Variable, element, data set, and observation

This lesson will explain the meaning of variable, element, data set, and observation. These are some important basic terms to understand in statistics. 

Pretend that you use cluster sampling to estimate the number of gifted students each state has. You pick 5 states and you ended with the following sample. 

Note that the table below does not show real statistical data.

States in the USA       Number of gifted students
Massachusetts          500

New York




Data set

The information given in the table above is a data set. It is just a collection of data usually organized with a table.


Each of the states listed in the table is an element or member of the sample. For example, New York is a member or element of the sample.

An element could be an item, a state, a person, and so forth.           


The value assigned to only one element is called an observation. For example, 600 is an observation. An observation is also called measurement.


Anything that can take on different values is called a variable. Therefore, number of gifted students is a variable since it has different values.

Other examples of variables could be number of students who graduate from college, income of senior citizens, types of health insurance plans people enrolled in.

Notice that the variable types of health insurance plans will not give you numbers. More on this type of variable in the next lesson.

You can use any letter of the alphabet to represent a variable. The ones that we prefer to use are x, y, or z.

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