 What you need to know

Things to remember:

• We find the median by putting our numbers in order and searching for the middle number.
• When the numbers are in order, crossing them off in pairs, one on each end, will help you find where the middle number is.

The median, like the mean, is a way of finding a statistical average. The median is the middle number in an ordered list. Lists aren’t always ordered though, so ordering is often our first step.

Find the median of the following set of data

3          8          2          0          1          5          7

Step 1:  Put the numbers in order.

Note: It doesn’t matter if you put them in order from biggest to smallest or smallest to biggest, but USUALLY we’d go from smallest to biggest.

3          8          2          0          1          5          7

0          1          2          3          5          7          8

Step 2: Cross off the outside numbers in pairs until you get to the middle.

0          1          2          3          5          7          8

0          1          2          3          5          7          8

0          1          2          3          5          7          8

0          1          2          3          5          7          8

The median is 3.

Hint: The median is useful if you have a number that doesn’t seem right, like if it is really big or small (this is called an outlier). For example, if you got a measurement of 500cm when measuring somebody, you wouldn’t want this to affect your average.

Things get a little trickier if we have an even number of data.

Find the median of the following set of data

5          7          2          8

Step 1:  Put the numbers in order.

5          7          2          8

2          5          7          8

Step 2: Cross off the outside numbers in pairs until you get to the middle.

2          5          7          8

2          5          7          8

2          5          7          8

Hmmmmm. We’ve got to the middle, but there isn’t anything there. Let’s go back one.

2          5          7          8

So, we have 5 and 7 in the middle together. To find a median, we have to find the mean of these two numbers.

$$5+7=12$$

$$12\div2=6$$

So, the median is 6!

Example Questions

Step 1:  Put the numbers in order.

Note: It doesn’t matter if you put them in order from biggest to smallest or smallest to biggest, but USUALLY we’d go from smallest to biggest.

6          5          9          2          8

2          5          6          8          9

Step 2: Cross off the outside numbers in pairs until you get to the middle.

2          5          6          8          9

2          5          6          8          9

2          5          6          8          9

The median is 6.

Step 1:  Put the numbers in order.

Note: It doesn’t matter if you put them in order from biggest to smallest or smallest to biggest, but USUALLY we’d go from smallest to biggest.

2          8          4          1          10        6

1          2          4          6          8          10

Step 2: Cross off the outside numbers in pairs until you get to the middle.

1          2          4          6          8          10

1          2          4          6          8          10

1          2          4          6          8          10

We now need to find the mean of 4 and 6.

$$4+6=10$$

$$10\div2=5$$

So, the median is 5!