Percentiles and Quartiles
So far, we have learned how to describe the center and spread of data. Another important question we often ask is:
Where does a particular value stand compared to the rest of the data?
Percentiles and quartiles help us understand the relative position of data values within a dataset.
What Is a Percentile?
A percentile tells us the value below which a certain percentage of the data falls.
For example:
- The 50th percentile means 50% of the data is below that value
- The 90th percentile means 90% of the data is below that value
Percentiles are widely used in exams, performance analysis, and rankings.
Real-World Example (Percentile)
If a student scores in the 85th percentile on an exam, it means:
The student performed better than 85% of the students who took the exam.
Numerical Example (Percentile)
Consider the following sorted data:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100
The 50th percentile (median) lies in the middle of the data.
The 90th percentile is the value below which 90% of the data lies. In this dataset, that value is 90.
What Are Quartiles?
Quartiles divide the data into four equal parts. Each part contains 25% of the data.
There are three main quartiles:
- First Quartile (Q1) – 25th percentile
- Second Quartile (Q2) – 50th percentile (Median)
- Third Quartile (Q3) – 75th percentile
Quartiles Explained Visually
| Quartile | Percentile | Meaning |
|---|---|---|
| Q1 | 25% | 25% of data lies below this value |
| Q2 | 50% | Middle of the dataset (Median) |
| Q3 | 75% | 75% of data lies below this value |
Numerical Example (Quartiles)
Consider the sorted dataset:
5, 10, 15, 20, 25, 30, 35, 40
Step-by-step:
- Q2 (Median) = average of 20 and 25 = 22.5
- Lower half: 5, 10, 15, 20 → Q1 = average of 10 and 15 = 12.5
- Upper half: 25, 30, 35, 40 → Q3 = average of 30 and 35 = 32.5
Real-World Example (Quartiles)
In salary analysis, quartiles are often used to show income distribution.
For example:
- Q1 shows the lower-paid group
- Q2 shows the median income
- Q3 shows the higher-paid group
Why Percentiles and Quartiles Matter
- They show relative position, not just averages
- They help compare individuals fairly
- They are resistant to extreme values
That is why they are commonly used in exams, analytics, and performance reports.
Quick Check
If a value is at the 75th percentile, what does it mean?
Practice Quiz
Question 1:
Which quartile represents the median?
Question 2:
What percentile corresponds to Q3?
Question 3:
Which measure is more useful for rankings?
Mini Practice
A student is placed in the 40th percentile of a test.
- Did the student score above or below average?
- Did they perform better than half the students?
What’s Next
In the next lesson, we will begin Probability Basics, which forms the foundation for understanding uncertainty and chance.