Paired records and frequency tables
Preserve paired categorical records, construct frequency tables and recover missing counts
- Keep each pair intact One record contributes one count to the cell matching both categories
- Categories must be clear Choose non-overlapping categories that account for every included record, or state how missing or other values are handled
- Check both sets of margins All row totals and all column totals must give the same grand total
- Transpose with the labels A displayed row may represent either variable. The category, not its position, determines the meaning
- Recover rather than guess Subtract the other cells in a known margin to find a missing frequency
- Do not infer a cause A frequency table describes the recorded data. It does not by itself show why a pattern occurred
Worked example
Twelve cards are classified by colour and shape. Blue-round: 4; blue-square: 3; red-round: 2; red-square: 3. Find the Blue total, Round total and grand total
- \(\displaystyle 4+3=7\)Blue includes both shapes
- \(\displaystyle 4+2=6\)Round includes both colours
- \(\displaystyle 7+5=12\)Add the two colour totals, counting every card once
Common mistakes
Difficulty levels
Questions about this topic
Can two records have the same pair?+
Yes. Each distinct record contributes a separate count even if its category values match
Why do row and column totals agree?+
Both count every included record exactly once
Does the explanatory variable always go in columns?+
No. The displayed labels state which way the table is arranged
How should missing categories be handled?+
State the rule. For example, use a separate missing category or clearly describe excluded records
Is a zero cell an impossible outcome?+
Not necessarily. It means no such case was recorded in this collection
Are conditional percentages covered here?+
This placement develops count-table construction. Conditional probabilities and later group comparisons use these counts with explicitly chosen denominators
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 4: Probability