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Discrete and Continuous Data

Introduction

Data collection may include words, numbers, measurements, observations, or merely descriptions of various objects. There are many different forms of data, just as there are several ways to create data. Data might be structured or unstructured. Aside from that, there are qualitative and quantitative data. Finally, there are discrete and continuous data.

Let us use the students in a classroom as an illustration. The number of students in attendance today is discrete data, whereas the height of the students is an example of continuous data.

A set of numbers is often made up of discrete (countable) or continuous (measurable) variables. Depending on whatever category the data belongs to, you should investigate it differently. This will also affect the measurement.

This article will define discrete and continuous data, explain their distinctions, discuss their significance to statistics, and give some examples.

What is Discrete Data?

Definition

Discrete data is a term used to describe data sets with countable values that can only take a finite set of values. Data that is discrete cannot be measured.

Only a finite set of values are allowed for a count involving integers in a discrete data set. One cannot split this kind of data into separate components. When determining whether it is discrete, consider the data’s count and whether it can be broken down into smaller components 

Let us say, for instance, that the number of students in a classroom is discrete data. We cannot have 0.50 or half a student. Discrete variables are those that are non-negative, countable, and finite integers. 

Due to its simplicity in computation and summarization, this data type is mostly used for straightforward statistical analysis. In most cases, pie charts, stem-and-leaf plots, and bar graphs are used to display discrete data.

Examples of Discrete Data

Examples of discrete data that could be collected include:

( 1 ) How many students showed up for the class;

( 2 ) How many buyers have purchased a particular item;

( 3 ) The quantity of food that people buy per day;

( 4 ) How many computers are in each department;

( 5 ) The number of goods you purchase each week at the supermarket store;

( 6 ) The number of shoes in a person’s collection;

( 7 ) The number of meeting attendees;

( 8 ) How many employees in a company;

( 9 ) How many pets are in the clinic; and 

( 10 ) The number of books on a shelf.

And a lot more. Remember that data is discrete if it is countable and cannot be split into smaller components. 

Discrete Data Visualized in a Graphical Format

Discrete data is typically used for fundamental statistical analysis since it is easy to compute and summarize. Typically, discrete data is displayed using bar graphs, pie charts, stem-and-leaf plots, frequency tables, and line plots. The most effective way to display discrete data is with a bar graph since either vertical or horizontal bars may clearly show finite values.

Example 1 

In a survey conducted by the school, it was found that among Grade 8 students, 35 chose mathematics as their favorite subject, followed by 20 choosing English, 25 choosing Science, 15 choosing Physical Education, and 10 selecting History. Show this data using a frequency table, line plot, and bar graph.

Solution:

The number of students who like or prefer a particular type of subject is an example of discrete data. The following images show how to visualize the data in a frequency table, line plot and bar graph.

( a ) Frequency Table

Favorite Subject
SubjectTallyNumber of Students
Mathematics35
English20
Science25
Physical Education15
History10
Total105

( b ) Line Plot

( c ) Bar Graph

Example 2

View the information below to see what customers buy from a grocery store. Show the data using a bar graph and identify whether it is discrete or not.

Purchased ItemsMilkBreadMeatCondimentsFruits
Number of People2127301512

Solution:

Since the data show the number of people who bought certain items is countable or finite, then the set of data presented is discrete. To represent the gathered data through a bar graph, let us have the purchased items on the x-axis while the number of people on the y-axis. The table below shows an example of the data in a bar graph.

Important Discrete Data Properties

Because discrete data is straightforward to summarize and compute, it is frequently employed in elementary statistical analysis. Let’s examine a few more important properties of discrete data.

( a ) Discrete data consists of discrete variables that are non-negative, countable, and finite (4, 8, 12, 16, and so on). The values cannot be divided into smaller components or pieces.

( b ) Discrete data is not measurable. For example, the height of students can be measured using a scale; hence, height is not discrete.

( b ) Simple statistical techniques like bar charts, line charts, or pie charts make it simple to represent and demonstrate discrete data. 

( c ) Large sample sizes are necessary for statistical analysis and graphing of discrete data. It can be time-consuming, expensive, and labor-intensive to gather a sizable adequate sample. On the other hand, if the data categories are clearly defined, it may be simpler to collect than continuous data.

( d ) Discrete data can also be categorical, meaning they can have only a small number of possible values, like a person’s gender, marital status, and payment method. A frequency table that displays the number of each category in the data sample can be used to summarize discrete data. 

What is Continuous Data?

Definition

A continuous data set represents a scale of measurement that includes fractions and decimals in addition to whole numbers. A type of numerical data known as continuous data refers to the undetermined number of possible measurements between two realistic points. 

Accuracy is the key component of continuous data. These data sets frequently have variables with decimal points. Values like height, weight, length, temperature and other similar metrics would be included in continuous data sets. They are items that can be quantified in decimals and fractions.

