Discrete Data

The term data originates from the Latin word “datum,” meaning “something given.” After forming a research question, data is continuously gathered through observation. Once collected, it is organized, summarized, classified, and often displayed graphically for better understanding.

Data is generally categorized into qualitative and quantitative types.

Types of Data
Within quantitative data, there are two further classifications: discrete and continuous data.

Discrete Data
Discrete data is data that can take only specific, fixed values. These values are distinct and cannot be divided into smaller parts. In other words, discrete data includes a limited set of whole numbers or integers, and cannot be expressed in fractions or decimals. Each value stands on its own and can only be counted, not measured.

Example: What is the number of students present in the classroom today?
This is discrete data because the answer will always be a whole number that can be counted (like 25 or 30), not a fraction or decimal.
 

There are many types of data that we know of, but two of the main or important data types are discrete and continuous. The differences between discrete and continuous data are mentioned below.

 

Discrete data can be gathered by counting the number of values. To analyze the discrete data, we need to find patterns of trends and insights. A few of the steps are as follows:

Step 1: First, we collect and organize the discrete data clearly in a table or list. 

Step 2: Next, we choose a graph or a measure (mean, median, mode) to calculate the data collected.

Step 3: Look for any patterns or trends.

Step 4: Answer any questions that are based on the data analysis gathered.

Graphical representation of discrete data 

To represent discrete data graphically, the following types of graphs can be used:

• Graphs (bar charts, pie charts, pie diagrams, dot plots, etc.)

• Frequency table

• Line plot (number line)

Graphs are one of the most suitable ways to represent discrete data. The reason is graphs can present finite values clearly, such as in bar graphs or pie charts.

Frequency tables represent discrete values through tally marks and the frequency of each variable.

On number lines, each value is marked with the variable.

Discrete data can be represented using different types of graphs. The most commonly used methods are:

• Bar Graph
• Frequency Table
• Line Plot (Number Line)
   

A bar graph is the most effective way to display the discrete data because each bar clearly shows a separate, countable value, either vertically or horizontally.

A frequency table uses tally marks to show how often each value appears, along with the frequency of each category.

A line plot represents discrete data by marking the values above a number line.

Example:
A survey was conducted among 18 children about their favorite indoor games. The results were as follows:

• 7 children like Ludo
   
• 4 children like Chess
   
• 3 children like Carrom
   
• 4 children like Snakes and Ladders
   

This represents discrete data because the number of children per game is an integer.

The data can be shown using three types of graphical representations:
 

• A bar graph illustrating the number of children who prefer each game.
   
• A frequency table with tally marks and corresponding frequencies.
   

A line plot displaying each child’s game choice on a number line.

To master discrete data, focus on understanding that it deals with countable, distinct values. Practice identifying patterns, organizing data into tables or charts, and distinguishing it from continuous data to improve accuracy in analysis.

• Always identify values that are countable and distinct, such as the number of books or students.
   
• Organize discrete data using tables, bar graphs, or pie charts for better understanding.
   
• Practice solving problems involving counting, probability, and comparisons regularly.
   
• Learn to distinguish discrete data from continuous data by checking if fractional values are possible.
   
• Observe patterns and repetitions in data sets to make analysis and predictions easier.
   
• Encourage children to count everyday items, like pencils, toys, chairs, or books, that help them to see that discrete data is all about whole numbers.
   
• Ask simple questions such as “How many apples do we have?” or “How many students picked chocolate ice cream?” to show that discrete data comes from things we can count one by one.
   
• Remind children that discrete data never includes decimals or fractions. These numbers come from counting objects, not measuring them.
   
• Allow children to create bar graphs or tally charts using classroom data. Discrete data is ideal for such visual representations.

There are many uses for discrete data in our day-to-day life. Let us now see the various fields and applications we use in discrete data:

• Business and Marketing: We use discrete data in business and marketing to calculate the number of purchases made by a customer in a month. To check the page views, clicks on ads, or number of unique visitors. We also use it in survey responses, inventory management and loyalty programs.

• Healthcare and Medicine: Discrete data is widely used in medicine and healthcare to calculate the patient counts, disease cases. Discrete data in healthcare includes patient counts, disease case numbers, birth and death rates, and the number of hospital visits of different types of patients.

• Education and Academia: The concept of discrete data is widely used in education and academics. We use it to check the student attendance, to check the marks obtained in an exam, to check the number of courses enrolled in a semester. Furthermore, we also use it to see the number of books issued to a student and to count the number of graduating students each year.
  
   
• Counting inventory in store: The number of products like shoes, books, or smartphones in stock can only be whole numbers, making it discrete data.
  
   
• Tracking student attendance: The number of students present in a class each day is counted in whole numbers, which is a discrete data example.