Difficulty of a Level Discrete or Continuous

Statistics and data management sciences require a deep understanding of what is the difference between discrete and continuous data  set and variables.

The similarity is that both of them are the two types of quantitative data also called numerical data. However, in practice, many data mining and statistical decisions depend on whether the basic data is discrete or continuous.

On this page you will learn:

• What is discrete data?Definition and examples.
• What is continuous data?Definition and examples.
• Discrete vs Continuous Data:Diferences.
• Comparison chart/infographic in PDF

What is Discrete Data? Definition, Examples, and Explanation

If you have quantitative data, like a number of workers in a company, could you divide every one of the workers into 2 parts? The answer is absolutely NOT. Because the number of workers is discrete data.

Let's define it:

Discrete data is a count that involves integers. Only a limited number of values is possible. The discrete values cannot be subdivided into parts. For example, the number of children in a school is discrete data. You can count whole individuals. You can't count 1.5 kids.

So, discrete data can take only certain values. The data variables cannot be divided into smaller parts.

How to display graphically discrete data?

We can display discrete data by bar graphs. Stem-and-leaf-plot and pie chart are great for displaying discrete data too.

Discrete data key characteristics:

• You can count the data.It is usually units counted in whole numbers.
• The values cannot be divided into smaller pieces and add additional meaning.
• You cannot measure the data. By nature, discrete data cannot be measured at all. For example, you can measure your weight with the help of a scale. So, your weight is not a discrete data.
• It has a limited number of possible values e.g. days of the month.
• Discrete data is graphically displayed by a bar graph.

Discrete data may be also ordinal or nominal data (see our post nominal vs ordinal data).

When the values of the discrete data fit into one of many categories and there is an order or rank to the values, we have ordinal discrete data. For example, the first, second and third person in a competition.

Discrete data may be also nominal where the data fit into one or more categories where there is no any order between the values. For example, the eye color can fall in one of these categories: blue, green, brown.

Examples of discrete data:

• The number of students in a class.
• The number of workers in a company.
• The number of parts damaged during transportation.
• Shoe sizes.
• Number of languages an individual speaks.
• The number of home runs in a baseball game.
• The number of test questions you answered correctly.
• Instruments in a shelf.
• The number of siblings a randomly selected individual has.

What is Continuous Data? Definition, Examples, and Explanation

As we mentioned above the two types of quantitative data (numerical data) are discrete and continuous data. Continuous data is considered as the opposite of discrete data.

Let's see the definition:

Continuous data is information that could be meaningfully divided into finer levels. It can be measured on a scale or continuum and can have almost any numeric value. For example, you can measure your height at very precise scales — meters, centimeters, millimeters and etc.

You can record continuous data at so many different measurements – width, temperature, time, and etc. This is where the key difference with discrete data lies.

The continuous variables can take any value between two numbers. For example, between 50 and 72 inches, there are literally millions of possible heights: 52.04762 inches, 69.948376 inches and etc.

A good common rule for defining if a data is continuous or discrete is that if the point of measurement can be reduced in half and still make sense, the data is continuous.

How to display graphically continuous data?

We can display continuous data by histograms. Line graphs are also very helpful for displaying trends in continuous data.

So let's sum the key points.

Continuous data key characteristics:

• In general, continuous variables are not counted.
• The values can be subdivided into smaller and smaller pieces and they have additional meaning.
• The continuous data is measurable.
• It has an infinite number of possible values within an interval.
• Continuous data is graphically displayed by histograms.

In comparison to discrete data, continuous data give a much better sense of the variation that is present.

In addition, continuous data can take place in many different kinds of hypothesis checks. For example, to evaluate the accuracy of the weight printed on the product box.

Examples of continuous data:

• The amount of time required to complete a project.
• The height of children.
• The amount of time it takes to sell shoes.
• The amount of rain, in inches, that falls in a storm.
• The square footage of a two-bedroom house.
• The weight of a truck.
• The speed of cars.
• Time to wake up.

When it comes to sampling methods, the measurement tool could be a restricting factor for continuous data. For example, if I say that my height is 65 inches, my height is not exactly 65 inches. That's just what my scale shows me. In fact, my height might be 65.76597 inches.

This should be taken into consideration if you perform market research and be careful about different scales, measurements, data collection methods, and data collecting tools.

Comparison Chart: Discrete Data vs Continuous Data

It is quite sure that there is a significant difference between the discrete and continuous data sets and variables. As they are the two types of quantitative data (numerical data), they have many different applications in statistics, data analysis methods, and data management.

Numerical data always include measuring or counting of numerical values. That is why, when we do something with discrete and continuous data, actually we do something with numerical data.

Some analyses can use discrete and continuous data at the same time. For instance, we could make a regression analysis to check if the weight of product boxes (here is the continuous data) is in synchrony with the number of products inside ( here is the discrete data).

Download the following comparison chart/infographic in PDF: Discrete data vs continuous data

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Source: https://www.intellspot.com/discrete-vs-continuous-data/

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