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Average and spread


If you have a set of data, say exam marks or heights, and are told to find the ‘average’. So what’s an average? An average indicates the typical value of a set of data, and it could be done in three different ways, which are  are mean, median and mode.

(a)The median

The median is the middle number. The data is arranged in order from the smallest to the largest; the middle number is then selected. This is really the central number of the range and is called the median.

If there are two ‘middle’ numbers, the median is in the middle of these two numbers.

(b)The mean

The mean is the most common measure of average. All the data is added up and the total divided by the number of items.

This is called the mean and is equivalent to sharing out all the data evenly.

(c)The mode

The number of items which occurs most frequently in a frequency table is selected. This is the most popular value and is called the mode (from the French ‘à la mode’ meaning ‘fashionable’).

Each ‘average\ has its purpose and sometimes one is preferable to the others.

The median is fairly easy to find and has an advantage in being hardly affected by untypical values such as large or very small values that occur at the ends of the distribution.

(d)Range

In addition to knowing the centre of a distribution, it is useful to know the range or spread of the data.
Range = (largest value) - (smallest value)
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