Range
Maximumβminimum.
π― Learning Objectives
- calculate range;
- identify lower and upper quartiles;
- calculate interquartile range;
- calculate semi-interquartile range;
- compare spread in context.
Introduction
This lesson develops Range, Quartiles and Interquartile Range 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.
Measures of Spread
Interquartile Range
IQR=QββQβ.
Semi-IQR
(QββQβ)Γ·2.
A smaller spread usually means the values are more consistent.
Worked Example
Ordered data: 2,4,5,7,8,10,12,15.
Qβ=(4+5)Γ·2=4.5; Qβ=(10+12)Γ·2=11; IQR=6.5.
π¦ Quartiles and Box Plot Explorer
Practice Questions
- Find the range of 3,7,8,9,15.
- Given Qβ=18 and Qβ=34, find IQR and semi-IQR.
- Team A has IQR 4; Team B has IQR 11. Which is more consistent?
- Why is IQR less affected by extreme values than range?
β Check Your Work
Show answers and working
- 15β3=12.
- IQR=34β18=16; semi-IQR=8.
- Team A, because its middle 50% is less spread out.
- IQR uses the middle half of the data and ignores the most extreme quarter at each end.
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
- Range uses extremes.
- IQR describes the middle 50%.