Grouped frequency tables
Every record must belong to exactly one class
- Cover every observation Choose non-overlapping intervals that include the minimum and maximum. Tally each observation once, including repeats
- State the convention For whole-number records, 20–29 includes 20 and 29. For continuous measurements, 20 ≤ x < 30 includes 20 but excludes 30.
- Check the total The frequencies must sum to the number of observations. Retain empty classes with frequency zero
- Percentage frequency Divide the class frequency by the total and multiply by 100. Round only at the end
Worked example
Group these waiting times in minutes: 0.4, 1.8, 2.0, 2.3, 3.1, 4.6, 5.9, 6.0, 6.2, 8.4, 10.1, 11.8. Use classes 0 ≤ x < 4, 4 ≤ x < 8 and 8 ≤ x < 12. Find the frequencies and percentages to one decimal place where necessary
- \(\displaystyle 5+4+3=12\)All twelve observations are counted exactly once
- \(\displaystyle \frac{5}{12}\times100\approx41.7\%\)Keep the exact count and total until the final percentage is rounded
- \(\displaystyle 41.7+33.3+25=100\)The displayed percentages total 100% in this example. That is not guaranteed for every rounded table
Common mistakes
Difficulty levels
Questions about this topic
Are equal widths compulsory?+
These tasks use equal widths. Unequal-width groupings are possible, but histogram height then needs special care
Should I omit a zero-frequency class?+
Keep it. Zero is useful information and the numerical intervals must remain in order
Can grouped data give an exact mean?+
Usually no. The individual values have been lost; a midpoint calculation is an estimate
What does 2.0–2.9 mean?+
Here it names recorded tenths from 2.0 through 2.9 inclusive. The next recorded tenth is 3.0
Why might percentages total 99.9%?+
Separately rounded percentages need not total exactly 100%, although their unrounded values do
Does a wider class mean more observations were collected?+
No. It combines more of the existing numerical range. Check that the total frequency stays fixed
Can I compare two datasets if their groupings are different?+
Use a common grouping and scale where possible. Different widths or starting points can hide or exaggerate differences
Why use inequalities for continuous measurements?+
They state exactly which boundary is included and cover values such as 2.95 without gaps. A list of recorded tenths requires an explicit rounding convention
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 5: Statistics