Exploring data: graphs and numerical summaries
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# 5.9 A note on accuracy

To what accuracy should you give the results of calculations? If you look through the examples in this section, you will find that, in general, results have been given either to the same accuracy as the data or rounded to one decimal place or one significant figure more than is given in the data. There is no hard and fast rule about what you should do: appropriate accuracy depends on a number of factors including the reliability of the data and the size of the data set. However, you should avoid either rounding the data too much, so that valuable information is lost, or too little, thus suggesting that your results are more accurate that can be justified from the available data.

As a rough guide, it is usually satisfactory to round a result to one significant figure more than is given in the data. But note that this rough guide applies only to results quoted at the ends of calculations: intermediate results should not be rounded. If you round a result and then use the rounded value in subsequent calculations – for instance, if you use a rounded value for the mean when calculating the standard deviation of a data set – then this sometimes leads to quite serious inaccuracies (known as rounding errors).

In Example 1, the mean was rounded to two decimal places before calculating the residuals. The squared residuals were also rounded before finding the standard deviation. This was done simply for clarity of presentation.

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