Difference Between a Continuous and Discrete Variable
Data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which a piece of information or inferences is created. There are different types of data that we use to get information. The two broad categories of data are discrete and continuous data.
Let's understand these two types of data, their similarities, and differences, and how these are used.
What are the Types of Data in Statistics?
There are two major categories of data that are used in statistics or data analysis. These two major categories of data are
- Qualitative Data
- Quantitative Data
What is Qualitative Data?
Qualitative also known as categorical data are the ones that can be sorted by category, but not by number. Qualitative data can answer questions such as "how this has happened" or "why this has happened".
Examples of qualitative data are
- Colours e.g., the colour of hair, colour of eyes, colour of skin, etc.
- Names of person e.g., Amit, Manoj, Swati, Pankaj, etc.
- Names of places e.g, New Delhi, Tokyo, New York, London, etc.
- Nationality e.g. Indian, Chinese, Japanese, German, American, etc.
There are two general types of quantitative data
- Nominal Data
- Ordinal Data
What is Quantitative Data?
Quantitative data are the data that answer key questions such as "how many, "how much" and "how often". Quantitative data are expressed as a number or can be quantified. Simply put, it can be measured by numerical variables. Quantitative data are easily amenable to statistical manipulation. They can be represented by a wide variety of statistical types of graphs and charts such as line graphs, bar graphs, histograms, pie charts, scatter plots, etc.
Examples of quantitative data are
- Scores on tests and exams e.g. 54, 78, 96 and etc.
- The weight of a person or a subject
- Your shoe size
- The temperature in a room
There are two general types of quantitative data
- Discrete Data
- Continuous Data
Maths can be really interesting for kids
What is Nominal Data?
Nominal data is one of the types of qualitative information which helps to label the variables without providing the numerical value. The name 'nominal' comes from the Latin word "nomen" which means 'name'. Nominal data is also called the nominal scale. It cannot be ordered and measured. Examples of nominal data are letters, symbols, words, gender, etc.
The nominal data are examined using the grouping method. In this method, the data are grouped into categories, and then the frequency or the percentage of the data can be calculated. These data are visually represented using the pie charts.
What is Ordinal Data?
Ordinal data/variable is a type of data that follows a natural order. The significant feature of the nominal data is that the difference between the data values is not determined. This variable is mostly found in surveys, finance, economics, questionnaires, and so on.
The ordinal data is commonly represented using a bar chart. These data are investigated and interpreted through many visualization tools. The information may be expressed using tables in which each row in the table shows a distinct category.
What is Discrete Data?
Discrete data can take only discrete values. Discrete information contains only a finite number of possible values. Those values cannot be subdivided meaningfully. Here, things can be counted in whole numbers.
To put in other words, discrete data can take only certain values. The data variables cannot be divided into smaller parts. For example, the number of children in a family can be 1 or 2. It cannot be 1.5 or 1.8, or 1.72.
For example number of students in the class, the number of runs scored by a batsman, the number of children in a family, and the number of days in a month.
Key Characteristics of Discrete Data
Discrete data is often used in simple statistical analysis because it's easy to summarize and compute. Let's look at some of the other key characteristics of discrete data.
- Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers (5, 10, 15, and so on).
- Discrete data can be easily visualized and demonstrated using simple statistical methods such as bar charts, line charts, or pie charts.
- Discrete data can also be categorical – containing a finite number of data values, such as the gender of a person.
- Discrete data is distributed discretely in terms of time and space. Discrete distributions make analyzing discrete values more practical.
What is Continuous Data?
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 weight of a person, height of a person, speed of a car, amount of water in a glass.
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.
You can record continuous data at so many different measurements – width, temperature, time, etc. This is where the key difference from discrete types of data lies.
Key Characteristics of Continuous Data
Unlike discrete data, continuous data can be either numeric or distributed over date and time. This data type uses advanced statistical analysis methods considering the infinite number of possible values. Key characteristics of continuous data are:
- Continuous data changes over time and can have different values at different time intervals.
- Continuous data is made up of random variables, which may or may not be whole numbers.
- Continuous data is measured using data analysis methods such as line graphs, skews, and so on.
- Regression analysis is one of the most common types of continuous data analysis.
Difference Between Discrete and Continuous Data
Following are the differences between Discrete and Continuous data,
A good great rule for defining if 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.
Practice Problems
Categorize the following data as discrete or continuous
- Speed of bike running
- Number of students in your class
- Distance between two cities
- Height of a person
- Number of wickets taken by a bowler
- Speed of the ball thrown by a bowler
- Weight of your school bag
- Number of pens in your instrument box
- Room temperature
- Number of people in a room
FAQs
What is the difference between discrete and continuous data?
Discrete data is a numerical type of data that includes whole, concrete numbers with specific and fixed data values determined by counting. Continuous data includes complex numbers and varying data values measured over a particular time interval.
What are examples of discrete data?
Discrete data is information that we collect that can be counted and that only has a certain number of values. Examples of discrete data include the number of people in a class, test questions answered correctly, and home runs hit.
What are examples of continuous data?
Continuous data is data that can take any value. Height, weight, temperature, and length are all examples of continuous data. Some continuous data will change over time; the weight of a baby in its first year or the temperature in a room throughout the day.
Conclusion
All of the different types of data have a critical place in statistics, research, and data science. Every type has its own advantages in a particular situation where they are used. Data types help organizations and businesses from all industries help in presentation and making inferences.
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- Multiplication and Division of Fractions
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Source: https://codinghero.ai/discrete-and-continuous-data/
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