Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Descriptive Statistics

Statistics plays an important role in the description of mass phenomena. It offers methods to summarize a collection of data. These methods may be numerical or graphical, both of which have their own advantages and disadvantages. Graphical methods are better suited for the recognition of patterns in the data, whereas numerical methods give well-defined measures of some properties. In general, it is recommended to use both approaches for the description of data.

Descriptive statistics is a branch of statistics which tries to describe observed data by collective parameters. It does not make any statements on the underlying population but simply describes the data as they are. Descriptive statistics uses the following ways to characterize and visualize the data:

  • Tabulation: Tabulating data is perhaps the most primordial way as the data are simply listed as they have been measured. The most common tabular representation is the arrangement in a matrix or grid, where the columns are the variables and the rows are the observations. A drawback of this primitive approach can be seen in the substantial difficulties of human beings to interpret numeric tables without additional data analysis.
  • Graphical representation: a graphical representation is more suited to immediately recognize relationship among the data. This is due to the visual perception system of humans, which is very good at recognizing patterns. However, one should be cautious when looking at graphical diagrams as the human perception system may be misleaded by specially designed diagrams. Typical graphical representations used in descriptive statistics are histograms, pie charts, or box plots.
  • Statistical parameters: Parameters describing one or more aspects of a dataset offer certainly the most neutral way to characterize the data. Typical parameters are the mean, the median, the standard deviation, or the correlation. However, since statistical parameters are univariate by their nature they largely reduce the information contained in the data.

Another major branch of statistics which extends and complements the mere description of data is inferential statistics.

Last Update: 2012-10-08