The Wisdom of the Crowd

Sir Francis Galton was a statistician in the 19th century. Thanks to him we have concepts such as correlation and standard deviation.  Galton, it would seem, thought through the filter of statistics, a genius who produced hundreds of papers and books on fields as diverse as meteorology, historiometry and psychometrics and who pioneered the use of questionnaires to gather better information for his statistical analyses.

Last week, at my school’s Open Evening, we conducted a mathematical experiment based on one of Galton’s observations.  Galton was at a county fair in 1906 where he came across a competition to guess the weight of an ox.  The statistician in him was intrigued, and following the event he studied the 800 or so entries, stumbling upon a remarkable observation: the median estimate (which he termed the vox populi) was accurate to within 0.8% and the mean of the estimates was in fact completely correct*.

We were pretty intrigued, so we decided to conduct our own experiment.  Unfortunately the ox didn’t pass the Health and Safety checks, so utilising child labour and bribery instead we counted midget gems into a huge jar and then asked visiting parents and children to guess how many there were.  To ensure they didn’t influence each other, no-one saw any previous estimates.

The jar of midget gems (the morning after – it was full but didn’t stay so for long).  Our results are below.

midgetgems

By the end of the evening we had 114 estimates, ranging from 170 to 2120.  Their mean was 730.

The actual number of midget gems?

731.

Wow.


* This story opened James Surowiecki’s 2004 book The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations.

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One comment

  1. Reblogged this on mho maths and commented:
    Look, stats isn’t boring! I love doing these Wisdom of the Crowd exercises when teaching averages. Another way of doing it is to display a random scattering of dots on the screen (about 40 or so). Get everyone individually to provide an estimate then calculate the mean.
    A really interesting addition to this is to do it once getting everybody to call out their estimate. Then, before calculating the mean, give everyone the chance to change their estimate and record them all a second time.
    This can lead to regression to the mean, and standard deviation if you like.
    See – stats isn’t boring!

    Liked by 1 person

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