Discrete vs. Continuous Data: All You Need to Know

We rely on numbers to tell the time, measure things, understand reports, and more. This article explores the two data types these numbers typically fall into—discrete and continuous variables. It helps you know what they mean and their applications, similarities, differences, and features.

Discrete and continuous data are often structured data—structured and unstructured data (1) are two other unique data types. 

The global business sphere generates about two exabytes of this data daily: about 2,000 trillion bytes of data every day. IDC predicted that the worldwide volume of newly created data would grow 44 times to 35 Zettabytes (35 trillion gigabytes) in 2020.

According to most estimates, ten to 20 percent of this data is structured data—discrete and continuous data.

Let’s explore these data types.

Discrete vs Continuous Data: Similarities and Differences

Before diving into their similarities and differences, let’s take a look at what they mean.

What Is Discrete Data?

A discrete data is a variable that’s countable in a finite amount of time.

‘Discrete’ is an English word that means separate, distinct, individual, and not connected to or part of something else. Discrete data are concrete, round, and unique numbers that are not part of a whole—instead, they’re whole numbers.

This data type only takes specific values, and the variables are not divisible.

For instance, the number of cars in a garage is discrete, and the number is not divisible. You can count up to nine vehicles, but there could never be something like nine and a half cars.

Of course, this is because a car is not divisible into two.

The United States population estimate is at 331,002,651 people (2). 

Something like 331,002,651.5 people is never obtainable anywhere; this is because a half-human doesn’t exist, making population figures discrete variables.

Other examples of discrete data include:

  • The number of students in college
  • The number of words in this article
  • The number of houses in the city
  • Number of days in the month
  • Number of Covid-19 cases
  • Number of books in the library
  • The number of UN member-nations

What Is Continuous Data?

Continuous data is a quantitative data type that’s hard to count, and it’s easily divided into smaller meaningful units.

To be ‘continuous’ means to go on without a break, cessation or interruption. Continuous data lies between two whole numbers, and this makes it exist in a continuum. For instance, infinite numbers of possible values lie between two and three, for example, 2.000001, 2.1707430, 2.999999, and up to infinity. 

This data type can take any value and often changes with time. A straightforward way to determine if data is continuous is to divide the measurement into two and see if it still makes sense.

One and a half cars don’t make sense, but two and a half liters of water or 4.25 yards of fabric do, of course, because 0.5 liter and 0.25 yards are meaningful units for measuring water and fabrics, respectively.

Other examples of continuous data include:

  • The temperature in California
  • The heights of pupils in a classroom
  • The population growth rate
  • Speed of a car
  • The Square of a football field
  • Weight of newborn babies in a hospital

Discrete vs Continuous Data Similarities

Discrete and continuous data share some similarities. Here are some of them:

  • Statisticians can extrapolate and interpolate the two data types. Extrapolation uses historical trends of data to forecast the future, while interpolation estimates the unknown value in a time series.
  • Discrete and continuous data are both quantitative data.
  • The two data types are also sometimes qualitative.
  • Discrete and continuous data are easily representable in graphs.
  • They provide valuable insights for data-driven decision-making.
  • Discrete data can easily convert to continuous data and vice versa.
  • Users can evaluate them using both mathematical and statistical techniques.
  • Survey forms help in collecting the data.
  • Discrete and continuous data have wide use cases.

Discrete vs Continuous Data Differences

We’ve seen their similarities, let’s explore the key areas they differ:

  • Discrete data countable while continuous are not but measurable.
  • It’s easy to divide continuous data into smaller meaningful data, which doesn’t work for continuous data.
  • Discrete data usually occurs in whole numbers, while continuous data often exist as fractions and decimals.
  • Discrete data shows scattered data points on a scatter plot, while the scattered diagrams of continuous data show some pattern.
  • Histograms are great for presenting continuous data, while bar charts and pie charts work best for discrete data.
  • Continues can take any value, while discrete data only takes a specific value.
  • Continuous variables are dependent on time, while discrete data doesn’t.
  • Discrete data have a finite number of values between data intervals, while continuous have an infinite number of possible values.
  • Measurement devices help users collect continuous data, while headcounts are the most seemingly effective ways to collect discrete data.

Advantages and Disadvantages

Discrete and continuous data are both beneficial to data analysts, and they also have their shortcomings. Here we’ll take a quick dive at their advantages and disadvantages.

