two middle numbers, take the mean of them. The median of 1, 2, 3, 4, 5, 6, and 7 is 4. The median of 1, 2, 3, and 4 is (2 + 3) / 2, or 2.5.

range: this is the biggest number in a set minus the smallest number. The range of 1, 4. 9, and 12 is (12 - 1), or 11.

I think that's all correct. Hope that helps.

Edit:

All definitions are correct except that the range is not an average, it is a measure of spread. To be considered along with more complicated stuff like inter-quartile ranges, standard deviations and so on.

Edit2:

In analysis there are several other ways to calculate the "average":

Range Average is the mean of the lowest and highest values.

Quartile mean is taking the center most 50% of the values adding them up and dividing by the number of them.

Quartile Range Average is adding the 1st and 3rd quartiles and dividing by two. (the 1st quartile is the value that is greater then 25% of the values and less then 75% and the 3rd quartile is greater then 75% and less then 25%). "Bucket Modes" can also be calculated for an average. A bucket mode is calculated by finding the mode not of a single value but over a range of values or the range of values that combined have the greatest occurrence.

Any method can also be calculated be excluding data points. The most common is to exclude outliers. Outliers can be defined as any of the top and or bottom data points that lie in the top or bottom x% (i.e. exclude the top 3% or the top 15%). Outlier can be defined as being over x deviations away from a central point where x is typically 3, 2, or 1.5 but can actually be any number).

In some analysis the number crunchers can and often do through out any numbers that they suspect are questionable, don't look right, or they do not want to use.

In statistics they also use a term "Expected Value" to refer to an average. Depending on the dispersion of the data the method of calculating the Expected Value changes. Often, this becomes a calculus or differential problem. The basic idea is the that the expected value is calculated to make the sum of the differences between the data points and the Expected Value to be the smallest.

This is not an exhaustive list. When modeling the world, analysis can create various schemes for defining a way to calculate average. The idea is to create a way to calculate a number that will express the central tendency of the data points or to come up with a value that can be used to correctly estimate the data points in calculations.

Answer 2

The median is one measure of the average,