Discrete Data - Math Steps, Examples & Questions (2024)

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Request a demo

In order to access this I need to be confident with:

Addition and subtraction 2D shapes 3D shapes

Introduction

What is discrete data?

Common Core State Standards

How to recognize discrete data

Discrete data examples

Example 1: recognizing types of dataExample 2: recognizing types of dataExample 3: recognizing types of data

How to analyze discrete data

Example 4: analyzing and then answering a question - discrete dataExample 5: analyzing and then answering a question - discrete dataExample 6: analyzing and then answering a question - discrete data

Teaching tips for discrete data

Easy mistakes to make

Related types of data lessons

Practice discrete data questions

Discrete data FAQs

Next lessons

Still stuck?

Math resources Statistics and probability Types of data

Discrete data

Here you will learn about discrete data, including what it is, how to collect it and how to graph and analyze it.

Students first learn to work with discrete data in first grade and expand their knowledge and use of data as they progress through the grades.

What is discrete data?

Discrete data includes numeric data values that are countable.

Some common examples of discrete data sets include:

  • The shoe size of everyone in a family
  • Number of likes on a post over time
  • Number of students in each classroom of a school
  • Number of adoptions at a pet shelter each month

Discrete data can be collected through questionnaires, surveys, interviews, or observations.

Once the data has been collected, it can be graphed, which provides a visualization of the data. Pictographs and bar graphs (or bar charts) are common ways to represent discrete data. You can also use histograms, box plots, pie charts, or frequency tables, however note that these can also be used for continuous data.

Besides graphs, data analysis of discrete data may include calculating the mean, median, range or mode. Particularly if the data is being used for statistical analysis.

Finally, the graphs and/or measures of center can be used to answer questions about the data.

For example,

How many cats do the students in my class have?

Discrete Data - Math Steps, Examples & Questions (3)

The data is discrete, because there are a limited number of answers. You can’t have 0.5 of a cat, just like you can’t have 10,000.

Once the data is collected, you can use a bar graph to display it.

Discrete Data - Math Steps, Examples & Questions (4)

Now, you can use the data in the table and the bar graph to answer questions like…

  • What is the most common number of cats? 0 cats
  • What is the most number of cats? 5 cats
  • How many more students have 2 cats than 1 cat? 2 students

What is discrete data?

Discrete Data - Math Steps, Examples & Questions (5)

Common Core State Standards

How does this apply to 1 st grade math, 2 nd grade math, 3 rd grade math, 4 th grade math, 5 th grade math and 6 th grade math?

  • Grade 1 – Measurement and Data (1.MD.C.4)
    Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
  • Grade 2 – Measurement and Data (2.MD.D.9)
    Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
  • Grade 3 – Measurement and Data (3.MD.B.3)
    Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.

    For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.

    Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

  • Grade 4 – Measurement and Data (4.MD.B.4)
    Make a line plot to display a data set of measurements in fractions of a unit (\cfrac{1}{2}, \, \cfrac{1}{4}, \, \cfrac{1}{8}) . Solve problems involving addition and subtraction of fractions by using information presented in line plots.

    For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

  • Grade 5 – Measurement and Data (5.MD.B.2)
    Make a line plot to display a data set of measurements in fractions of a unit (\cfrac{1}{2}, \, \cfrac{1}{4}, \, \cfrac{1}{8}) . Use operations on fractions for this grade to solve problems involving information presented in line plots.

    For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

  • Grade 6 – Statistics and Probability (6.SP.B.5)
    Summarize numerical data sets in relation to their context.

Discrete Data - Math Steps, Examples & Questions (6)

[FREE] Types of Data Check for Understanding (Grade 6 to 7)

Discrete Data - Math Steps, Examples & Questions (7)

Use this quiz to check your grade 6 to grade 7 students’ understanding of types of data. 15+ questions with answers covering a range of 6th and 7th grade types of data topics to identify areas of strength and support!

DOWNLOAD FREE

x

Discrete Data - Math Steps, Examples & Questions (8)

[FREE] Types of Data Check for Understanding (Grade 6 to 7)

Discrete Data - Math Steps, Examples & Questions (9)

Use this quiz to check your grade 6 to grade 7 students’ understanding of types of data. 15+ questions with answers covering a range of 6th and 7th grade types of data topics to identify areas of strength and support!

DOWNLOAD FREE

How to recognize discrete data

In order to recognize discrete data:

  1. Look for data that uses only numbers.
  2. Look for numbers that are a finite set.

Discrete data examples

Example 1: recognizing types of data

Is the data set below discrete? Why or why not?

Discrete Data - Math Steps, Examples & Questions (10)
  1. Look for data that uses only numbers.

The data shows how many cans were donated by how many children. This data uses only numbers.

2Look for numbers that are a finite set.