Discrete Data Advantages

Here are some of the advantages of discrete data:

  • The values are easy to count and often don’t require expensive instruments to collect the data.
  • Discrete data is easy to present in graphs, making the data easily understandable.
  • Statisticians can extrapolate the data series to forecast the future.
  • It provides valuable insights to individuals, businesses and governments.

Continuous Data Advantages

Here are some of the advantages of continuous data:

  • Continuous data is easy to divide into smaller units.
  • The data always end products of precise measurement.
  • Continuous data can take an infinite number of values, making them more accurate than discrete data.
  • Like discrete data, continuous data easy to present in graphs provides valuable insights, and data analysts can extrapolate it.
  • Continuous data can show how variables change over time, for example, population growth rate.
  • Fractions (continuous data) help people quickly see how variables make up a whole or proportion of a variable to the whole, for example, the proportion of houses in Michigan to the entire U.S.
  • Plotting continuous data on a scatter plot helps analysts determine the relationship between variables.

Discrete Data Disadvantages

Here are some of the disadvantages of discrete data:

  • A scatter plot of discrete variables doesn’t show any relationship between the variables.
  • Discrete data is easy to divide into smaller manageable units.
  • The data contains fewer details like continuous data.
  • They are not products of precise measurement.

Continuous Data Disadvantages

Here are some of the disadvantages of continuous data:

  • It’s difficult to count and read.
  • Continuous data has a lot of gray areas; they’re confusing to work with.
  • Measuring or collecting continuous data might require investment in costly devices.

Discrete vs Continuous Data: Side-by-Side Comparison

We’ve just seen the areas discrete and continuous data share some similarities, where they differ and their advantages and, of course, their disadvantages.

But how do they compare side-by-side?

Let’s take a look.

Key Characteristics

Discrete and continuous data are identifiable by their distinct features. How do these data types compare in key characteristics?

Discrete Data Key Characteristics

Here are the key defining features of discrete data:

  • Discrete data usually occurs in whole numbers
  • The data is easily countable
  • It’s impossible to divide them into meaningful units
  • Discrete data is finite; it has a limited number of possible values, for example, the world’s population.
  • It’s often unquantifiable with measuring devices, like with scales, meters, tape rules and others.
  • Discrete data is best shown graphically with bar charts, pictograms, pie charts, scatter plot graphs.
  • It’s generally independent of time. This data type doesn’t show any relationship with time.

Continuous Data Key Characteristics

Here are the key differentiating features of continuous data:

  • Continuous data are decimals.
  • The data easily divides into smaller meaningful units
  • People can measure continuous data. A thermometer can measure temperature, while a rain gauge can take recordings of a rainfall volume.
  • Continuous data is best shown graphically with histograms and line graphs.
  • Continuous data are often dependent on time. The data values always change with time, for example, room temperature, car speed, and a baby’s weight. 
  • The data is infinite within an interval (let say, between five and seven).

The Key Takeaway

The primary defining feature of discrete is, it’s countable while continuous data is not.

Value

What type of numerical values do they assume?

Discrete Data Value

Discrete data often occurs as whole numbers.

As a whole number, this data type has no fractional parts. It contains only specific defined values. Some categorical variables, like ‘male’ and ‘female,’ could also occur as discrete data.

Of course, this means discrete data are not only quantitative data but could sometimes occur as qualitative data—this happens when a variable can ONLY  take one value from a limited range of values.

Other examples of categorical discrete data include:

  • Blood group (a person can only have one blood group. There are no grey areas)
  • Genotype (AA, AS, SS)
  • Military ranks
  • Marital status

Continuous Data Value

Continuous data could also be categorical or numeric.

This data type could have any value from a potentially infinite range. Continuous data has a lot of grey areas. The color ‘yellow’ is a continuous data because it has different shades, and some could not be easily distinguishable.

Other examples of categorical continuous data include:

  • Language (a person can speak more than one language)
  • Nationality 
  • Religion (though it’s rare to see people that profess two different faith at the same time, many are irreligious. This gray area makes this continuous data)

As a numerical value, continuous data exist as a fraction or decimal. 

A newborn baby could weigh 2.5 kilograms, 2.03 kilograms, or 2 kilograms. The value could be anything; it doesn’t always have any specific defined value.

