Basic science: understanding numbers

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# 4.2.2 Using averages

When the average of a dataset is presented to you, you need to consider which type of average has been used. Consider the average number of feet a person has. Most people in the world have two feet, so the modal value will be two. Similarly, if you were to use the median average, you would also find the answer to be two, as a very small minority of people have fewer than two feet, so two would remain the middle number.

However, if you were to calculate the mean, you would find that the answer is no longer two. There are a minority of people with fewer than two feet, for a variety of reasons, but this is enough to reduce the mean ever so slightly. As a result, almost everyone has more than the mean number of feet.

That’s enough about feet. Let’s instead consider the average of a scientific dataset. Average monthly rainfall is worked out from the recorded rainfall for that month over a specified number of years. The numbers below are the recorded January rainfall (in millimetres) for London, UK over 10 years. For simplicity these are arranged in order of smallest to highest.

17, 19, 51, 56, 69, 72, 72, 74, 75, 77

The data show that January rainfall has ranged from 17 mm to 77 mm in the ten years that this dataset covers. The mean average rainfall is 58 mm to 2 sig figs. Do you agree that the average rainfall should be reported to 2 sig figs?

The median rainfall is the middle value in this list. Because there are an even number of years in the sample, there is not a single middle value. Instead, both 69 and 72 are the middle numbers. The median is calculated as the number midway between these two numbers and is therefore 71 mm to 2 sig figs. The mode is the most common value, which is 72 mm.

This demonstrates perfectly the sensitivity of the mean average to extreme values. The mean average is lower than the median or mode averages due to the two very dry Januarys, which experienced only 17 and 19 mm of rain.

You will return to average rainfalls later this week when you look at plotting and interpreting graphs.

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