Statistical concepts
Population refers to the entire group for which a statistical survey has been conducted. If there is talked
about 19 years old, so the population is all 19-year-olds in the world. As can already be seen from the example, it is impossible to get data from the entire population for research. For this reason, statistical studies use a sample, in which case a smaller group is used to describe the data of the population in question.
The sample (and also the population) consists of observations. Observation is, for example, all collected data of one 19-year-old, such as gender, height, municipality of residence, etc. A statistical variable is a property whose value varies for different observations. For example, the sample in Figure 1 includes gender, education, occupation and salary as statistical variables. The gender, judging by this image, can be either female or male. Education varies between primary and secondary level education.
The apples I bought cost half of the pears but they were two times tastier.When dealing with statistical data, you MUST be aware of what kind of variables are used. In previous sentence, price is numerical but taste is categorical variable. Categorical variables cannot be compared like mentioned in the sentence. What does it even mean: two times tastier? Is it based on my taste or yours?
As can be seen in Figure 2, statistical variables are divided into categorical variables and numerical variables.
Categorical variables divide observations in mutually exclusice groups (sex, opinion etc.) For example, the program of a university student is in a nominal scale, as it only divides students according their major. If groups could be sorted in a logical order, the variable is said to be in an ordinal scale. For example, education has a logical order: primary school, secondary school, tertiary level etc.
Numerical variables are naturally real numbers:
- If a property does not disappear at zero, then a variable is in an interval scale (temperature). Ratio of actual values have no meaning.
- If the property "disappear" with the value 0, the variable is in a ratio scale. Ratio of actual values has a meaning: an object A of 15 kg, an object B of 45 kg => the object B on 3 times heavier than the object A. The unit of variables in an interval or in a ratio scale is not fixed. For example, weight can be given in kilograms or in pounds.
- If the variable behaves like in a ratio scale BUT the unit is fixed, then the variable is in an absolute scale (the number of people).