Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Basic Concepts Definition of basic terms Population and Sample  
See also: Venn diagram, parameters, distribution, random variable, representative samples  
Population and Sample
In applied statistics, we have to differentiate strictly between populations and samples. Consider a box containing 500 balls of three different colors. This set of balls is called the population. Descriptive statistical measures e.g. the mean or the standard deviation, or in our example the number of red, green and blue balls, are called parameters if they are calculated from the population. If you select for example 50 balls out of this box  a subset of the population  this set of 50 balls is called a sample. A descriptive measure referring to a sample  here the number of red balls in the box estimated from the sample of 50 balls  is called an estimate (or statistic). Parameters are depicted by Greek letters, estimates are depicted by Latin letters.
The population, which is the basis of a statistical survey, has always to be defined in an exact way (which is not always easy) in order make sure that the results are comparable. The best way to go is to define not only the factual prerequisites ("what has to be analysed") but also the spatiotemporal general framework. In our example of 500 balls, the size of the population is finite. In many cases  especially with real measurements  the population size is infinite. For example, if the variable of interest is the concentration of oxygen in air, measured with some analytical device. The population is the (infinite) set of all (possible) measurements (= results derived from the analytical instrument). Another example is the number of cars driving on a particular section of a highway in the morning between 7am and 10am. The population of this variable is the number of cars using this highway during the defined time interval each day  as long as the highway exists.


Home Basic Concepts Definition of basic terms Population and Sample 
Last Update: 20121008