Graphical Descriptive Techniques

All economic decisions must be made in the present under conditions of uncertainty about the future.   Thus, even if economic agents are able to formulate a rational strategy for achieving their objectives, they face unpredictable events in the future as they attempt to implement the strategy.  Statistical analysis provides a method of improving the possibility of success by incorporating better information from past events.

The first step in the process of statistical analysis is the identification of the population of interest.  Out of the undifferentiated natural and social environment, certain characteristics are defined and then applied to select out objects of interest.  In economics, these objects are often human beings, typically described as economic agents, although the population of interest may also be outcomes of the economic relationships between and among human beings, such as incomes, prices or quantities of output of particular commodities.  The unpredictable quantitative nature of certain objects, again incomes,  prices and output come to mind, defines such objects, for statistical purposes, as variables.  Collections of actual measurements of variable values is called data.

Data, which is by necessity information about the past, is the raw material that can be used to generate useful information for assessing future outcome probabilities. Raw data is rarely informative enough to be of immediate use.  In order for this data to serve this purpose, it must be transformed.  A first step in such a transformation may be the reorganization of the data into numerical categories and the subsequent presentation of this categorical information in graphical form.  What are some ways of doing this?
 
 

• Frequency Distribution

One way to present the raw data is to organize it into distinct numerical categories.  These categories can be thought of as sort of file folders, where each file folder represents data that falls within a given interval or range (We could write the range on the outside of the file folder).  These intervals are sometimes called classes.  If you assume, for the sake of visualizing this process, that the variable measurements are on index cards, then the process of organizing the data into classes is the process of placing the appropriate index cards into the appropriate file folders (classes).  The textbook provides the following formula for dividing data observations into classes (There is no firm rule here, but this method works as well as any):

Approximate class width=(Largest value minus smallest value) divided by the number of classes.

We can use the results of this reorganization to construct a frequency distribution.  Each class in the distribution has class limits [a minimum and maximum value for observations (index cards) placed into that class].  Let's take a simple example:  The price of a textbook was collected from several online booksellers and brick and mortar booksellers with the results as follows:  $90, $85, $78, $90, $92, $75, $85, $81, $95, $62, $75, $70, $90, $91, $82.  Firstly, apply the formula for determining class width.  What is the result?  Now place the observations in the relevant classes.  What you will have is a very meagre frequency distribution.  Why doesn't it make sense to construct a frequency distribution from the above data?  Try constructing your own example with more data (or find an example on the web or in a book in the library).
 
 

• Click here to read about histograms (courtesy David M. Lane)

 

 
 
 
 
 

To be continued.