The number of cans donated is NOT continuous. You can’t donate \cfrac{1}{3} of a can and at some point a number like 10,000,000 is unreasonable. The data has a set number of possible responses, so it is discrete.

Example 2: recognizing types of data

Is the data set below discrete? Why or why not?

Discrete Data - Math Steps, Examples & Questions (11)

Look for data that uses only numbers.

The data shows how many employees are ages 16 to 20. This data uses only numbers.

Look for numbers that are a finite set.

Example 3: recognizing types of data

Is the data set below discrete? Why or why not?

Discrete Data - Math Steps, Examples & Questions (12)

Look for data that uses only numbers.

How to analyze discrete data

In order to analyze discrete data:

  1. Collect discrete data.
  2. Choose a graph or measure of center to calculate.
  3. Answer questions based on the data analysis.

Example 4: analyzing and then answering a question – discrete data

Scenario: Students in your class use leaves as a part of an art project. You wonder, “How many leaves did students in my class use for the art project?”

Collect discrete data.

Choose a graph or measure of center to calculate.

Answer questions based on the data analysis.

Example 5: analyzing and then answering a question – discrete data

Scenario: A grocery store keeps track of how many customers visit each day.

Collect discrete data.

Choose a graph or measure of center to calculate.

Answer questions based on the data analysis.

Example 6: analyzing and then answering a question – discrete data

Scenario: You wonder, “What year were my family members older than me born?”

Collect discrete data.

Choose a graph or measure of center to calculate.

Answer questions based on the data analysis.

Teaching tips for discrete data

  • Include activities where students collect their own discrete data by creating surveys, conducting interviews or doing experiments. Then analyzing what they’ve collected and drawing conclusions based on the data. This will help students develop a complete understanding of discrete data.
  • Give students a mixture of categorical, discrete and continuous data and have them sort each set into the correct category. Then have students discuss similarities and differences between the data types.

Easy mistakes to make

  • Confusing discrete vs. continuous data
    Since both involve numbers, it is not always easy for students to understand the difference of discrete data vs. continuous data.

    Use a number line to explain the key difference – highlighting that discrete data is data that only includes the specific values (like the ones shown on the number line), but the continuous data includes all values (including the ones between the numbers shown – an infinite number of possible values).

    Examples of discrete data (specific values on the number line – only those labeled)…

    Discrete Data - Math Steps, Examples & Questions (19)
    Examples of continuous data (all values on the number line – those labeled and not labeled)…
    Discrete Data - Math Steps, Examples & Questions (20)
  • Thinking discrete data is only whole numbers
    While discrete data sets often include whole numbers, this is not the only type of numbers that can be used.

    For example,
    Shoe sizes are a discrete data set and include sizes like 6.5 and 9.5, which include decimals.

Related types of data lessons

  • Types of data
  • Quantitative data
  • Qualitative data
  • Primary data
  • Secondary data

Practice discrete data questions

1. Which question will collect discrete data?

What is your favorite color?

Discrete Data - Math Steps, Examples & Questions (21)

What is the temperature outside?

Discrete Data - Math Steps, Examples & Questions (22)

What is your shoe size?

Discrete Data - Math Steps, Examples & Questions (23)

What day of the week is it?

Discrete Data - Math Steps, Examples & Questions (24)

Discrete data collects only numbers.

These questions have answers that are NOT numbers:

  • What is your favorite color? Possible answers: Red, blue, green…
  • What day of the week is it? Possible answer: Monday, Tuesday…

Discrete data has a set number of possible responses.

This question does NOT have a set number of responses:

  • What is the temperature outside? 5^{\circ}, 5.1^{\circ}, 5.13^{\circ}, 5.137^{\circ}, etc. – the possible temperature answers are infinite

The question “What is your shoe size?” is answered with a finite set of numbers, so it will provide a discrete data set.

2. Which question will collect discrete data?

What month were you born?

Discrete Data - Math Steps, Examples & Questions (25)

How many cars in the parking lot are blue?

Discrete Data - Math Steps, Examples & Questions (26)

What speed does a turtle move?

Discrete Data - Math Steps, Examples & Questions (27)

What is your pet’s name?

Discrete Data - Math Steps, Examples & Questions (28)

Discrete data collects only numbers.

These questions have answers that are NOT numbers:

  • What month were you born? Possible answers: March, April, May…
  • What is your pet’s name? Possible answer: Flower, Fluffy, Rainbow…

Discrete data has a set number of possible responses.

This question does NOT have a set number of responses:

  • What speed does a turtle move? 4 \; mph, \, 3.9 \; mph, \, 3.94 \; mph, \, 3.9453 \; mph etc. – the possible speed answers are infinite.

The question “How many cars in the parking lot are blue?” is answered with a finite set of numbers, so it will provide a discrete data set.

