## Statistical Moments (and the Shape of Distributions)The mean and the variance provide
information on the location and variability (spread, dispersion) of a set of
numbers, and by doing so, provide some information on the appearance of the
distribution (for example, as shown by the histogram) of the numbers. The mean and variance are the first two For comparison, the
is
by definition is equal to zero. (One
might think of the mean as being that value of The second moment is recognized as the numerator of the variance
which gives information on the spread or scale of the distribution of numbers. The
third moment, is used to define the
Skewness is a measure of the symmetry of the shape of a distribution. If a distribution is symmetric, the skewness will be zero. If there is a long tail in the positive directin, skewness will be positive, while if there is a long tail in the negative direction, skewness will be negative. The fourth moment, is used to define the kurtosis of a distribution:
Kurtosis is a measure of the flatness or peakedness of a distribution. Flat-looking distributions are referred to as “platykurtic,” while peaked distributions are referred to as “leptokurtic.” |