Page 173 - BA2 Integrated Workbook - Student 2017
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Risk 1: summarising and analysing data
4.2 Median
The median is defined as the middle of a set of values, when arranged in ascending
(or descending) order. This overcomes the above problem of skewed distributions
which can have unrepresentative mean values. The median will have half the
distribution above it, and half below.
The median is also unaffected by any particularly large or unusual individual
measurements whereas the mean would be.
If we rearrange our example in ascending order:
7 6 8 9 5 6 7 12 9 4 5 6
4 5 5 6 6 6 7 7 8 9 9 12
What is the middle number of a list of 12? With a little thought, you can see that there
are two ‘middle’ values, the sixth and seventh. The median is thus taken to be the
mean of these two values:
(6 + 7) ÷ 2 = 6.5
In the case of an odd number of values, the determination of the median is even
easier, as there is a clear single middle item in an odd number of values. In general,
if there are n observations, the position of the median is given by (n + 1) ÷ 2. .
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