Statistical skillsThe median

The median is the middle number. To calculate the median of any set of numbers, you need to write the numbers in order.

To find the median number:

• Put all the numbers in numerical order
• If there is an odd number of results, the median is the middle number
• If there is an even number of results, the median will be halfway between the two central numbers

Finding the median with an odd number of results

Finding the median with an even number of results

To find the median of numbers: 5, 11, 12, 4, 8, 21

Put the results in order: 4, 5, 8, 11, 12, 21

Find the two numbers in the middle: 4, 5, 8, 11, 12, 21

We need to find the value which is halfway between them.

Finding the median from a frequency table

Here are Kieran's results in a frequency table.

From the table, we can find the total number of albums:

As the results are in a table, they are already ordered for us. In this case, as there are 12 results. The median is between the 6th and 7th result.

We look at the frequency column and determine when the cumulative frequency passes the 6th and 7th results.(There is an explanation of cumulative frequency on page 2)

The first row has cumulative frequency 1.

The second row has cumulative frequency 5.

The third row has cumulative frequency 8.

The third row passes the 6th and 7th results so the median must be in there.

Median is 11 tracks.

For example:

For 5 numbers, the median is the (5 + 1) ÷ 2 = 3rd result

For 6 numbers, the median is the (6 + 1) ÷ 2 = 3.5th result (between the 3rd and 4th).