๐ฏ Learning Objectives
- construct cumulative-frequency tables;
- plot upper class boundaries;
- draw an ogive;
- estimate median and quartiles;
- calculate IQR from a curve.
Introduction
This lesson develops Cumulative Frequency and Ogives 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.
Cumulative Frequency
Cumulative frequency is a running total.
| Class | f | CF |
|---|---|---|
| 0โคx<10 | 4 | 4 |
| 10โคx<20 | 7 | 11 |
| 20โคx<30 | 9 | 20 |
Reading an Ogive
Move horizontally from the desired cumulative frequency to the curve, then vertically to the data axis.
๐ Ogive, Median and Quartile Explorer
Edit frequencies. The cumulative frequencies, ogive and estimated quartile positions update.
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
- Find the final cumulative frequency in the table.
- For N=80, state the positions of Qโ, median and Qโ.
- Which boundary values are plotted on the horizontal axis?
- If Qโโ18 and Qโโ42, find IQR and semi-IQR.
โ Check Your Work
Show answers and working
- 20.
- Qโ at 20th value, median at 40th, Qโ at 60th.
- The upper class boundaries.
- IQR=42โ18=24; semi-IQR=12.
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
- CF is a running total.
- Ogives estimate median, quartiles and IQR.