Numerical methods


Numerical methods for summarizeing data can be classified into two categories:

1. Measures of location
2. Measures of variablitiy

We can add to these two a third one:

3. Measures of relative location



Measures of location

These measures give an idea about "where" the data are. They include:

a. Mean
b. Median
c. Mode
d. Percentiles
e. Quartiles



Measures of variability

These measures allow the observer to detect how much variation the data show.
Variation in data is an indication of uncertainty, and in management it is
looked at as a sign of risk.

They include:

a. Range
b. Interquartile range
c. Variance
d. Standard deviation
e. Coefficient of variation




Measures of relative location

The most important measure of relative location is the z-score. This measure
gives an indication of how distant the variable at hand is from the estimated
mean. That is, the z-score for item i (i=1,...,n) is:


    z-score(i) = [value(i) - sample mean] / (sample standard deviation)


Since the z-score is divided by the standard deviation, its value is
interpreted as the number of standard deviations from the mean. The location
of two different samples can be compared using this score.




Reference:

Anderson, D.R., D.J. Sweeny, and T.A. Williams (1999):  Statistics for
Business and Economics. South--Western.