Basic Math: The Median

The median is the middle number in a sorted list of numbers. In other words, it is the value that separates the higher half from the lower half in a data sample, population or probability distribution.

The benefit of median, particularly versus another type of average such as a mean, is that the median is not skewed by a small number of extremely large or small values. In this way, it can sometimes be more illustrative of the data set than a simple average. To say it another way, the median may sometimes be a better way to say what a “typical” value is. 

To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest. The median can be used to determine an approximate average, or mean, but is not to be confused with the actual mean.

Calculating the Median:

1. Sort the data set in ascending or descending order.
2. The median value in an odd-number data set is that number in the middle with the same number of values higher and lower than itself. 
3. In an even-numbered data set, the middle 2 values are averaged (added together and divided by two) to provide the median.

Example 1: take the numbers 1,3,3,6,7,8,9. The median is 6. There are 3 numbers larger and 3 numbers smaller.

Example 2: take the numbers 1,2,3,4,5,6,8,9. The median is 4.5. There are 3 numbers larger and 3 numbers smaller than the two remaining (4 and 5).

Remember, before calculating the median, the numbers must be sorted in ascending or descending order.

Excel Syntax
=MEDIAN (number1, [number2], …)

Arguments
number1 – A number or cell reference that refers to numeric values.
number2 – [optional] A number or cell reference that refers to numeric values.

In practice, I use medians frequently as my targets for net worth, as the net worth data for Americans captured and reported by the IRS is frequently done so using median values. In this type of calculation, understanding how much different a mean average is to a median average can be crucial. In fact, that difference alone frequently tells a story.