Continuous and Discrete Data in Graphs
In 6th grade graphing, continuous data is plotted as a connected solid line because all values between the plotted points are meaningful — for example, time and distance where you can travel for 1.5 hours. Discrete data is plotted as separate unconnected points because only specific values make sense — for example, number of concert tickets where 2.5 tickets is impossible. Choosing the right graph type is crucial for accurately representing real-world data. This distinction from Reveal Math, Course 1, Module 7 prevents a common graphing error in 6th grade math.
Key Concepts
Property Continuous Data: Data that can take any value within a range, including fractions and decimals. It is graphed using a solid line . Discrete Data: Data that can only take specific, separate values, such as whole numbers. It is graphed using distinct, unconnected points (or sometimes a dashed line).
Examples Continuous Data: The relationship between time traveled, t, and distance covered, d. Since you can travel for partial hours (like 1.5 hours) and cover partial miles, the graph is drawn with a solid line. Discrete Data: The relationship between the number of concert tickets purchased, n, and the total cost, c. Since you cannot buy a fraction of a ticket (like 2.5 tickets), the graph is drawn with distinct points.
Explanation When graphing real world relationships, the context determines whether the data is continuous or discrete. Continuous data can include partial values like fractions, so the points are connected with a solid line to show that all values between the points are valid. Discrete data involves quantities that cannot be broken down into smaller parts, such as people, tickets, or books. For discrete data, unconnected points are used to indicate that intermediate values are impossible.
Common Questions
What is the difference between continuous and discrete data?
Continuous data can take any value in a range, including fractions and decimals (like time or temperature). Discrete data can only take specific separate values, usually whole numbers (like number of people or tickets).
How do I graph continuous data?
Connect the data points with a solid line to show that all values between the points are valid and meaningful.
How do I graph discrete data?
Plot each data point as a separate dot but do not connect them, since values between the plotted points are not possible.
Is the relationship between hours worked and pay continuous or discrete?
It is typically continuous, since you can work for fractional hours (like 2.5 hours) and earn a fractional amount. Graph it with a solid line.
Is the relationship between number of books ordered and total cost continuous or discrete?
It is discrete, since you can only order a whole number of books. Graph it with separate unconnected points.
When do 6th graders learn about continuous vs. discrete data in graphs?
Module 7 of Reveal Math, Course 1 covers this in the Relationships Between Two Variables unit.