Functional Skills: Mean, Median, Mode and Range

Whenever people talk about an average value, they are usually referring to the mean. To calculate the mean, we need to add up all the values and divide by the number of values:

$text{Mean} = dfrac{text{Total of values}}{text{Number of values}}$

Note: the mean is affected by outliers – values that lie far outside the rest of the data.

The median is the ‘middle value’ of a data set. In order to find the median, we first have to put the data in order of size. There are then two methods we can use:

1. Cross out the first and last values, then the second and second last values and so on. Eventually we will be left with one or two numbers, depending on whether we had an odd or even number of values to begin with. If only one value is left, this is the median; if two values are left, the median is halfway between the two.
2. Let the number of values we have to begin with be $n$. We can calculate the position of the median value using the formula:

$text{Median} = dfrac{n+1}{2}$

Whatever number the formula gives, we count that number along the list of values. If the formula gives us a decimal, e.g. $10.5$, the median is half-way between the tenth and eleventh values.

The mode is the most frequent value in a data set. Finding the most is simple – just look for the value that occurs the most often.

Note: it is possible to have more than one mode or no mode at all if there are no repeated values.

Unlike the mean, median and mode, the range is not a type of average. The range is a measure of spread – it tells us how spread out our data is. To find the range, we subtract the smallest value from the largest value:

$text{Range} = text{Largest value}-text{smallest value}$