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

## Observations and Variables

We call a set of data derived from an object (experimental unit) an observation. Each object is measured according to various aspects, such as temperature, concentration of some constituents, frequency of occurrence of some phenomenon, etc. Each of these aspects is denoted as a variable or feature.  By assembling all available data on all objects we can build a matrix - a table where the columns represent the variables and the rows represent the measured observations.

As an example, we can take the list of physical characteristics of 10 persons. The objects of the matrix are the persons, the variables are the measured properties, such as the weight or the color of the eyes.

 Age[years] Sex Weight[kg] Eye Color Body Temperature[°C] individuum 1 42 female 52.9 brown 36.9 individuum 2 37 male 87.0 green 36.3 individuum 3 29 male 82.1 blue 36.4 individuum 4 61 female 62.5 blue 36.7 individuum 5 77 female 55.5 gray 36.6 individuum 6 33 male 95.2 green 36.5 individuum 7 32 female 81.8 brown 37.0 individuum 8 45 male 78.9 brown 36.3 individuum 9 18 male 83.4 green 36.6 individuum 10 19 male 84.7 gray 36.1

Depending on the nature of the measured item and the measurement process the variables may be further classified into discrete (nominal and ordinal scales) and continuous variables (interval and ratio scales). See the topic Scale of Measurement for more. The eye color is a discrete variable, the weight or the body temperature is a continuous variable.