Grade by Grade
D. Data · Data Literacy and Probability

Discrete and Continuous Data

D1.1 A1About 45 minutes
Learning goals
  • I can explain the difference between discrete and continuous data.
  • I can give my own examples of discrete data and continuous data.
  • I can decide whether a data set is qualitative, discrete or continuous, and explain my thinking.

Words to know

qualitative data
Data that is words or categories, like favourite season or type of tree.
quantitative data
Data that is numbers, which you get by counting or measuring.
discrete data
Quantitative data that is counted. Only certain separate values are possible, with gaps in between (you can have 2 or 3 pets, but not 2.5 pets).
continuous data
Quantitative data that is measured. Any value in a range is possible, including values in between (an icicle can be 2.7 cm or 2.75 cm long).
precision
How exact a measurement is. A more precise tool lets you record more decimal places.

Remember from Grade 4

Qualitative data is words or categories (favourite winter sport: skating, skiing, hockey). Quantitative data is numbers (how many minutes you skated). This year we split quantitative data into two kinds.

Counting or measuring?

Think about these two questions:

  • How many pets does your family have?
  • How long is the icicle hanging from the roof?

Both answers are numbers, so both are quantitative data. But they are different kinds of numbers.

You find the number of pets by counting: 0, 1, 2, 3... Nobody has 2.5 pets. This is discrete data. Only certain separate values make sense, and there are gaps between them.

You find the length of an icicle by measuring. It might be 2 cm, 2.7 cm, or 2.75 cm. Every value in between is possible. This is continuous data. There are no gaps.

A row of icicles of many different lengths hanging from a snowy roof edge against a blue sky.
Counting the icicles gives discrete data. Measuring how long one icicle is gives continuous data, because any length in between is possible. AI-generated image
Discrete: number of pets (counted)012345Continuous: icicle length in cm (measured)0123452.7
Top: discrete data can only land on the dots (0, 1, 2, 3, 4 or 5 pets). Bottom: continuous data can land anywhere on the bar, like 2.7 cm.

The "in between" test

To decide, ask: Does a value in between make sense?

  • 3.5 goals in a hockey game? No. Goals are counted. Discrete.
  • 3.5 kg for a pumpkin? Yes. Mass is measured. Continuous.

Common discrete data: numbers of people, pets, books, goals, cars, votes.

Common continuous data: length, height, distance, mass, time, temperature, volume.

For continuous data, the numbers we write down are rounded. A stopwatch might show 12.3 seconds, and a better one might show 12.34 seconds. The real time could be any value; our tool decides how precise we can be.

Is the data words or numbers?QUALITATIVEwords or categoriesfavourite seasonCounted or measured?DISCRETEcounted, with gaps3 pets, 31 studentsCONTINUOUSmeasured, no gaps2.7 cm, 17.8 swordsnumberscountedmeasured
Two questions sort any data. Words are qualitative. For numbers, ask: was it counted (discrete) or measured (continuous)?
Worked example

Example 1: Sort the data

Sort each into qualitative, discrete or continuous:

  1. the number of hockey cards in a collection
  2. the length of a maple leaf
  3. favourite season
  4. the time it takes to run 100 m
  5. the number of students on a school bus
  6. the mass of a pumpkin
  1. Is it words or numbers? Favourite season is a word (winter, spring...), so it is qualitative.
  2. For the others, ask: counted or measured? Does a value in between make sense?
  3. Hockey cards and students on a bus are counted. You can't have 45.5 cards or 31.5 students. Discrete.
  4. Length, time and mass are measured. A leaf can be 9.4 cm, a run can take 17.8 s, a pumpkin can be 4.35 kg. Continuous.

Qualitative: 3. Discrete: 1, 5. Continuous: 2, 4, 6.

Worked example

Example 2: One topic, two kinds of data

Maya wants to know how much Grade 6 students read. Write one question that collects discrete data and one that collects continuous data.

