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The average trap
Have you ever read a sentence like: “The average european drinks 1 litre of beer per day”? Did you ask yourself who this mysterious “average european” was and where you could meet him? Bad news: you can’t. He or she doesn’t exist. In some countries, people drink more wine than beer. How about people who don’t drink alcohol at all? And children? Do they drink 1 litre per day too? Clearly this statement is misleading. So how did this number come together?
People who make these kind of claims usually get hold of a large number: e.g. every year 109 billion liters of beer is consumed in Europe. They then simply divide that figure by the number of days per year and the total population of Europe, and then blare out the exciting news. We did the same thing two modules ago when we divided healthcare expenditure by population. Does this mean that all people spend that much money? No. It means that some spend less and some spend more – what we did was to find the average.The average makes a lot of sense – if data is normally distributed. Normal distribution is the classic bell shaped curve.
The image above shows three different normal distributions. They all have the same average. And yet they are clearly different.What the average doesn’t tell you is the range of data.
Most of the time we do not deal with normal distributions either: take e.g. income. The average income (something frequently reported) would suggest that half of the people would earn less and half of them would earn more than the average. This is wrong. In most countries, many more people earn below the average salary than above it. How? Incomes are not normally distributed. They show a peak around a certain level and then have a long tail towards large salaries.
The chart shows actual income distribution in US$ for households up to 200,000 US$ Income from the 2011 census. You can see a large number of households have incomes around 15,000-65,000 US$, but we have a long tail skewing the average up.
If the average income rises, it could be because most of the people are earning more. But it could also be that a few people in the top income group are earning way more – both would move the average.
Task: If you need some figures to help you think of this, try the following:
Imagine 10 people. One earns 1€, one earns 2€, one earns 3€… up to 10€. Work out the average salary.
Now add 1€ to each of their salaries (2€, 3€….11€). What is the average?
Now go back to the original salaries (1€, 2€, 3€ etc) and add 10€ only to the very top salary (so you have 1€, 2€, 3€… 9€, 20€). What’s the average now?
Economists recognise this and have added another value. The “ GINI-Coefficient ” tells you something about the distribution of income. The “GINI-Coefficient”” is a little complicated to calculate and beyond the scope of this basic introduction. However, it is worth knowing it exists. A lot of information gets lost when we only calculate an average. Keep your eyes peeled as you read the news and browse online.
Task: Can you spot examples of where the use of the average is problematic?
More than just your average…
So if we’re not to use the average – what should we use? There are various other measures which can be used to give a simple mean figure some more context.
- Combine the average figure with the range; e.g say range 20-5000 with an average of 50. Take our beer example: it would be slightly better to say 0-5 litres a day with an average of 1 litre.
- Use the median: the median is the value right in the middle where 50% of values are above and 50% of values are below. For the median income it holds true that 50% of people earn less and 50% of people earn more.
- Use quartiles or percentiles: Quartiles are like the median but for 25,50 and 75%. Percentiles are the same but for varying percent ranges (usually 10% steps.) This gives us way more information than the average – it also tells us something about the distribution of data (e.q. do 1% of the people really hold 80% of the wealth?)