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Mode, Median and Mean

While the mode, median and mean are all measures of average, there are fundamental differences between them all: when you hear politicians splitting hairs, they are often splitting hairs over the difference between the average – mean – value, or the typical – median – value for example.

Here is a list of properties of the mean, median and mode, illustrated using the list of numbers 2, 4, 6, 2, 3.

Mean – the average – found by adding up the numbers and dividing by the length of the list of numbers. The average of the above list is

The mean takes every value into account. It is the most accurate overall of the three measures of average.

The mean can be influenced extremely by extreme values. The mean of the numbers 2,4, 3, 12 isThe last value 29 is an anomaly. If we exclude it the mean isThis susceptibility of the mean to the influence of extreme values is a real disadvantage. Using it to calculate the average family income will result in Bankers bonuses and the Duke of Westminster's vast rental income being taken into account. 50% of income is earned by 5% of the population – the mean ignores this skewed distribution of income, making the typical income seem much larger than it is.

The mode is the most common value. The mode of the list 2, 4, 6, 2, 3 is 2. The mode can also be skewed by the circumstances in it is applied. If you apply it to the distance run by marathon runners for example, the mode will probably be 26 miles 385 yards – the distance of the race. Once someone has finished, they stop. Some people will not finish. Some people will not stop at the finish line – they will run forever. The most of most income distributions is quite low – either nothing or maybe the minimum wage, depending on whether you take the populace or only the employed population into account.

The median is the most typical value. It will measure the wage of the common man, and is probably the most useful single measure of the average wage for example. On the other hand the miserable poor and the stinking rich are not taken into account. The rich people represent the spark of genius that makes the economy advance. They invest and invent: take them away and we are all just average.

None of these measures is perfect. How to measure someone's pay if they have an expense account? You will be comparing wage earners with someone who gets free money frankly. And then how to compare with MP's, who have been making a criminal living out of every British taxpayer for the past 30 years?