3. Which question will NOT collect discrete data?

How many seconds does it take to run 100 m?

Discrete Data - Math Steps, Examples & Questions (29)

How many siblings do you have?

Discrete Data - Math Steps, Examples & Questions (30)

How many tickets were sold each day?

Discrete Data - Math Steps, Examples & Questions (31)

How many students are in each class?

Discrete Data - Math Steps, Examples & Questions (32)

Discrete data uses only numbers and all the questions have numbers as answers.

Discrete data has a set number of possible responses.

This question does NOT have a set number of responses:

  • How many seconds does it take to run 100 \; m? \, 11 seconds, 11.1 seconds, 11.13 seconds, 11.137 seconds, etc. – the possible amount of time answers are infinite.

4. Which table shows discrete data?

Discrete Data - Math Steps, Examples & Questions (33)

Discrete Data - Math Steps, Examples & Questions (34)

Discrete Data - Math Steps, Examples & Questions (35)

Discrete Data - Math Steps, Examples & Questions (36)

Discrete Data - Math Steps, Examples & Questions (37)

Discrete Data - Math Steps, Examples & Questions (38)

Discrete Data - Math Steps, Examples & Questions (39)

Discrete Data - Math Steps, Examples & Questions (40)

Discrete data collects only numbers.

The second table has answers that are NOT numbers:

  • What is your favorite pet? Possible answers: cat, dog, fish, bird

Discrete data has a set number of possible responses.

The first and third table do NOT have a set number of responses:

  • How many inches did it rain each day? 1.2 inches, 1.23 inches, 1.231 inches etc. – the possible length answers are infinite.
  • How long does it take each cheetah to run 50 \; m? \; 2 seconds, 2.4 seconds, 2.43 seconds, etc. – the possible amount of time answers are infinite.

The last table includes data for the question “How many push-ups did you do each week?” which is answered with a finite set of numbers, so the data set includes only discrete values.

5. Which graph does NOT show discrete data?

Discrete Data - Math Steps, Examples & Questions (41)

Discrete Data - Math Steps, Examples & Questions (42)

Discrete Data - Math Steps, Examples & Questions (43)

Discrete Data - Math Steps, Examples & Questions (44)

Discrete Data - Math Steps, Examples & Questions (45)

Discrete Data - Math Steps, Examples & Questions (46)

Discrete Data - Math Steps, Examples & Questions (47)

Discrete Data - Math Steps, Examples & Questions (48)

Discrete data collects only numbers – all graphs show a numerical data set.

Discrete data has a set number of possible responses.

The last graph does NOT have a set number of responses:

  • What is the temperature throughout the day? 50 degrees, 50.1 degrees, 50.13 degrees, 50.132 degrees, etc. – the possible answers are infinite.

A line graph always represents continuous data.

6.

Discrete Data - Math Steps, Examples & Questions (49)

How many more people ate exactly 2 slices than 1 slice?

2

Discrete Data - Math Steps, Examples & Questions (50)

10

Discrete Data - Math Steps, Examples & Questions (51)

20

Discrete Data - Math Steps, Examples & Questions (52)

1

Discrete Data - Math Steps, Examples & Questions (53)

Each pizza represents 10 people.

So 10 people had 1 slice and 30 people had exactly 2 slices.

30 slices – 10 slices = 20 slices

Discrete data FAQs

Are integers continuous?

The set of integers is an infinite set. However, data wise they are considered a countable set and therefore used to represent discrete data.

Is ordinal data discrete?

No, though ordinal data is represented with digits, they are used to define an order, not an amount. Knowing that one runner finished 1 st and another 2 nd, tells you the order in which they finished, but gives no indication of the amount of time it took each runner or the numerical value of the distance between their finishes.

The next lessons are

  • How to find the average in math
  • Representing data
  • Frequency table
  • Frequency graph

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

Discrete Data - Math Steps, Examples & Questions (54)

Find out how we can help your students achieve success with our math tutoring programs.

Introduction

What is discrete data?

Common Core State Standards

How to recognize discrete data

Discrete data examples

Example 1: recognizing types of dataExample 2: recognizing types of dataExample 3: recognizing types of data

How to analyze discrete data

Example 4: analyzing and then answering a question - discrete dataExample 5: analyzing and then answering a question - discrete dataExample 6: analyzing and then answering a question - discrete data

Teaching tips for discrete data

Easy mistakes to make

Related types of data lessons

Practice discrete data questions

Discrete data FAQs

Next lessons

Still stuck?

x

[FREE] Common Core Practice Tests (3rd to 8th Grade)

Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.

Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!

Download free

We use essential and non-essential cookies to improve the experience on our website. Please read our Cookies Policy for information on how we use cookies and how to manage or change your cookie settings.Accept

Discrete Data - Math Steps, Examples & Questions (2024)

FAQs

What are 5 examples of discrete data? ›

Other examples of discrete variables include the following:
  • The number of books you check out from the library.
  • The number of heads in a sequence of coin tosses.
  • The result of rolling a die.
  • The number of patients in a hospital.
  • The population of a country.

