Trciky averages
Which measure of average is appropriate depends not only on the data, but also on the question. For example, here's a story from the Manchester Evening News, telling us about how much money the average person is going to spend on things like Christmas presents, food and drink. They report the 'average', which is a bit vague, but let's assume it's the mean. Should they have used the mean?
The problem with money is that it frequently has a skewed distribution - some people spend a lot, most spend some, and a few spend a little. So, what measure should we use? The mean, the median (or something more obscure like the geometric mean)? For example, if 9 people spend 10 pounds on shopping, and 1 spends 910, the mean spend is 100 pounds. The median spend is 10 pounds. Which one is correct?
That depends on who you are, and what you want to know. The story is written well, because it's written from the perspective of the shops, and they report the mean. If I am a shop, I want to know how much money I am going to take in, if 1000 people come through my door. And, given that the mean is 100 pounds, the answer is 100,000 pounds.
If I am a person, I might want to know how much money to spend on my friends, to look about the same as them. The mean here is useless, and we instead want the median. Spending the median (a tenner, in this case) means that half the people will spend more, and half will spend less, and we'll be in the middle.
(Of course, another problem is that of getting things like confidence intervals and p-values. Economists have to grapple with that one a lot, but other social scientists, thankfully, can leave it to them - most of the time).
The problem with money is that it frequently has a skewed distribution - some people spend a lot, most spend some, and a few spend a little. So, what measure should we use? The mean, the median (or something more obscure like the geometric mean)? For example, if 9 people spend 10 pounds on shopping, and 1 spends 910, the mean spend is 100 pounds. The median spend is 10 pounds. Which one is correct?
That depends on who you are, and what you want to know. The story is written well, because it's written from the perspective of the shops, and they report the mean. If I am a shop, I want to know how much money I am going to take in, if 1000 people come through my door. And, given that the mean is 100 pounds, the answer is 100,000 pounds.
If I am a person, I might want to know how much money to spend on my friends, to look about the same as them. The mean here is useless, and we instead want the median. Spending the median (a tenner, in this case) means that half the people will spend more, and half will spend less, and we'll be in the middle.
(Of course, another problem is that of getting things like confidence intervals and p-values. Economists have to grapple with that one a lot, but other social scientists, thankfully, can leave it to them - most of the time).
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