Meaning before format
Classify the property as recorded. Separate an underlying continuous quantity from its rounded reading or an ordered band
- Nominal categories Labels with no inherent ranking, such as travel method. Digits can be labels too
- Ordinal categories Ordered levels or bands, such as low, medium and high. Equal numerical gaps are not implied
- Discrete numerical Separate possible numerical values, often whole-number counts
- Continuous numerical A measured quantity can vary throughout an interval. Rounding restricts its recorded precision
- Rounded measurement Keep units and stated precision. A measurement rounded to whole minutes is not the same variable as a count of visits
- Banded measurement Store the category boundaries and which endpoints are included. Do not present band midpoints as exact observations
- Identifiers and ratings Keep a codebook. Identifier numbers have no numerical magnitude; rating codes imply order, not necessarily equal intervals
Worked example
Waiting times are 8.2, 13.4, 18.7 and 22.6 minutes. The report retains only the bands 0 to less than 10, 10 to less than 20, and 20 to less than 30 minutes. Classify the original variable and the banded variable, then count the middle band
- \(\displaystyle \text{continuous}\)Original waiting time is a measured duration
- \(\displaystyle \text{ordinal}\)Saved band labels have an inherent order and conceal exact times
- \(\displaystyle 13.4,\ 18.7\quad\Rightarrow\quad 2\)These two times are at least 10 but less than 20 minutes
Common mistakes
Difficulty levels
Questions about this topic
Does a decimal always mean continuous?+
No. The meaning of the variable matters. Decimal category codes are still codes, and rounded measurements describe an underlying continuous quantity
Are whole-number measurements discrete?+
The underlying measured quantity is generally continuous even if the instrument records whole units. State whether you mean the quantity or its finite recording grid
Is a number of people continuous when it is large?+
No. A large count still takes separate whole-number values
Why is a rating ordinal?+
The levels have an order. Equal differences in the printed codes do not prove equal differences in the rated quality
What happens when a measurement is grouped?+
If only an ordered band label is retained, the recorded variable is ordinal and exact values are lost. A histogram may group numerical measurements for display without replacing the underlying raw variable
Can a category be written with digits?+
Yes. Postcodes and participant IDs are nominal identifiers. Keep their codebook and preserve meaningful leading zeros
How do I avoid gaps and overlaps?+
Write every boundary and its inclusion rule. For example, 10 to less than 20 is followed by 20 to less than 30
Why must two variables be paired?+
To study their relationship, both must refer to the same observational unit and compatible time period
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 5: Statistics