6. Discrete and Continuous Data

The data we’ve looked at, throughout this course, have had a fixed range of values.

This data is known as, Discrete Data.

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We have not yet encountered data that could take any value within a defined range, known as, Continuous Data.

In this lesson, we’ll explore the difference between discrete and continuous data. Discrete data, refers to variables which can only take a specific, clearly defined, set of values.

Each of these values is distinct. And there’s a clear step between each value, with no other values in between.

Most commonly, discrete data, refers to data that can be counted using whole numbers.

Let’s consider the test-scores example, from a few lessons ago. In this test, students could score from zero to 50 points.

In this case, there are 51 possible values for a student’s test-score.

We can come-up with the numbers between zero and 50, that are not valid values, like, 36.5 or 46.72263.

As a result, the test-scores are discrete data.

Although most discrete data, refers to things we can count easily, it does not have to be numeric.

Non-numeric categories could be described as discrete data.

For example, the list of colors offered by a car manufacturer, may be extensive, but is limited. And can be called, discrete data.

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When discrete data is numeric, it’s not limited to whole numbers.

Consider the restaurant revenue, from the previous lesson.

Because money comes, in clear steps of one cent, it’s a discrete variable, as well.

In theory, the restaurant could make any amount of money. However, the revenue is still discrete. Because we can think of values that are not possible. Such as $1,000 and 17.6 cents.

Let’s now, consider continuous data.

Continuous data, refers to variables that can take-on an infinite number of different values.

Let’s assume, we measure the height of a group of people, in meters. We might measure one person as, 1.6 meters tall.

However, the person is probably not exactly 1.6 meters tall.

Maybe, they’re actually 1.581 meters tall and we just rounded that up, to 1.6.

But maybe, the person isn’t 1.581 meters tall either.

Maybe, they’re actually 1.58067 meters tall and we just can’t measure that, precisely.

In fact, if we had the ability to measure height with absolute precision, we could continue being infinitely, more and more precise about this person’s height.

As a result, we can say, that height is a continuous variable. Because we cannot define a specific set of values, that incorporate every possible height of any human being. To think of it another way, let’s assume, that any human in the world, will be between 0.5 and 2.5 meters tall.

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If this is the case, then, any value within that range, could be a valid height, for a human being. One person could be exactly 1.7 meters tall. Another could be 1.543454.

Someone else could be 1.865 meters tall and so on.

We cannot come-up with an impossible value in this range, like we could, with discrete data.

It’s not always clear, whether a variable is continuous or discrete.

In some cases, it may make sense, to ignore the proper classification of a variable.

Let’s consider money again.

In the real-world, we can only earn or spend money, in discrete units.

Therefore, we should, in theory, consider money to be a discrete variable.

However, to a business or government, whose income and expenditure, can be measured in millions or even billions, one or two cents, is unlikely to be a significant step-change.

As a result, money can be treated like continuous data, to these organizations.

Ultimately, whether data is discrete or continuous, can be based on what you’re doing with it. Rather than, some fixed, unchangeable property of the data. Understanding whether your data is discrete or continuous, will help you understand, how to go about analyzing it.

For example, analyzing continuous data, will often require you to create data bins, like we saw in the previous lesson.

However, you might be able to analyze discrete data, without doing this. Depending on how many values are present.

In the next lesson, we’ll look at, Correlation. Which is one of the most important, but often misunderstood concepts in Statistics.

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