- The curve is characteristically bell-shaped. The highest point of the curve is in the
centre and the tails extend out both sides of the centre to the ends of the distribution in
a smooth fashion. - The curve is symmetric. If the curve were folded in half at the centre, the left side
would be a mirror image of the right side.
The normal distribution is useful for not only providing a standard against which other
empirically derived distributions can be compared, but it also plays a very important role
in inferential statistics. The reason is because many naturally occurring phenomena, such
as height or weight of subjects, approximate to a normal distribution in the population.
Many statistical tests assume values in a data set represent a sample from a population
which has an underlying normal distribution.
When looking at a data distribution it is sometimes difficult to judge how non-normal
the data is. Two measures of shape sometimes help, these are skewness and kurtosis.
Skewness is an index of the extent to which a distribution is asymmetrical or non-
normal. (Recall a normal distribution is perfectly symmetrical.) A skewed distribution
departs from symmetry and the tail of the distribution could extend more to one side than
to the other. This would indicate that the deviations from the mean are larger in one
direction than the other. If the tail of a distribution extends to the right it has a positive
skew (think of positive as being on the right side). The mean is pulled to the right of the
median. If the tail of a distribution extends to the left it has a negative skew (think of
negative to the left side). The mean is pulled to the left of the median.
Figure 3.17: Positively and negatively
skewed distributions
Initial data analysis 67