Which is an example of discrete data responses? ›

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 discrete data in classroom? ›

When values in a data set are countable and can only take certain values, it is called discrete data. For example, number of students in a class, number of players required in a team, etc. We can easily count the variables in a discrete data.

What is a discrete data question? ›

Discrete data is a count that involves integers — only a limited number of values is possible. This type of data cannot be subdivided into different parts. Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers.

What is an example of discrete in math? ›

Objects that are studied in discrete mathematics are largely countable sets such as formal languages, integers, finite graphs, and so on. Due to its application in Computer Science, it has become popular in recent decades. It is used in programming languages, software development, cryptography, algorithms etc.

What are the 10 examples of discrete random variables? ›

The following are 10 examples of discrete random variables:

The number of possible outcomes of a fair coin flip. The number of students present in the classroom. The number of awards received during the academic year. The daily incidence rate of covid cases.

What is a discrete question? ›

This means that discrete data only involves answering yes or no questions, such as "Does a product work?" The only possible answer is "yes" or "no," and these are discrete answers.

What is an example of data in math? ›

Data in math is a collection of facts and figures that can be in any form—numerical or non-numerical. Numerical data is the one you can calculate, and it is always collected in number form, such as scores of students in class, wages of workers in an organization or height of players on a football team, etc.

How to know if data is discrete or continuous? ›

Values: Discrete data represents exact figures you can count, such as the numbers of students in a class. In contrast, continuous data often includes measurable values representing a range of information, such as the extent of the difference between the shortest and tallest student in a class.

What is an example of a discrete object in math? ›

Discrete objects are those which are separated from (not connected to/distinct from) each other. Integers (aka whole numbers), rational numbers (ones that can be expressed as the quotient of two integers), automobiles, houses, people etc. are all discrete objects.

What is an example of discrete data in healthcare? ›

Number of visits to hospital in a year, number of children in a family, number of admitted patients in a hospital ward, number of missing teeth etc. are some of the examples for discrete variables. Discrete variables are usually counts.

What is not an example of discrete data? ›

For example, you can measure your height and weight, so it's not discrete data. If you aren't sure whether your data is discrete, try to put "the number of," in front of it. For example, "The number of customers who purchased from us last month," or, "The number of employees the company has."

What does discrete data look like? ›

Data that can only take certain values is called discrete data or discrete values. This is data that can be counted and has a limited number of values. It usually comes in the form of whole numbers or integers. These values must fit into certain categories and can't be broken into smaller parts.

What are the two types of discrete data? ›

1.1 - Types of Discrete Data
  • Nominal (e.g., gender, ethnic background, religious or political affiliation)
  • Ordinal (e.g., extent of agreement, school letter grades)
  • Quantitative variables with relatively few values (e.g., number of times married)

What is an example of a discrete sample? ›

Tossing a coin (object with two distinct sides) is an example of discrete sample space. Generally, a discrete sample space does not contain decimal values. In the case of a single toss, the sample space has two elements: {Head, Tail}, or {H, T}, or {0, 1}.

What are 5 examples of continuous random variables? ›

Continuous random variables have many applications. Baseball batting averages, IQ scores, the length of time a long-distance telephone call lasts, the amount of money a person carries, the length of time a computer chip lasts, and SAT scores are just a few.

What are 5 examples of variables? ›

Definition. A variable is any characteristic, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.

What are the 5 examples of data? ›

  • Data collection:
  • Examples of data collection:
  • Monthly bills of a person.
  • Number of students in a class.
  • Number of persons liking a particular food.
  • Number of warehouses in a factory complex.
  • Number of hours spend on daily activities.

What type of data is discrete? ›

Data that can only take certain values is called discrete data or discrete values. This is data that can be counted and has a limited number of values. It usually comes in the form of whole numbers or integers. These values must fit into certain categories and can't be broken into smaller parts.

References

Top Articles
Latest Posts
Recommended Articles
Article information

Author: Lidia Grady

Last Updated:

Views: 5635

Rating: 4.4 / 5 (45 voted)

Reviews: 92% of readers found this page helpful

Author information

Name: Lidia Grady

Birthday: 1992-01-22

Address: Suite 493 356 Dale Fall, New Wanda, RI 52485

Phone: +29914464387516

Job: Customer Engineer

Hobby: Cryptography, Writing, Dowsing, Stand-up comedy, Calligraphy, Web surfing, Ghost hunting

Introduction: My name is Lidia Grady, I am a thankful, fine, glamorous, lucky, lively, pleasant, shiny person who loves writing and wants to share my knowledge and understanding with you.