35 The normal curve
The ‘normal’ curve plays a pivotal role in statistics. It has been called the equivalent of
the straight line in mathematics. It certainly has important mathematical properties but
if we set to work analysing a block of raw data we would rarely find that it followed a
normal curve exactly.
The normal curve is prescribed by a specific mathematical formula which
creates a bell-shaped curve; a curve with one hump and which tails away on
either side. The significance of the normal curve lies less in nature and more in
theory, and in this it has a long pedigree. In 1733 Abraham de Moivre, a French
Huguenot who fled to England to escape religious persecution, introduced it in
connection with his analysis of chance. Pierre Simon Laplace published results
about it and Carl Friedrich Gauss used it in astronomy, where it is sometimes
referred to as the Gaussian law of error.
Adolphe Quetelet used the normal curve in his sociological studies published
in 1835, in which he measured the divergence from the ‘average man’ by the
normal curve. In other experiments he measured the heights of French conscripts
and the chest measurements of Scottish soldiers and assumed these followed the
normal curve. In those days there was a strong belief that most phenomena were
‘normal’ in this sense.
The cocktail party
Let’s suppose that Georgina went to a cocktail party and the host, Sebastian,
asked her if she had come far? She realized afterwards it was a very useful
question for cocktail parties – it applies to everyone and invites a response. It is
not taxing and it starts the ball rolling if conversation is difficult.
The next day, slightly hungover, Georgina travelled to the office wondering if
her colleagues had come far to work. In the staff canteen she learned that some
lived around the corner and some lived 50 miles away – there was a great deal of
variability. She took advantage of the fact that she was the Human Resources
Manager of a very large company to tack a question on the end of her annual
employee questionnaire: ‘how far have you travelled to work today?’ She wanted