Discrete data refers to specific, distinct values or outcomes, often derived from countable items or events.
For example, the number of students in a class, the number of cars in a parking lot, and the types of fruits in a basket are all examples of discrete data.
Features of discrete data include:
- Countable: Values are distinct and can be counted individually.
- Finite Values: Even if there are many, there’s a finite number of possible values.
- Non-Continuous: There are gaps between values; it doesn’t take on every possible value within a range.
- Categorical or Numeric: Can be qualitative (like “yes” or “no”) or quantitative (like the number of apples).
- No Decimal or Fractional Values: Values are whole numbers, not fractions or decimals (Oakshott, 2020; Pooja, 2023).
A benefit of discrete data is that it provides clear, distinct categories or values, making it straightforward to analyze and interpret (Kirk, 2016). However, a limitation is that it cannot capture nuances or values between categories, potentially missing finer details or gradations present in continuous data.
Examples of Discrete Data
- Number of students in a classroom: Students can be individually counted, but you can’t have a fraction of a student.
- Number of eggs in a carton: Eggs are whole items, so you’ll never find half an egg in a carton, ensuring countable, whole values.
- Types of shoes in a closet: Shoes are categorized into distinct types such as sandals or sneakers, without intermediate categories between them.
- Number of apps installed on a phone: Apps are tangible entities; a phone can’t have 2.5 apps installed, only whole numbers.
- Number of tickets sold for a movie: Tickets represent whole entities, and you can’t sell a fraction of a movie ticket.
- Number of languages spoken by an individual: People speak whole languages; one can’t speak half of a language.
- Types of vehicles in a parking lot: Vehicles are distinctly categorized, for instance, you can’t have a vehicle that’s simultaneously a car and a motorcycle.
- Number of pizzas ordered for a party: Pizzas are ordered in whole units; one doesn’t order 1.5 pizzas but rather one or two.
- Number of attendees at a conference: Attendees are countable entities; there isn’t a scenario where half a person attends.
- Types of beverages in a fridge: Beverages fall into distinct categories, such as milk or soda, without a beverage being both simultaneously.
- Number of posts on a social media profile: Posts are individual entities, so a profile can’t have a fraction of a post.
- Number of siblings one has: Siblings are individual people, so counts are always whole numbers without fractions.
- Types of animals in a zoo: Animals are grouped into specific species, and there isn’t an animal that’s half-elephant and half-lion.
- Number of goals scored in a soccer match: Goals are counted as whole units; teams can’t score a fraction of a goal.
- Number of books borrowed from a library: Books are tangible items; a borrower can’t borrow a fraction of a book
- Number of chairs in a dining room: Chairs are tangible items, so a room can’t contain a fraction of a chair.
- Types of fruits in a basket: Fruits are distinctly categorized, like apples or oranges, without any fruit being a mix of both.
- Number of pages in a book: Pages are countable entities, so a book can’t have, for example, 120.5 pages.
- Types of coins in a wallet: Coins are differentiated by their denominations, such as nickels or dimes, without a coin being both at once.
- Number of songs in a playlist: Songs are individual entities; a playlist can’t have a portion of a song separate from the rest.
- Number of light bulbs in a box: Light bulbs are tangible items; a box can’t contain a fraction of a light bulb.
- Types of birds in a park: Birds are categorized into specific species, like sparrows or eagles, without a bird being a mix of the two.
- Number of keys on a keychain: Keys are countable entities, so a keychain can’t hold two-thirds of a key.
- Types of fish in an aquarium: Fish are grouped by species, such as goldfish or tetras, without a fish being both simultaneously.
- Number of pencils in a drawer: Pencils are tangible items, and a drawer can’t contain a fraction of a pencil.
Sub-Types of Discrete Data
We can break discrete data down into four sub-types. These are: nominal, ordinal, binary, and count data. Each is presented below:
|Type of Data||Definition||Example|
|Nominal Data||Data that can be categorized but not ordered or measured (Thiagarajan, 2023).||Colors: red, blue, green|
Gender: male, female
|Ordinal Data||Data that can be categorized and ordered, but the distances between categories are not uniform or meaningful (Dhingra, 2023).||Ratings: low, medium, high|
Education level: high school, bachelor’s, master’s, PhD
|Binary Data||A special type of nominal data with only two possible outcomes.||Outcome of a coin toss: heads or tails|
Response to a question: Yes/No
Presence of a feature: Present/Absent
|Count Data||Represents the number of occurrences of an event.||Number of students attending a seminar|
Number of cars passing through a toll in an hour
Number of apples sold in a day
Discrete vs Continuous Data
Discrete and continuous data represent two fundamental types of quantitative information, and each has its unique characteristics and applications.
Discrete data is characterized by distinct, separate values. Continuous data, conversely, originates from measurements that can take on an infinite number of values within a given range (Evans, 2019). For example, the measurement of the weight of a fruit or the height of a person would yield continuous data (Kirk, 2016).
There’s no inherent gap between possible values in continuous data. If you were to measure the length of a piece of string, it could be 20 cm, 20.05 cm, 20.055 cm, or any value in between, depending on the precision of your measuring tool.
While both types of data provide valuable insights, their nature dictates how they should be analyzed.
Discrete data often lends itself to specific statistical methods that rely on counting and frequencies. In contrast, continuous data can have more specific mathematical procedures applied to it (Kirk, 2016). In particular, ordinal data is extremely useful for statistical analysis, allowing for multiplication and division of the statistics to make useful quantifiable comparisons.
Strengths and Limitations of Discrete Data
Discrete data has several strengths.
Firstly, it’s often straightforward to collect, understand, and interpret since the values are clear and distinct. This clarity allows for accurate counting and reduces ambiguity, particularly when comparing results or aggregating data (Privitera, 2022).
Another advantage is its applicability in many real-world scenarios, such as inventory management, where one needs exact counts of items.
Discrete data also generally requires simpler tools and methods for analysis, making it more accessible for those who aren’t well-versed in advanced statistics.
However, discrete data also comes with its limitations.
One major drawback is its inability to capture nuances or values between distinct categories, potentially overlooking finer details or gradations present in continuous data. This characteristic might make discrete data less suitable for contexts requiring a more detailed or granular analysis.
Additionally, in cases where data naturally falls on a continuous scale, artificially categorizing it into discrete values might lead to a loss of information or introduce biases.
Finally, while its simplicity can be a strength, it can also be a limitation: certain complex analyses or predictions might be challenging or inaccurate using only discrete data (Banchs & Pop, 2021).
Banchs, R. J., & Pop, M. R. (2021). The Quality Improvement Challenge: A Practical Guide for Physicians. Wiley.
Dhingra, H. (2023). ICSE Robotics and Artificial Intelligence. Goyal Brothers Prakashan.
Evans, C. W. (2019). Engineering Mathematics: A Programmed Approach (3rd ed.). CRC Press.
Kirk, A. (2016). Data Visualisation: A Handbook for Data Driven Design. SAGE Publications.
Oakshott, L. (2020). Essential Quantitative Methods: For Business, Management and Finance. Macmillan Education UK.
Pooja, D. (2023). Data visualization with Python: Exploring Matplotlib, Seaborn, and Bokeh for interactive visualizations. BPB Publications.
Privitera, G. J. (2022). Research Methods for the Behavioral Sciences. New Jersey: SAGE Publications.
Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]