The Key Takeaway

Discrete and continuous data don’t always exist as numerical values; they could also be qualitative.

Some situations could make seemingly continuous data discrete. For instance, 2.3 is continuous data, but when it occurs in a set with specifically defined values like (2.3, 3.3, 4.3, 5.3), the values become discrete variables.

Religion could also become a discrete variable if it addresses the gray area with close-ended values like:

  • Christianity
  • Islam
  • Others
  • None

Scatter Plot

How do discrete and continuous look when plotted on a scatter graph? 

A scatter plot is a statistical tool for analyzing the relationship between two variables to determine how closely related they’re. 

The plot uses colorful dots to represent the data points. The pattern of data points’ scatter diagram shows the nature and strength of the relationship.

  • A positive relationship means an increase in the value of Y also increases the value of X, while a decrease in Y will decrease the value of X. The scatter diagram shows an upwardly increasing trend. 
  • A negative relationship has an inverse relationship—meaning an increase in Y’s value will cause X to decrease. In contrast, a decrease in the latter will cause the value of Y to increase. The scatter diagram shows a downward trend. 
  • The dots in strong relationships are very close to each other. 
  • The data points of weak relationships appear to shy away from each other.
  • Scattered data points without a clear pattern mean there is no relationship between the two variables.

Discrete Data Graphs

A plot of a discrete variable on a scatter chart often has an undefined data points pattern.

The graph shows there’s no relationship between ‘age’ and ‘internet usage.’

Continuous Data Graphs

The data points of continuous variables on a graph take the shape of a straight line.

This graph shows a clear relationship between planting days and plant height; the plants grew taller with each passing day.

The pattern of the scatter diagram shows a strong positive relationship between the two variables.

The Key Takeaway

Plotting discrete data on a graph often gives a random scatter diagram, while the scatter diagram of continuous variables shows some relationships.

Graphical Representations

Bar charts, pie charts, histograms also provide ways to represent discrete and continuous data graphically. But which of these representations best suit these data types?

Here’s what we found.

Discrete Data Graphical Representation

Bar and pie charts are two great ways to present discrete data.

A bar chart or graph presents categorical data using rectangular bars with heights or lengths that are proportional to the value they represent. The bars could be vertical or horizontal.

Bar graphs make comparing data easily understandable and at a single glance. The bar height or length differences give people a quick insight into how the data categories compare.

Here’s a simple column bar chart.

Image Credit: Smashing Magazine

A pie chart uses ‘pie slices’ to illustrate relative data sizes.

The pie chart, also known as ‘circle chart,’ divides the pie or circle into sectors that form a proportion of the whole. Each sector or pie slice represents a particular category of the data and often comes with vibrant colors that make the pie chart colorful and appealing to the eyes.

The pie charts, just like statistical graphs, also help people quickly compare data sizes without overwhelming them with figures. 

Here’s an example of a simple pie chart.

Continuous Data Graphical Representation

Histograms are great for showing continuous data.

The graph is helpful when dealing with a large volume of data, like national population data. It helps users organize data series into predetermined ranges or groups and plot them with rectangular bars with heights representing their values.

The key difference with a bar chart is that histograms come in handy for presenting numeric data groups, while bar charts help present categorical data.

A histogram is an intuitive way to show the number of times a variable occurs within a specified range.

The U.S Census Bureau might use a histogram to depict the age distribution. 

Since it’s impractical to plot the frequency of each age (the number of times each occurs), the Bureau might consider condensing the data series into age groups like: 

  • 0-10 
  • 11-20
  • 21-30
  • 31-40
  • 41-50
  • 51-60
  • 60 and above

Here’s a simple histogram.

The graph’s first column shows data for all possible weight ranges between 132.5 and 134.5, and values within this data range are infinite, making histograms great options for continuous data.

The Key Takeaway

Bar charts work best for presenting discrete data, while histograms best suit continuous data. While a bar chart can graphically show the sex distribution, the histogram works best for presenting age distribution, weight, height, and other continuous data. 

Use Cases

In which areas do discrete and continuous data find applications? Understanding their use cases helps gain a more profound understanding of these data types. 

Here, we’ll be looking at the same use cases to learn how they compare.

