Page 209 - BA2 Integrated Workbook STUDENT 2018

Risk 1: Summarising and analysing data

Measures of spread

Having obtained an average value to represent a set of data, it is natural to question
the extent to which the single value is representative of the whole set. To do this we
have to consider how ‘spread out’ the individual values are around the average.

5.1 Range

The range is defined as the highest value minus the lowest value. For example, if
measuring heights then the range is the difference in height between the tallest and
shortest persons measured.

However, this definition can be misleading. Where the data is arranged in classes:

Range = Upper most interval limit – Lowest interval limit

Where the data is not grouped, the range is best viewed as the number of values
from the very bottom to the very top and is given by:

Range = Highest value – Lowest value + 1

These apparently different definitions amount in practice to the same thing.

In our example:

4 5 5 6 6 6 7 7 8 9 9 12

The range is 12 – 4 + 1 = 9

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