Different Types of Data

Statistics revolves around the analysis of variables. A variable is the thing which we are measuring when we collect data. Suppose a teacher takes a survey amongst his students. If he wants to analyze their shoe size, the variable being measured would be shoe size. Often, experiments involve several variables, so it is important (especially when using calculators and software) to indicate which variable you are analyzing.

Qualitative data cannot be defined directly with numbers.
For shoes, qualitative variables could include: color, brand, smell, material, style...

Quantitative data inherently involves the use of numbers.
For shoes, quantitative variables could include: size, price, height, heel length, weight...

Though shoe size and weight are both quantitative variables that can be used to describe a shoe, the two are fundamentally different types of measurements. Shoe size is a discrete measurement because there are very specific shoe sizes, with no other choices. For instance, you may buy either a size 7 or size 7.5 shoe, but not a size 7.25... A shoe's weight is a continuous measurement. There are in fact an infinite number of possible weights for a shoe, even between 7kg and 7.5kg....

Shoe size moves in well-defined steps, so it is a good example of a discrete variable.

A shoe's weight may take any value within a range, so it is a good example of a continuous variable.