# What is the difference between discrete data and continuous data? Do data ranking a TV show on a scale from 1 to 4 count as discrete or continuous?

Jul 28, 2017

A good analogy is this:

Discrete data is to integers as continuous data is to real numbers.

#### Explanation:

Discrete data can only take on countably many values. The values may be integers, rationals, or irrationals; that doesn't matter. What matters is the acceptable data points fall into distinct "number categories". Quite often, it makes sense that discrete data are measured without any kind of "margin of error".

Examples include things like:

• number of children in a family (0, 1, 2, 3, ...)
• things rated on a scale from 1 to 5 (1, 2, 3, 4, 5)
• cups of flour in different recipes ($0 , \frac{1}{4} , \frac{1}{2} , \frac{3}{4} , 1 , 1 \frac{1}{4} , \ldots$)
• etc.

Continuous data can take on infinitely many values, with potentially limitless decimal digits. Because of that, we usually define a precision level to which we round such data. As such, it is easy to see there may be a margin of error for each data value.

Examples include:

• time taken to run 100 metres (rounded to nearest 0.01 second)
• length of a drive to work (rounded to nearest 0.1 km)
• weight of students' backpacks (rounded to nearest gram)
• etc.

With these definitions in mind, it is easy to see that data ranking a television show on a scale of 1-4 counts as discrete data. The possible values are finite, and they are like notches on a ruler.