Numerical data is discrete when it is counted (siblings: 0, 1, 2, …) and continuous when it is measured (a 100 m time can be any value, such as 14.37 s). Measured values are always rounded to some precision.
How many siblings do you have? How long does it take you to run 100 m? One answer is always a whole number; the other could be anything in between.
Statistics starts with data: values collected to answer a question. Numerical data comes in two kinds:
Discrete data is counted: number of siblings, goals scored, cars in a car park. It takes separate values, usually whole numbers.
Continuous data is measured: height, time, mass, temperature. It can take any value in a range; we round it when we record it.
The kind of data changes how you collect it, and how you display it later in this unit.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Which can be 152.5?
Ask of each one: is it counted, or measured?
TryTry it on the board and compare the result with your prediction.
Add a time
Times can land between the marks. Could you add 14.35 s? What would you need to measure it?
Try it yourselfYour edits are saved in this browser.
These are 100 m times in seconds. Add a time of 14.3 s (click the line, or type it in the box). Was your prediction right about measuring?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Counted or measured
Here is how to tell the kinds apart.
Worked exampleBefore each step, say what you think comes next.
siblings: 0,1,2,3Counted: separate values, no values in between. Discrete.
height: 152.5 cmMeasured: any value in a range. Continuous.
152.5≈152.47…A measurement is rounded to the precision of the instrument (here 0.1 cm).
shoe size: 7,7.5,8Fixed steps with nothing in between: discrete, even with halves.
Sort each one: discrete or continuous?
Read Ava's reasoning. Can a shoe size be 7.3?
Discrete or continuous?
Number of pets
Mass of a backpack in kg
Goals scored in a match
Time to solve a puzzle
Daily rainfall in mm
Number of letters in a name
Ava decides what kind of data shoe size is. Click the line where her reasoning goes wrong.
ModifyChange the problem on purpose and see what happens.
One change at a time
Each task changes one thing.
PractiseA few on your own, to check you have it.
Kinds of data
Review: which is bigger, 14.3 or 14.25? Type the bigger one.
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Your own measured data
Then: if you rounded your times to the nearest second, how many different values would be left?
Try it yourselfYour edits are saved in this browser.
Need a hint?
Every value must be more than 13 and less than 14.
Another hint
Type them in the box, such as 13.2, 13.5, …
Make a data set of 6 swim times, all between 13 s and 14 s.
Use the board. This ticks when you get there.
For teachers
Students sort numerical variables into discrete (counted) and continuous (measured), place a measured value between whole numbers on a dot plot, and see that measurements are always rounded to some precision (AC9M7ST01, node 1). About 35 minutes.
I can say whether numerical data is discrete (counted) or continuous (measured).
I can explain why a measurement is always rounded, and choose a sensible precision.
Before class
Try the Run board first. This short lesson opens the Data unit; the next lesson calculates mean, median, mode and range.
The one idea: counted data takes separate values (discrete); measured data can be any value in a range (continuous). The common mistake is treating any decimal as continuous (shoe sizes, prices); it is planted in Ava's reasoning.
Age and money are worth discussing rather than ruling on: age is measured time recorded in whole years; money is counted in cents but has so many values that it is often treated as continuous.
Running the lesson
Predict: take a show of hands; ask each group how they decided.
Run: ask whether a 14.35 s time is possible and what would measure it.
Investigate: build a two-column list on the board (counted / measured) from students' own examples.
Modify: let the age question be a short debate.
Make: ask what happens to the six times if rounded to whole seconds.
When students get stuck
A student calls any decimal data continuous (Ava's mistake). Ask: What values are possible between 7 and 7.5 for a shoe size? Fix: Fixed steps with nothing in between: discrete.
A student calls large counts continuous. Ask: Is it counted or measured? Fix: Counted, however big: discrete.
Stretch and support
Stretch: Find a variable that could be recorded either way, depending on how you collect it (time in whole minutes, or measured with a stopwatch).
Support: Ask 'Could you have half of one?' and 'Is it counted or measured?' for every variable.
Where it leads
Next: Mean, median, mode and range (node 2), then choosing the most useful measure (node 3).
Where it leads: histograms for continuous data and sampling (Year 8 statistics).
What each step is for
which can be 152.5?: Committing to which variable can take the value 152.5 shows whether they think in terms of counting versus measuring.
add a time: Placing a value between whole numbers on a measured scale shows that continuous data can fall anywhere, limited only by how precisely it is measured.
counted or measured: Counted gives discrete data, measured gives continuous; and measured values are always rounded. Ava's mistake thinks any decimal means continuous.
one change at a time: One change at a time: the same topic counted or measured, money, a rating scale, then the edge case of age, which is measured but usually recorded as a count of years.
kinds of data: Classifying variables from contexts, choosing a precision, and spotting rounding, mixed; the review keeps decimals fresh.
your own measured data: Building a data set whose values all lie between two whole numbers shows that continuous data needs decimals, and that more precision separates values that rounding would merge.
Now you can
Say whether numerical data is discrete (counted) or continuous (measured).
Explain why a measurement is always rounded, and choose a sensible precision.