Classifying variables
Classify the variable family first, then choose a subtype. The meaning and origin of the values matter more than whether the values are written as words or digits
\[\text{categorical}\;\text{or}\;\text{numerical}\;\longrightarrow\;\text{subtype}\]
- Find the variable family Values that name or group things are categorical. Values that are counted or measured are numerical \(\displaystyle \text{names or groups}\Rightarrow\text{categorical},\quad\text{counts or measurements}\Rightarrow\text{numerical}\)
- Separate categorical variables Nominal categories are names only. Ordinal categories have an inherent order \(\displaystyle \text{car, bus, train}\Rightarrow\text{nominal},\quad\text{poor < fair < good}\Rightarrow\text{ordinal}\)
- Separate numerical variables Discrete variables arise from counting. Continuous variables arise from measuring and can take values in a range \(\displaystyle \text{number of pets}=0,1,2,\ldots\Rightarrow\text{discrete},\quad\text{height}=\text{a measured value}\Rightarrow\text{continuous}\)
- Look past numeric codes Digits used as labels do not make a variable numerical. Check what the values represent \(\displaystyle \text{rating codes }1,2,3,4,5\Rightarrow\text{ordinal categorical}\)
Worked example
A school survey records each student's satisfaction with the canteen as 1 = very low, 2 = low, 3 = medium, 4 = high or 5 = very high. Classify the variable
\[1,2,3,4,5\quad\text{with an inherent order}\]
- \(\displaystyle \text{The values are ordered response codes, not counts.}\)The digits name levels of satisfaction rather than counting objects
- \(\displaystyle \text{categorical}\)The values describe response groups
- \(\displaystyle \text{ordinal}\)The response groups have an inherent order from very low to very high
Common mistakes
Reading numeric codes as measurements
✕\(\displaystyle \text{a rating of }4\text{ stars is a discrete numerical variable}\)✓\(\displaystyle \text{a rating of }4\text{ stars is an ordinal categorical variable}\)
Digits can be category codes, so their appearance does not make the variable numericalMissing the category order
✕\(\displaystyle \text{poor, fair, good, excellent}\Rightarrow\text{nominal}\)✓\(\displaystyle \text{poor, fair, good, excellent}\Rightarrow\text{ordinal}\)
The categories have an inherent order, so the variable is ordinalCalling a measurement discrete
✕\(\displaystyle \text{length measured to 1 decimal place}\Rightarrow\text{discrete}\)✓\(\displaystyle \text{length measured to 1 decimal place}\Rightarrow\text{continuous}\)
A measured quantity can take values in a range; recording to a fixed precision does not make it a countDifficulty levels
introClassify an unambiguous count, measurement, named category or ordered category
standardClassify numeric codes and measurements recorded to a fixed number of decimal places
challengeClassify ordered measurement bands, wide-range counts and mixed variables
examChoose one label from the four-way classification with misconception-based distractors
Questions about this topic
What makes a variable categorical?+
A categorical variable records names or groups. Arithmetic on the category labels is not meaningful
What is the difference between nominal and ordinal data?+
Nominal categories have no inherent order. Ordinal categories have a meaningful order, even when their labels are words or numeric codes
What is the difference between discrete and continuous data?+
Discrete data arise from counting particular values. Continuous data arise from measuring and can take any value in a range
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 12, VCE Units 3 & 4, General Mathematics, chapter 1: Data distributions
In this chapter
Classify a variable as nominal, ordinal, discrete or continuousBuild a frequency and percentage frequency tableBuild a bar chart from a frequency tableConstruct or read a percentage segmented bar chartRead values from a frequency table or bar chartReport on the distribution of a categorical variableGroup numerical data into class intervalsConstruct a histogram from a frequency tableRead values from a histogramChoose an appropriate display for a variableDescribe the shape of a distributionConstruct a dot plot from raw dataConstruct an ordered stem plot from raw dataFind the mean and the median, and choose between themFind measures of centre from a frequency displayWork backwards from a mean or medianFind the range, the quartiles and the IQRCalculate the standard deviation from the formulaApply the 68–95–99.7% ruleProduce a five-number summary and construct a boxplotFind the fences and identify outliersRead values and percentages from a boxplotCompare a numerical variable across groupsTransform and interpret a distribution on a base-10 log scaleDecide whether the normal model is applicableCalculate a standard score or actual valueCompare observations from different distributions using z-scoresUse z-score boundaries to estimate normal-model percentages and countsInfer a normal-model mean or standard deviation