 A continuous data set typically requires the use of a tool, such as a ruler, measuring tape, scale, thermometer, etc., to create the numbers. Since they are frequently derived from precise measurements, these numbers are often not as neat and orderly as those in discrete data. Measuring a specific issue over time enables us to establish a specified range where we may expect to collect additional data.

Examples of Continuous Data

The following are some examples of continuous data sets, which represent a scale of measurement that includes whole numbers, fractions, and decimals.

( 1 ) The newborn baby’s weight.

( 2 ) The height of the students in school.

( 3 ) The room’s temperature.

( 4 ) The volume of water in the tank

( 5 ) Length of films.

( 6 ) The amount of time racers take to the finish line.

( 7 ) The speed of vehicles.

( 8 ) The blood pressure of patients in the hospital.

( 9 ) The amount of time people need to travel to work.

( 10 ) The area of the residential lots owned by the community.

And a lot more. Remember that data is continuous if it can be quantified in decimals and fractions.

Important Continuous Data Properties

Continuous data, in contrast to discrete data, employ sophisticated statistical analysis techniques while considering the countless potential values. The following are important properties of continuous data:

( a ) Continuous data is measurable. To create the numbers, a continuous data set typically requires the use of a tool, such as a ruler, measuring tape, scale, thermometer, etc.

( b ) Random variables, which might or might not be whole numbers, make up continuous data. The values have additional meaning and can be broken into smaller and smaller pieces. Within an interval, there are an endless number of possible values.

( c ) Continuous data can have various values at various points in time and changes over time.

( d ) Line graphs, skews, histograms, and other data analysis techniques are used to display continuous data. One of the most popular kinds of continuous data analysis is regression analysis.

( e ) Continuous data is effective; a small amount can reveal a great deal about the data. Continuous data can be summarized using descriptive statistics to determine the average and standard deviation. Calculating skews and kurtosis is also possible.

Continuous Data Visualized in a Graphical Format

A continuous data set represents a scale of measurement that includes fractions and decimals in addition to whole numbers. Accuracy is the key component of continuous data. These data sets frequently have variables with decimal points. 

Let’s say, for illustration, that we have a frequency distribution table that displays the amount of time (in minutes) it takes employees to drive from the office to their residences on any particular day.

Time (t)

45.535.416.552.4
32.721.622.427.6
23.88.318.828.5
5.936.354.541.2
10.612.158.243.6

The given set of data is continuous since time is measurable, and it may include whole numbers, decimals, and fractions. The figure below shows the data in graphical format using a histogram.

Discrete vs Continuous Data

Both forms of data are important for statistical analysis. Before making any judgments or assumptions regarding the relevant data type, it is essential to be aware of certain significant differences between the two.

Let us use the following table to show the difference between discrete and continuous data:

Discrete DataContinuous Data
Definition:
Discrete data is a term used to describe data sets with countable values that can only take a finite set of values.A continuous data set represents a scale of measurement that includes fractions and decimals in addition to whole numbers.
Is it countable?
YesNo
Is it measurable?
NoYes
Type of Numbers Used
Whole numbersReal numbers
Graph
Bar graphHistogram
Examples
The number of competitors in a raceThe time it took each racer to cross the finish line
The number of boys in a classroomThe height and weight of the students
The number of vehicles using the highwayThe rate at which cars travel along a highway
A building’s total number of roomsThe temperature in each room in the building
The number of sold water bottlesThe volume of water in a swimming pool

Advantages and Disadvantages of Discrete and Continuous Data

The advantages and disadvantages of discrete and continuous data are presented in the table below.

AdvantagesDisadvantages
Discrete
It is simple to read and spot patterns in discrete data.It exclusively uses whole numbers, making it more challenging to analyze because values cannot be broken down into smaller parts or components.
Discrete data can be easily included in a wide range of graph types.Discrete data cannot yield additional insights since it is less detailed than continuous data.
You do not need large amounts of discrete data to make inferences or valid analyses.Data that is discrete might not be as accurate as data that is continuous.
Continuous
Continuous data is accurate.Working with continuous data can be confusing.
Presenting more complex data with continuous data is more practical.Specific measurement techniques are constrained.
Few data points can be used to draw conclusions, and small samples can still yield reliable analysis.Continuous data collection can be more expensive because it frequently requires more time.

The Importance of Discrete and Continuous Data

When working with various forms of data, it is essential to know them. Data can be numerical or descriptive, and both forms can be discrete or continuous. You can evaluate and interpret your data more effectively if you understand the differences between discrete and continuous data. Both types of data should be gathered and examined to produce well-rounded findings and studies.

More Examples

Example 1

The following information was gathered when 20 families were surveyed regarding the number of electric fans they owned:

1, 1, 2, 3, 4, 6, 5, 2, 3, 7, 4, 2, 2, 5, 1, 3, 8, 5, 3, 9

Answer each question.

