Quartiles and IQR
Quartiles split data into four parts; IQR = Q3 − Q1.
Key idea
Quartiles split data into four parts; IQR = Q3 − Q1.
In depth
Quartiles split ordered data into four equal parts: Q1 (25th percentile), Q2 (median), Q3 (75th). The interquartile range IQR = Q3 − Q1 measures the spread of the middle half and ignores outliers.
Worked example
Data 2, 4, 6, 8, 10, 12, 14: Q1 = 4, Q3 = 12, IQR = 8.
Formula
Real-world uses
- Comparing salary ranges between jobs or the middle half of athlete times
Common mistake
Including the median in both halves inconsistently when n is odd.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Quartiles and IQR?
Quartiles split data into four parts; IQR = Q3 − Q1. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Quartiles and IQR?
The key formula is IQR = Q₃ − Q₁.
Where is Quartiles and IQR used in real life?
Real-world examples: Comparing salary ranges between jobs or the middle half of athlete times.
What should I learn before Quartiles and IQR?
Make sure you are comfortable with Range, the previous topic in Probability & Statistics.
What is a common mistake with Quartiles and IQR?
Including the median in both halves inconsistently when n is odd.
How can I practise Quartiles and IQR?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Quartiles and IQR?
Move on to Box Plots next.
Related advanced topics in Probability & Statistics
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.
- Weighted Mean – Average where values have different importance.