The 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 the mean of the two central numbers.

Finding the median with an odd number of results

Using the same example, find the median number of tracks on Kieran's CDs.

Kieran's results were:

10  14  10  12  10  11  12  10  11  9  12

• Put the numbers in numerical order:
• 9  10  10  10  10  11  11  12  12  12  14

• Find the middle number:
• 9  10  10  10  10  11  11  12  12  12  14

The middle number is 11, so the median is 11.

Finding the median with an even number of results

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

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

• Find the middle number or numbers:
• 4 5  8  11  12  21.

If there are two central numbers, we need to find their mean.

The median is therefore:

(8 + 11) ÷ 2 = 9.5

Finding the median from a frequency table

• From the table, we can find the total number of CDs:
• 1 + 4 + 2 + 3 + 0 + 1 = 11 CDs

As the results are in a table, they are already ordered for us. In this case, the median is the 6^th result.

Looking at the table we can see that the first 5 CDs have either 9 or 10 tracks. The 6^th CD has 11 tracks. Therefore, this is the median.

If there are n results, the median will be the ^{n + 1}₂^th result.

For example:

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

For 6 numbers, the median is the (6 + 1) ÷ 2 = 3.5^th result.