Median and Mean

Median

The median is the second of the three 'm' words which children associate with averages and easily confuse... As with the mode, it's an easy figure to find although it can take a little working out. The median is the middle figure. The one which stands in the middle when you put all the data in order from smallest to largest (or largest to smallest, it really doesn't make any difference!)

For example, if you want to find the median figure from the following set of data, you need firstly to arrange the figures in order.

Once arranged from smallest to largest, we get:

As there are seven figures, the one in the middle will be the fourth. In this case, it is '6' and this is the median.

The rule for finding the median is easy as long as the number of items in the list is an odd number. In the example, there was a clear 'middle' figure so we could simply state it. However, it is conceivable that a paper may ask for a median figure from an even-numbered set of data. In this case, you need to find the halfway point between the two central figures and give this, rather than list both figures as you would with the mode.

What is the median figure in the following data?

Rearrange the numbers in order:

There are six numbers so the central one doesn't exist; the midway point is between the third and fourth number. Halfway between 4 and 5 is 4.5 ( 4 + 5 divided by 2 ).

The median figure is 4.5

Mean (Average)

The mean is the posh way of saying the average. It means the total divided by the number of items. Unlike the mode, range and median, the mean will require some proper maths to work out.

Find the mean of the following figures:

There are six terms in the data set. They can be added up together (6 + 4 + 8 + 10 + 9 + 5) to give 42.

The mean is the total divided by the number of items, so 42 ÷ 6 = 7. The mean is 7.

The answer that a child gets should always be looked at in retrospect and compared to the data set. If the average is outside of the range of the figures given, it is wrong. It is impossible to have an answer which is lower than the lowest figure in the series or is higher than the highest figure. Some common sense can save lots of marks and only takes a second to apply! Similarly, if the number is very close to either extreme of the figures, check them carefully.

What is the mean height of five children, whose heights are given below:

Firstly, as all of the heights are 1.xx we can discount this first digit and just put it back on at the end. We can only do this because all of the figures are 1.xx and if even one of them is different, it is not possible.

So, we can add them all together and divide by the number of heights (5)

Using our short-cut, all we really need to add are 4, 16, 30, 14 and 26. These add up to 90. 90 ÷ 5 = 18 so the average of these figures is 18; if we now replace the 1.xx that we took off to start with, the average height is 1.18m. If this short-cut complicates things for you, simply add all the heights together without amending them, and divide by 5. The answer will be the same.