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Almost all above average

This morning James Grime tweeted about a BBC News article, “‘Third of UK postcodes’ have slow broadband speeds“. This quotes Julia Stent, director of telecoms at uSwitch saying:

Britain might be riding the wave of a super-fast broadband revolution, but for 49% who get less than the national average broadband speed, the wave isn’t causing so much a splash as a ripple.

Now, the thrust of the article, that broadband speeds are undesirably slow in some parts of the country, might be valid, but the appeal to the “average” is a very weak argument (Update [23:47]: Although, please see the comment below). The result that 49% are below average should not come as a big surprise!

James, rightly, questions which average is most appropriate, but I am more interested in a tweet by Ian Preston:

We can make almost everyone above average if we are happy for one person to be really badly off.

This, of course, is quite right.

Unless I’m reading it wrong (and I may well be), the Bank of England’s Lending to Individuals December 2011 has outstanding net lending to individuals as £1451.4 billion. The UK Office for National Statistics gives the Public Sector Net Debt excluding financial interventions as £988.7 billion (January 2012) and Total population (UK) as 62.3 million (mid-2010).

If we gave one person all that debt and everyone else zero, then a simple average would be £2.44 trillion divided by 62.3 million people, which is £39,167

Since almost everyone is worth zero, we would almost all be 39 thousand pounds above average. Sound good? This would sort out Government debt and make almost all of us “above average”. And if we’re “above average” then, erm, everything is fine, right?

(Flaws in the argument left as an exercise for the reader!)

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About the author

  • Peter Rowlett teaches mathematics at university and is interested in maths education and communicating maths. His column at The Aperiodical is Travels in a Mathematical World.

6 Responses to “Almost all above average”

  1. Tony

    Many years ago an optician told me my eyesight was “average”. I replied that I was surprised because all my friends seemed to be able to see much better than I could, to which he replied that “almost everybody has better than average eyesight.” (Which is possibly true.)

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  2. Peter Rowlett

    Isn’t this like “most people have an above average number of legs”? I don’t have any numbers to back this up and I know eyesight is less discrete than a missing leg or two, but still: some people have poor to no eyesight; no one has better than two eyes that don’t need glasses.

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  3. Peter Rowlett

    In relation to the opening bit of this:

    By email, Katie Steckles pointed out this post by Ben Goldacre on the same subject.

    Commenters on Ben’s post say that it’s mathematically possible for less than 49% to be below the mean but that practically it shouldn’t come as a surprise for broadband speeds. This is how I read it, and I guess James did too given his tweet “Half of us have less than average broadband speed shocker”.

    However, commenter @AllTheGraemeS suggests that the quote is saying “those 49% who get below average get a rum deal” rather than calling for “everyone to be above average”, i.e. saying “the slow end of the distribution is objectively too slow” rather than “slow relative to the average”. Reading it again I can see this is probably there in the text, although it is a bit ambiguously put.

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