Seventy-one point four percent of statistics are made up

There are many times when I am amused or amazed by the use of statistics (and mathematics) in newspapers and magazines, sometimes because the writer has not understood what he or she is writing about, or because a sub-editor has allowed a numerical error or anomaly through to print, or because some number is just plain silly.

The claim in the title of this piece is one such.

My latest toe-curling experience has come from the magazine of a very large supermarket chain in the UK.  In the pages devoted to preparing for Christmas, there are the following statistics, with my comments in []:

• 8:39am - the time when the average family takes its first bite of chocolate on Christmas Day.  [Not 8:38 or 8:40, please note]
• 38 - the number of days women spend on average preparing for Christmas [how do you decide if a day is spent preparing for Christmas or dealing with daily living?]
• 27 - the number of mince pies we each consume over the festive season [not the average, but "the number"]
• 83 - square kilometres of wrapping paper will end up in UK bins this Christmas, enough to cover an area larger than Guernsey [It sounds an impressive figure, but that amounts to just over one square metre of wrapping paper per person in the UK.  That's about three sheets; how many sheets do you need for each large present?]

Now let's think how the first statistic might have been calculated.  Somebody wants to know how early in the morning people start eating chocolate on Christmas Day.  It's not a survey that they want to spend a great deal of money on, so they will interview a hundred or so people, probably not chosen in any well-designed sample.  And how will those people answer?  Nobody will answer to the nearest second, or even the nearest minute.  Answers will be "About nine am", "round about 11am", "when we finish breakfast, say 8:15am", "Whenever the kids open their stockings - last year at 6:15am". And of course those figures are not precise, and certainly not the result of a minute-by-minute analysis of the family's programme for Christ's Birthday.  Then the analyst takes the mean (or median, but probably not the mode!) and presents it as a scientific result.  So what might be a more convincing way of presenting such an earth-shattering statistic?  Perhaps: "Half the population of the UK have eaten some chocolate by 9am on Christmas Day" taking the median as the summary statistic that is most appropriate for such vague data.

The second and third statistic are probably derived in the same way; their analysis and derivation are left to the reader to consider.  And I have reinterpreted the fourth one for you.

Just remember - you will eat this number of mince pies: