What Does Median Mean?

The median is a central tendency, and with this measurement, you will find the observation or observations that are in the middle of the data set. The median is a good key measurement when the data set has extreme values, as these are not taken into account.

The median is the value of the middle observation when the values are sorted in ascending order.

Rule

ToFindtheMedian

• Sort the numbers in ascending order.

• When you have one number in the middle, this is the median. This happens when the number of observations is an odd number.

• When you have two numbers in the middle, you have to add them and divide the sum by two. The answer you get is the median. This happens when the number of observations is an even number.

Example 1

You asked eleven students in your class about how many pennies they have in their pocket. The result was:

$\begin{array}{cc}5\phantom{\rule{9.71999pt}{0ex}}20\phantom{\rule{9.71999pt}{0ex}}15\phantom{\rule{9.71999pt}{0ex}}30\phantom{\rule{9.71999pt}{0ex}}1\phantom{\rule{9.71999pt}{0ex}}84& \\ 52\phantom{\rule{9.71999pt}{0ex}}8\phantom{\rule{9.71999pt}{0ex}}32\phantom{\rule{9.71999pt}{0ex}}41\phantom{\rule{9.71999pt}{0ex}}18& \end{array}$

 $5\phantom{\rule{9.71999pt}{0ex}}20\phantom{\rule{9.71999pt}{0ex}}15\phantom{\rule{9.71999pt}{0ex}}30\phantom{\rule{9.71999pt}{0ex}}1\phantom{\rule{9.71999pt}{0ex}}84\phantom{\rule{9.71999pt}{0ex}}52\phantom{\rule{9.71999pt}{0ex}}8\phantom{\rule{9.71999pt}{0ex}}32\phantom{\rule{9.71999pt}{0ex}}41\phantom{\rule{9.71999pt}{0ex}}18$

What is the median?

First, sort the numbers in ascending order:

$\begin{array}{llll}\hfill & 1\phantom{\rule{7.92491pt}{0ex}}5\phantom{\rule{7.92491pt}{0ex}}8\phantom{\rule{7.92491pt}{0ex}}15\phantom{\rule{7.92491pt}{0ex}}18\phantom{\rule{7.92491pt}{0ex}}20\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & 30\phantom{\rule{7.92491pt}{0ex}}32\phantom{\rule{7.92491pt}{0ex}}41\phantom{\rule{7.92491pt}{0ex}}52\phantom{\rule{7.92491pt}{0ex}}84\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Here the middle number is 20, that is, the median is 20.

The median was 20 in Example 1. So there are just as many who have less than 20 pennies as there are people who have more than 20 pennies in their pocket.

In the example, there were 11 observations, which is an odd number. When you find the median of an odd number, there is always one number in the middle. If you had 10 observations, which is an even number, there would be two numbers in the middle. To find the median, you must then add the two numbers in the middle and then divide the sum by 2.

Example 2

You ask 10 other students in your class about how much money they have, and get these numbers:

$\begin{array}{cc}11\phantom{\rule{9.71999pt}{0ex}}101\phantom{\rule{9.71999pt}{0ex}}2\phantom{\rule{9.71999pt}{0ex}}8\phantom{\rule{9.71999pt}{0ex}}35& \\ 5\phantom{\rule{9.71999pt}{0ex}}48\phantom{\rule{9.71999pt}{0ex}}56\phantom{\rule{9.71999pt}{0ex}}8\phantom{\rule{9.71999pt}{0ex}}9& \end{array}$

 $11\phantom{\rule{9.71999pt}{0ex}}101\phantom{\rule{9.71999pt}{0ex}}2\phantom{\rule{9.71999pt}{0ex}}8\phantom{\rule{9.71999pt}{0ex}}35\phantom{\rule{9.71999pt}{0ex}}5\phantom{\rule{9.71999pt}{0ex}}48\phantom{\rule{9.71999pt}{0ex}}56\phantom{\rule{9.71999pt}{0ex}}8\phantom{\rule{9.71999pt}{0ex}}9$

What is the median?

You sort the numbers in ascending order

$\begin{array}{llll}\hfill & 2\phantom{\rule{7.92491pt}{0ex}}5\phantom{\rule{7.92491pt}{0ex}}8\phantom{\rule{7.92491pt}{0ex}}8\phantom{\rule{7.92491pt}{0ex}}9\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & 11\phantom{\rule{7.92491pt}{0ex}}35\phantom{\rule{7.92491pt}{0ex}}48\phantom{\rule{7.92491pt}{0ex}}56\phantom{\rule{7.92491pt}{0ex}}101\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

You now have two numbers in the middle, both 9 and 11. By using the average formula (of the two middle values), the median becomes
 $\frac{9+11}{2}=\frac{20}{2}=10$

The median is 10.