( a ) Identify the variable in the survey.

( b ) Classify the data, whether it is discrete or continuous.

( c ) Create a dot plot to show the data.

Solution:

( a ) The variable in the survey is the number of electric fans in each family.

( b ) The number of electric fans is countable; Hence, the data is discrete.

( c ) The figure below shows the data using dot plot representation.

Example 2

Let us say the weight in kilograms of apples sold on a specific day is as follows:

1.1, 3.2 , 4.5, 2.6, 6.7, 6.3, 5.9, 4.8, 2.4, 1.3, 5.2, 2.3, 5.3, 3.7, 2.8

Create a frequency table to organize the data, then graph it.

Solution:

Given that the supplied data is the measurement for weight and contains decimal numbers, the data set is continuous. To organize the data, the table below is used.

Weight of ApplesFrequency
1 kg – 2 kg2
2 kg – 3 kg4
3 kg – 4 kg2
4 kg – 5 kg2
5 kg – 6 kg3
6 kg – 7 kg2

The histogram is used to graph this continuous data. The x-axis shows the weight of apples in kilograms, while the y -axis is the frequency.

Summary

Definition

Discrete data is a term used to describe data sets with countable values that can only take a finite set of values. Data that is discrete cannot be measured.

A continuous data set represents a scale of measurement that includes fractions and decimals in addition to whole numbers.

Discrete Data Properties

The following list includes some important discrete data properties. 

( a ) Discrete data consists of discrete variables that are non-negative, countable, and finite.

( b ) The values cannot be divided into smaller components or pieces.

( c ) Discrete data is not measurable. 

( d ) Simple statistical techniques like bar charts, line charts, or pie charts make it simple to represent and demonstrate discrete data. 

Continuous Data Properties

The following list includes some important continuous data properties. 

( a ) Continuous data is measurable. 

( b ) Random variables, which might or might not be whole numbers, make up continuous data. 

( c ) Continuous data can have various values at various points in time and changes over time.

( d  ) Continuous data is effective; a small amount can reveal a great deal about the data. 

Frequently Asked Questions on Discrete and Continuous Data ( FAQs )

What are numerical data?

Quantitative data usually referred to as numerical data, is a sort of data that is expressed in numbers rather than words. The capacity to do arithmetic operations with these numbers sets numerical data apart from other number form data types.

Discrete data represents countable things, and continuous data are the two categories into which quantitative data is divided. And continuous data, which describes data measurement. The interval and ratio data, used to measure particular things, are further separated into continuous numerical data.

What are examples of discrete data?

Discrete data are countable values, and it includes the following examples:

The number of students at the conference.
The number of test questions.
The number of languages a person speaks.
The number of championships won by a sports team.
The number of employees working in the afternoon.
The number of purchased items in a grocery store.
The number of votes in an election.
The population of a town.

What are examples of continuous data?

Continuous data are measurable values, and it includes the following examples:

The height of the students.
The weight of sold fruits.
The room’s temperature.
The length of animals in the zoo.
The volume of water in the pool.
The customers’ waiting time.
The speed of vehicles passing the intersection.
The area of the residential lots in a town.

How can you tell if you are working with continuous or discrete data?

If you want to know if you’re working with discrete or continuous data, you might take a look at the following:

Countability of data

The data is most likely discrete if it can be counted. For instance, it is possible to count the number of kids in a classroom but not their weight or height. Another illustration of discrete data is the number of books on the shelf.

Data measurement

Data is most likely continuous if it can be measured. For instance, you can monitor the speed at which vehicles pass a highway, the weight of young children in a neighborhood, and the amount of time kids spend playing video games.

Can the data be divided into smaller parts?

Take the room’s temperature, for example. Data showing the temperature at 28, 28.5, and 29 degrees is recorded. Even so, having data values between two whole numbers, such as 28.5, makes sense. Additional examples are the size of the property in a neighborhood and the amount of water in a tank. These measures demonstrate that precise numbers, decimals, and fractions are significant and do not necessarily have to be whole numbers.

Type of graph

Bar graphs, pie graphs, and line graphs are frequently used with discrete data, whereas histograms, box plots, and scatter diagrams are frequently used with continuous data.

What are the limitations of discrete data?

There are several restrictions with discrete data:

( a ) It only employs whole numbers, which makes analysis more challenging because values cannot be divided into smaller pieces or components.
( b ) Since discrete data is less detailed than continuous data, it cannot provide further insights.
( c ) The accuracy of discrete data may not be as high as that of continuous data.

What are the limitations of continuous data?

There are several restrictions with continuous data:

( a ) Working with continuous data can be challenging.
( b ) There are limitations to several measurement procedures.
( c ) Because it typically takes more time, continuous data collection might be more expensive.

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