Discrete Data Use Cases

Discrete data has wide use cases. Let’s take a look at five:

  • The census bureau presents its national population figures as discrete data.
  • Hospitals use discrete data to maintain records of the number of births per month.
  • Schools keep their enrolment data as discrete data.
  • The Federal Aviation Administration uses discrete data to present their daily air traffic data.
  •  The ICE’s data on the number of illegal immigrants is discrete.

Continuous Data Use Cases

Here’s how continuous data compares to the above use cases:

  • The census bureau presents its population growth rates as continuous data.
  • Hospitals’ monthly birth rate is continuous data. 
  • Schools measure the rate of changes in their enrolment as continuous data.
  • The FAA uses continuous data to examine the rate of changes in daily air traffic.
  • The ICE could use the rate the number of illegal immigrants changes over time to evaluate their border policing policies’ effectiveness. 

The Key Takeaway

Users often rely on continuous variables to determine the rate some variables change over time—it measures the rate of changes in discrete variables. 

Data Collection

What is the best method for collecting discrete or continuous data from a data population or sample? 

A data sample is a subset of a larger data population. Users select them randomly from the data population when the population sizes are too large for a statistical test.

Discrete Data Collections

The most effective way for collecting discrete data is by counting the data population or samples. The census bureau collects data on the number of United States residents through headcounts.

Continuous Data Collections

Continuous data is not easily countable, so the best way for collecting the data is by measuring the variables using the proper measuring instruments.

Scales help hospitals collect data on the weight of newborn children; thermometer helps people collect data on temperature while barrels help OPEC members determine the volume of crude oil they’re exporting.

The Key Takeaway

Headcounts and measurement are the best ways for collecting discrete and continuous data, respectively. Statisticians also use survey forms to collect these data types.

Transformation

Discrete data is transformable to continuous data and vice versa, but how?

Let’s find out.

Discrete Data Transformation

A straightforward way to transform discrete data to continuous is by finding the mean value (average) of the data series. The mean value is the number expressing the central or typical value in a dataset.

You calculate the mean of a data series by adding the individual values and dividing by the number of times they occurred. 

Here’s an example of discrete data showing hypothetical air traffic for the first quarter of the year

  • January—2,883
  • February—5,993
  • March—4,829

Taking the mean of these values converts the discrete data to continuous data—that’s 4,568.3333. Since air traffic is not divisible into meaningful units, we approximate the figure to the nearest whole number.

Another intuitive way to transform discrete data to continuous is by converting the data series to a fraction. 

You do this by adding the individual data units and dividing them by the total.

The fraction of the January air traffic is 2,883 over 13,705 (that’s 2,883/13,705), and this equals 0.21, meaning January air traffic is two-tenth of the air traffic of the first quarter.

Continuous Data Transformation

As already hinted above, a simple way to convert continuous data into manageable units is by approximation. 

For instance, 4,568.333 air traffic volume doesn’t make sense, but approximating the value to the nearest whole number (discrete data) makes the data usable.

The Key Takeaway

Discrete data is easily transformable to continuous data using mean values and fractions, while approximation helps transform the former to discrete variables.

Here are what make this transformation vital:

  • Converting discrete data series to continuous data by calculating their means value helps statisticians measure the central tendency of discrete data series.
  • Converting to fractions helps statisticians determine how a variable compares to the whole.
  • Approximating continuous data to the nearest whole number helps transform them into manageable and workable units.

Natural Occurrences

Where can we see examples of discrete and continuous data occurring in nature?

Discrete Data Natural Occurrences

Here are just a few of them:

  • Number of trees in the forest
  • The number of animals in the jungle
  • Number of mountains in Africa
  • Number of oceans in the world
  • Number of days in a year

Continuous Data Natural Occurrences

Let’s take a quick look:

  • The amount of rainfall in last years
  • The volume of water in the oceans
  • The temperature of the arctic region
  • Height of mountains in the world
  • Amount of sunshine in a city

The Key Takeaway

Examples of discrete data in nature often occur in the things we can count, and as expected, examples of continuous data are in the things we can only measure.

Discrete Data vs. Continuous Data: Wrapping It Up

There’s no direct competition between these two data types. 

So, there’s no clear winner. Discrete and continuous data are essential, and both data types make mathematical and statistical analysis possible.

It’s challenging to carry out thorough research, whether qualitative or quantitative, without any of these data types.