Reporting a categorical distribution
Support a short description with the sample size, category names and relevant figures
- Mode Name the category with the largest frequency. If categories tie for the largest frequency, report the tie
- Evidence Give the count or percentage that supports the statement. A largest category need not contain more than half the sample
- Order Ordinal categories can be displayed in either consistent direction. Do not scramble their inherent order
- Scope Describe the sample unless its selection supports a wider conclusion
Worked example
Forty students choose one travel method: Walk 12, Bus 18 and Car 10. Describe the most common response
- \(\displaystyle 12+18+10=40\)There are 40 responses
- \(\displaystyle 18>12>10\)Bus has the largest count
- \(\displaystyle \frac{18}{40}\times100=45\)Bus was the most common travel method, chosen by 18 of the 40 students surveyed (45%). This is not a majority
Common mistakes
Difficulty levels
Questions about this topic
Can a distribution have tied modes?+
Yes. Report all categories tied for the greatest frequency. Do not choose one merely because it is listed first
Must the most common category exceed 50%?+
No. Most common means the largest category. A majority is more than half of the sample
Is descending ordinal order wrong?+
No. Both directions can preserve the scale. A scrambled sequence does not
Can percentages reveal the sample size?+
Not by themselves. Many sample sizes can produce the same percentages
Does choosing a report prove I can write one?+
No. Practise writing your own short description too, then check its sample, category names and supporting figures
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 2: Data distributions