** Discrete vs Continuous Data **

Data is the most salient entity in statistics as it is necessarily the “study of the collection, organization, analysis, and interpretation of data”. The numerical data used in statistics fall in to two main categories. They are discrete data and continuous data.

**What is discrete data?**

If the numerical data can take only an at most countable number of values, then such data is called discrete data. An at most countable number is either finite or countable. An example will illustrate this further.

A five question test is given to a class. The possible number of correct answers a student can get is 0, 1, 2, 3, 4, and 5: only 6 possibilities, and this is a finite number. Therefore, if we collect data of the number of questions correctly answered by a student, then that particular data will be discrete.

In a game, one has to shoot a target. If we collect the data of the number of times one shot until he hit the target, then the values will be 1, 2, 3, 4 … and so on. Theoretically, these values need not have a finite limit. But these values are countable. Hence, the data we collected as “the number of times one shot until he hit the target” is a discrete data.

Discrete data most commonly occurs when the data can take certain values or when counting is done to take the data.

**What is continuous data?**

The numerical data that can take all the possible values within a range is called continuous data. Hence, if a continuous data falls in the range 0 to 5, the data points can take any real number value in between 0 and 5.

For example, if we measure the height of the students in a class, then the data points can take any real number value within the range of height of humans. But, if we add an additional restriction as “a student’s height to the nearest centimeter”, then the collected data will be discrete since it can take only a finite number of values. Similarly, an unrestricted measurement would always yield a continuous set of data in theory.

• Discrete data can take at most countable number of values, whereas continuous data can take any number of values. • Discrete data usually occurs when data is collected by counting, but continuous data usually occurs when data is collected by taking measurements. |