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D1.1 · Distinguish discrete from continuous data

Learn to distinguish discrete from continuous data through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Data

How to tell whether data are counted or measured

Data are facts or values that we collect. Before deciding what a set of data tells us, ask how its values were found. Were items counted, or was something measured? This question helps us distinguish discrete data from continuous data. The examples in this lesson are hypothetical: they show possible situations, not real observations.

What you will learn

Explain the difference between discrete data and continuous data.
Use the way data are collected to classify them.
Explain why a whole-number answer does not always mean the data are discrete.

Start with counting and measuring

You already use two different ways to find out about things. You can count objects, such as the books on a shelf. You can also measure something, such as the length of a book. These ways of collecting information lead to two kinds of data.

Discrete data come from counting separate items or events. The possible values have gaps between them. For example, the number of books in a stack could be 0, 1, 2, or 3. A stack cannot have 2.4 books if you are counting whole books.

Continuous data come from measuring something that can take values between other values. For example, a book's length might be 20 centimetres, or a little more or less. A measurement can be reported with different levels of detail. The object does not suddenly change size when the measuring tool shows more detail.

A measurement is a value found by comparing something with a unit, such as centimetres or seconds. A count tells how many separate things there are. The unit or the way a question is worded can help you decide which kind of data you have.

Count separate items or events: discrete data.
Measure an amount that can vary between values: continuous data.

Use the collection method

To classify data, first identify exactly what is being recorded. Then ask how each value is found. If a person counts separate things, the data are discrete. If a person measures a quantity, the data are continuous.

Think of this as a decision rule, not a rule about how the answers look. Counts are often whole numbers, but a displayed number alone is not enough to classify data. A measurement can be rounded and written as a whole number. It is still continuous if it came from measuring a quantity.

For example, a record of how many students are in a room is a count. A record of students' heights is a measurement. Even if each height is rounded to a whole centimetre, the data are still continuous because height was measured.

The same subject can lead to either kind of data. Counting how many steps a person takes gives discrete data. Measuring the distance walked gives continuous data. The important clue is how the recorded value was obtained.

Name what each value describes before classifying it.
Ask: Was it counted, or was it measured?
Rounding a measurement does not change how the data were collected.

A careful way to explain your choice

A good classification includes a reason. Do not only write “discrete” or “continuous.” Say what was counted or measured. This makes your thinking clear and can help you catch a mistake.

Use this sentence frame: “These data are _ because they record the _ of separate items” or “These data are _ because they record a measurement of _.” Choose the kind that fits the collection method.

Some questions can sound unclear. For example, “How many centimetres long is the ribbon?” asks for a measurement, even though it begins with “how many.” Look at the quantity being recorded, not just one word in the question.

If you are unsure, picture how someone would collect the values. Would they count objects or events one by one? Or would they use a measuring tool to find an amount? That imagined collection method can make the difference clear.

Give both the data type and the reason.
Use the meaning and collection method, not one keyword, to decide.

Try the rule yourself

For each new set of data, pause before choosing a label. Identify what one value describes. Next, decide whether the value comes from counting or measuring. Finally, explain your choice in a sentence.

Keep the difference in mind: a count is about how many separate items or events; a measurement is about how much of a quantity there is. These simple questions are enough for this lesson's classification.

Identify the recorded quantity.
Decide whether it is counted or measured.
State the data type and explain why.

Two ways to collect data

Kind of data	How values are found	Example
Discrete	Count separate items or events	Number of books on a shelf
Continuous	Measure an amount	Length of a ribbon

Worked example

Books in a reading corner

A class makes a record of the number of books on each shelf. Is this discrete or continuous data? Explain.

Identify what is recorded
Each value tells how many books are on one shelf.
Decide how the value is found
The books are counted as separate items. A shelf can have 0 books, 1 book, or another whole number of books, but not part of a book as a count of books.
Classify and explain
These are discrete data because they record counts of separate books.

Answer: The data are discrete. They record counts of separate books.

Check: The reason is the counting method, not simply that the answers are whole numbers.

Worked example

Length of a ribbon

A student measures the length of a ribbon in centimetres. Is the recorded length discrete or continuous data? Explain.

Identify what is recorded
Each value describes the ribbon's length.
Decide how the value is found
Length is measured. A ribbon can have a length between two whole-centimetre marks, even if the student records only a rounded value.
Classify and explain
These are continuous data because they record a measurement of length.

Answer: The data are continuous. They record a measured length.

Check: Writing a length as a whole number of centimetres would not make it a count.

Worked example

Steps and distance

A student records the number of steps taken on a walk. Another record gives the distance walked. Classify each set of data and explain the difference.

Look at the number of steps
Steps are separate events that can be counted one at a time. The number of steps is discrete data.
Look at the distance
Distance describes how far the student walked. It is found by measuring, so it is continuous data.
Compare the collection methods
The two records are about the same walk, but they record different things. One is a count of steps; the other is a measurement of distance.

Answer: The number of steps is discrete data. The distance is continuous data.

Check: The topic alone does not determine the type. What is recorded and how it is found matter.

Common mistakes and how to avoid them

Calling data discrete just because the recorded values are whole numbers.

Correction: Check how the values were collected. A measured value can be rounded to a whole number and still be continuous.

Deciding from a single word such as “how many.”

Correction: Look at what is being recorded. A question about how many centimetres asks for a measurement of length.

Giving a label without a reason.

Correction: Name what was counted or measured so the classification is clear.

Lesson summary

Discrete data come from counting separate items or events.
Continuous data come from measuring a quantity that can vary between values.
Classify data by how the values are collected, not just by how the numbers are written.
Explain your choice by naming what was counted or measured.

Check your understanding

Question 1

A record shows how many chairs are in each classroom. Which kind of data is it?

Discrete, because chairs are counted as separate items
Continuous, because a classroom has a size
Continuous, because the record uses numbers
Discrete, because every number is a measurement

Show answer and explanation

Discrete, because chairs are counted as separate items

The values are counts of separate chairs, so the data are discrete.

Question 2

A student measures the time it takes to complete a task. Which kind of data is the time?

Discrete, because time is recorded with numbers
Continuous, because time is measured
Discrete, because a task happens once
Continuous, only if the answer has a decimal

Show answer and explanation

Continuous, because time is measured

The time is a measured quantity. It is continuous whether it is written as a whole number or with more detail.

Question 3

A list gives the number of pages in each book. Why are these data discrete?

Because pages are counted as separate items
Because all data written as numbers are discrete
Because book pages have a measurable length
Because a list cannot contain measurements

Show answer and explanation

Because pages are counted as separate items

The recorded value is a count of pages, so it is discrete.

Key terms

Data: Facts or values collected to describe something.
Discrete data: Data found by counting separate items or events.
Continuous data: Data found by measuring a quantity that can take values between other values.
Measure: To find the size or amount of something by comparing it with a unit, such as centimetres or seconds.
Count: To find how many separate items or events there are.
Round: To write a value in a simpler form, often with fewer details.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation D1.1. It is a study resource, not an official curriculum publication.

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