  1. Discrete data is counted. Count something about reading: books.
  2. Continuous data is measured. Measure something about reading: time.
  3. Make each question clear, with a time period, so everyone answers the same thing.

Discrete: "How many books did you finish in October?" Continuous: "How much time did you spend reading yesterday, in minutes?"

Think like a mathematician

Some data is tricky. When you are not sure, talk it through with someone: "What would a value in between look like here? Does it make sense?" Explaining your thinking out loud, and listening to a different idea, is how mathematicians sort out hard cases.

Just for fun

Riddle: What kind of data is a melting snowman's height?

Continuous! He shrinks a tiny bit every second, with no gaps. (Sorry, Frosty.)

Hands-on activity

Home data hunt

You need: paper, a pencil, and a ruler or measuring tape. A kitchen scale is a bonus.

  1. Make two columns: Discrete (I counted) and Continuous (I measured).
  2. Walk around your home. Find 5 things to count (for example: chairs, cans in the cupboard, windows, books on a shelf, people at dinner) and 5 things to measure (for example: length of a spoon, height of a door, mass of an apple, time to tie your shoes, length of a boot).
  3. Collect each piece of data and write it in the right column with its unit.
  4. Look at your continuous column. Could you have measured any of them more precisely? How?

What to look for: counts are whole numbers with no units like cm or kg; measurements have units and could have decimals.

Your turn

1

Is the number of maple trees in a park discrete or continuous?

2

Is the height of a maple tree discrete or continuous?

3

Is the temperature outside at noon discrete or continuous?

4

Is favourite type of pizza qualitative or quantitative?

5

Is the number of goals a hockey team scores in a season discrete or continuous?

6

Give one example of discrete data and one of continuous data about your school.

7

Why is the time to run around the track continuous data?

More practice: warm-up

1

Discrete data is usually ______. Continuous data is usually ______. (counted / measured)

2

Is the number of letters in your name discrete or continuous?

3

Is the mass of a backpack discrete or continuous?

4

Is eye colour qualitative or quantitative?

5

Is the amount of rain that fell last week (in mm) discrete or continuous?

More practice: on your own

1

Sort these: number of siblings, length of a snake, number of votes for class president, volume of water in a bathtub.

2

Write a question about winter that would collect continuous data.

3

Write a question about winter that would collect discrete data.

4

Leo says, "The number of cm in a ruler is 30, so length is discrete." Do you agree?

5

A stopwatch says a swimmer took 31.47 s. Is this data discrete or continuous? Could the real time be 31.468 s?

Challenge

1

Shoe sizes can be 5, 5½, 6, 6½... Is shoe size discrete or continuous? Explain.

2

Is the age of a person discrete or continuous? Explain why the answer can depend on how you record it.

3

Amounts of money are often treated as discrete data. Why? (Hint: think about the smallest unit.)

Check your understanding

Quiz

1.

Which data is discrete?

2.

Which data is continuous?

3.

What is the best test for continuous data?

4.

Favourite winter sport is:

5.

Which question collects continuous data?

6.

A thermometer reads −4.5°C. Temperature is:

For parents and teachers

What this lesson teaches: the difference between discrete data (counted, with gaps between possible values) and continuous data (measured, any value in a range is possible) (D1.1). It builds on Grade 4's qualitative and quantitative data. Talking through tricky cases with others practises the mathematical processes in Strand A (A1).

How to help at home:

  • Play "counted or measured?" in the car or at dinner: "The number of red lights we passed?" (discrete) "How long the trip took?" (continuous)
  • Use the "in between" test: "Could it be 2 and a half?"
  • Measure things with a tape measure, kitchen scale or timer so your child feels the difference between counting and measuring.

Common difficulties:

  • Thinking any data with decimals is continuous. Money has decimals but is counted in cents, so it is usually treated as discrete.
  • Thinking measurements are discrete because we write them as rounded numbers. The quantity is continuous; we round because our tools have limits.
  • Mixing up qualitative (words) with discrete (counted numbers).