๐ฏ Learning Objectives
- use tally marks correctly;
- construct ungrouped frequency tables;
- construct grouped frequency tables;
- check frequency totals;
- interpret frequencies in context.
Introduction
This lesson develops Tally and Frequency Tables from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
From Raw Data to a Table
Raw scores: 2, 4, 3, 2, 5, 4, 2, 3, 4, 2.
| Score | Tally | Frequency |
|---|---|---|
| 2 | |||| | 4 |
| 3 | || | 2 |
| 4 | ||| | 3 |
| 5 | | | 1 |
The sum of all frequencies must equal the total number of observations.
Grouped Frequency Table
| Time, t (minutes) | Frequency |
|---|---|
| 0โคt<10 | 3 |
| 10โคt<20 | 7 |
| 20โคt<30 | 5 |
๐ Live Tally and Frequency Table
Enter comma-separated responses using A, B, C or D.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- Construct a frequency table for 1,2,2,3,1,4,2,3,1,2.
- Find the total frequency in the grouped table above.
- Which interval is modal?
- Explain how you would check that a frequency table is complete.
โ Check Your Work
Show answers and working
- Frequencies: 1โ3, 2โ4, 3โ2, 4โ1.
- 3+7+5=15.
- 10โคt<20.
- Add all frequencies and compare the total with the number of raw observations.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Tallies organise counting.
- Frequency tables summarise how often values occur.