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Averages

I will keep it short and simple in this section!

Averages are so easy to calculate yet poorly applied these days that many people don't pay attention when so-called knowledgeable people present them.

In my opinion, the biggest plunders happen in the area of "economics." I must be careful with names, but I often listen to people on the television telling me about the average household income within a country and how this links to the wealth of that country. The same happens in the current public discourse about average wages within the NHS or the railway service. As much as I want it but I can rarely use these figures because the people who present this information rarely give advice about the data distribution. I know that this sounds absolutely geeky, but what follows next is a solid piece of statistics advice, so hear me out! I keep it entertaining for you!

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Here is a list of all household incomes of Brewlandia: By the way, these figures are not representative of any existing country but the pure imagination of my colorful mind. By pure coincidence, Brewlandia uses pound sterling as its official currency!

 ------- 30.500, 15.860, 19.210, 17,500, 22.900, 21.800, 50.400, 16.010, 60.500, 70.250 -------

The average household income is determined by adding all these figures and dividing them by the number of households.

Average household income of Brewlandia = 324.930 / 10 = 32.493GBP. As a spectator, I might be inclined to say: The country is doing well, as the average wages are pretty decent! But a savvy news consumer would object and ask what the median household income is. Median what?...

The median seeks to find the middle value of sorted data! For this, we would first need to sort all the listed incomes of Brewlandia, which would get us the following:

15.860, 16.010, 17.500, 19.210, 21.800, 22.900, 30.500, 50.400, 60.500, 70.250

The middle lies between 21.800 and 22.900, so we need to add these two together and divide it by two, which gives us: 22.350 as the median income.

The savvy consumer of today's news would then argue: Hold on, over half the nation's household incomes lie below 22.350, which is almost a third less than the average! Bingo!

You see, only 3 incomes (50.400, 60.500, and 70.250) are responsible for the relatively high average household income, which skews the outcome and make us believe things are pretty rosy. But by looking at the median too, we get the accurate picture so we can ask questions about income equality, etc…

Bare this in mind when you approach a set of data yourself! Always get an idea of the distribution of any data set first. A normal distribution which means relatively comparable figures, makes applying the mean /average more reasonable! However, as soon as we have some abnormal data, it pays to use the median!

Don't get fooled!

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