All characteristics of a subject that can be measured are variables. These characteristics can vary between different subjects within a sample or within a population (like income, sex, opinion). The use of variables is to indicate the variability of a value. As as example, the number of beers consumed per week by students. The values of a variable constitute the measurement scale. Several measurement scales, or ways to differ variables, are possible.The most important divide is that between quantitative and categorical variables. Quantitative variables are measured in numerical values, such as age, numbers of brothers and sisters, income. Categorical variables (also called qualitative variables) are measured in categories, such as sex, marital status, religion. The measurement scales are tied to statistical analyses: for quantitative variables it is possible to calculate the mean (i.e. the average age), but for categorical variables this isn't possible (i.e. there is no average sex.Also there are four measurement scales: nominal, ordinal, interval and ratio. Categorical variables have nominal or ordinal scales.The nominal scale is purely descriptive. For instance with sex as a variable, the possible values are man and woman. There is no order or hierarchy, one value isn't higher than the other.The ordinal scale on the other hand assumes a certain order. For instance happiness. If the possible values are unhappy, considerably unhappy, neutral, considerably happy and ecstatic, then there is a certain...

Randomization is important for collecting data, the idea that the possible observations are known but it's yet unknown which possibility will prevail. What will happen, depends on probability. The probability is the proportion of the number of times that a certain observation is prevalent in a long sequence of similar observations. The fact that the sequence is long, is important, because the longer the sequence, the more accurate the probability. Then the sample proportion becomes more like the population proportion. Probabilities can also be measured in percentages (such as 70%) instead of proportions (such as 0.7). A specific branch within statistics deals with subjective probabilities, called Bayesian statistics. However, most of statistics is about regular probabilities.A probability is written like P(A), where P is the probability and A is an outcome. If two outcomes are possible and they exclude each other, then the chance that B happens is 1- P(A).Imagine research about people's favorite colors, whether this is mostly red and blue. Again the assumption is made that the possibilities exclude each other without overlapping. The chance that someone's favorite color is red (A) or blue (B), is P(A of B) = P (A) + P (B).Next, imagine research...