A Common Data Shape


THE
NORMAL
LAW OF ERROR
STANDS OUT IN THE
EXPERIENCE OF MANKIND
AS ONE OF THE BROADEST
GENERALIZATIONS OF NATURAL
PHILOSOPHY  IT SERVES AS THE
GUIDING INSTRUMENT IN RESEARCHES
IN THE PHYSICAL AND SOCIAL SCIENCES AND
IN MEDICINE, AGRICULTURE, AND ENGINEERING 
IT IS AN INDISPENSABLE TOOL FOR THE ANALYSIS AND THE
INTERPRETATION OF THE BASIC DATA OBTAINED BY OBSERVATION AND EXPERIMENT
William Youden
A lot of data shows shapes for which --
The shape is (approximately) symmetric.
The shape shows a single hump.
Tails die out quickly, in particular, outliers are absent.

Examples:   Kinds of data which may show this pattern:
  • Human measurements such as height, chest size, weight, body temperature, ...
  • Sizes of other organisms.
  • Repeated physical measurements and other experimental error data.
    (An example:   100 measurements of speed of light )
  • Weight of airborne cadmium dust per cubic meter of air.
  • Course Grades (Not always though.) Example

We ignore the formula for this curve.   ( If you insist on seeing it, look in the supplementary web sites.)   Perhaps this curve is called the "normal" curve, because some people regard the symmetric, one hump, fast fading tail, shape as the normal (usual) shape of data. It is also called the "bell shaped curve".
This curve is a convenient appoximation, in rather the same way foresters use a cone as a convenient approximation to the volume of a tree. Though tree is not really a cone, the approximation may suffice.
The normal distribution obeys the "2/3 rule" closely. 68% of the probabilty of the normal curve lies within one standard deviation of the center of the normal curve.

Other material on to the normal distribution

 

William Knight