Percentile Rank, Percentile, quartiles,Deciles, median
Teaching Note: Percentile Rank
1. Introduction
In statistics, percentile rank is used to understand the position of a score in a group of scores. It shows the percentage of scores that fall below a particular value.
2. Meaning / Definition
Percentile Rank is the percentage of the total number of scores that lie below a given score in a distribution.
In other words, it tells how well a student performs compared with others in the group.
3. Formula
Percentile\ Rank = \frac{\text{Number of values below the score}}{\text{Total number of values}} \times 100
4. Example (Concept)
Suppose a student scored 450 marks and the percentile rank is 80.
This means:
- 80% of students scored below 450
- 20% of students scored above 450
So the student performed better than 80% of students in that group.
5. Example Problem
Find the percentile rank of 30 in the following data.
Data:
10, 15, 20, 25, 30, 35, 40, 45
Step 1: Total number of values = 8
Step 2: Number of values below 30 = 4
(10, 15, 20, 25)
Step 3: Apply formula
Percentile\ Rank = \frac{4}{8} \times 100
= 0.5 \times 100
= 50
Percentile Rank = 50
6. Interpretation
A percentile rank of 50 means:
- 50% of scores lie below 30
- 50% of scores lie above 30
Thus the score 30 is at the middle position of the data.
7. Educational Importance
- Helps compare students’ performance.
- Used in competitive examinations.
- Helps in ranking students in a group.
- Useful in educational measurement and evaluation.
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1. Percentile – Group Based
Percentile tells about the group performance.
Example:
In a class of 100 students, the 75th percentile score is 80 marks.
Meaning:
- 75 students scored below 80
- 25 students scored above 80
So here we are talking about the group distribution of scores.
👉 Therefore, Percentile focuses on the group.
2. Percentile Rank – Individual Based
Percentile Rank tells about one person's position in the group.
Example:
A student scored 80 marks in the same test.
If 75 students scored less than 80, then
Percentile\ Rank = \frac{75}{100} \times 100 = 75
Meaning:
The student performed better than 75% of the students.
👉 Therefore, Percentile Rank focuses on an individual.
Simple Way to Remember
- Percentile → Group → Score
- Percentile Rank → Individual → Percentage
Very Small Example (10 Students)
Marks:
20, 30, 40, 50, 60, 70, 75, 80, 85, 90
- 80th percentile score = about 80 marks
(80% students scored below this)
If Anu scored 80, then:
- Anu's Percentile Rank ≈ 80
Meaning Anu performed better than 80% students.
✅ One sentence summary
- Percentile → Position of a score in a group
- Percentile Rank → Position of an individual compared with the group
.
1️⃣ Percentile
Percentile is a value that shows the percentage of scores below a particular score in a group.
In simple words:
It tells how many students scored less than a particular score.
Example
Suppose 100 students wrote an exam.
If a student is in the 80th percentile, it means:
👉 The student scored higher than 80 students.
Only 20 students scored higher.
So,
80th percentile = score above 80% of students
2️⃣ Percentile Rank
Percentile Rank is the percentage of scores that fall below a particular score.
It shows the position of a student in comparison with others.
Formula
PR = \frac{B + 0.5E}{N} \times 100
Where:
- PR = Percentile Rank
- B = Number of scores below the score
- E = Number of scores equal to the score
- N = Total number of scores
3️⃣ Simple Example
Marks of students:
20, 30, 40, 50, 60
Find Percentile Rank of 40
Below 40 → 2 scores (20,30)
Equal to 40 → 1 score
Total students N = 5
PR = \frac{2 + 0.5(1)}{5} \times 100
PR = \frac{2.5}{5} \times 100
PR = 50
✅ Percentile Rank = 50
This means the student performed better than 50% of students.
4️⃣ Difference between Percentile and Percentile Rank
| Percentile | Percentile Rank |
|---|---|
| Value below which a percentage of scores fall | Percentage of scores below a given score |
| Example: 75th percentile | Example: PR = 75 |
| Used to locate position in distribution | Used to compare performance |
✔ Simple Example
If exam result shows:
Percentile Rank = 85
It means:
👉 You scored better than 85% of students.
Easy way to remember
Percentile → value (score point)
Percentile Rank → percentage of students below that score
Percentile and Percentile Rank (Simple Explanation)
1. Comparison Table
| Feature | Percentile | Percentile Rank |
|---|---|---|
| What is it? | A value (score) on the scale. | A percentage of people below a score. |
| Purpose | To find a cut-off point. | To know how well a person performed compared to others. |
| Input | Start with a percentage (e.g., 90%). | Start with a score (e.g., 70 marks). |
| Output | Gives the score value. | Gives the percentage rank. |
2. Percentile
Meaning
Percentile is the score below which a certain percentage of scores fall.
Example
Suppose 100 students wrote a test.
The teacher wants to know the 90th percentile.
This means:
➡ 90% of students scored below this mark.
After arranging the scores, we find:
90th percentile score = 85 marks
Interpretation
- 90 students scored less than 85
- 10 students scored above 85
So:
Input: 90%
Output: 85 marks
3. Percentile Rank
Meaning
Percentile Rank is the percentage of scores in a group that fall below a particular score.
Example
Suppose a student scored 70 marks.
After checking the class scores:
- 75 students scored below 70
Calculation
Percentile Rank = (Number of scores below the score / Total number of scores) × 100
Percentile Rank = (75 / 100) × 100
Percentile Rank = 75
Interpretation
The student performed better than 75% of students.
So:
Input: 70 marks
Output: 75%
4. Easy Way to Remember
- Percentile → Percentage → Score
- Percentile Rank → Score → Percentage
5. Simple Story Example
In a class of 100 students:
- The 80th percentile score = 78 marks
This means:
80 students scored below 78 marks.
Now suppose Rahul scored 78 marks.
So,
Rahul’s Percentile Rank = 80
Meaning:
Rahul performed better than 80% of the students.
6. One-Line Summary
- Percentile = Score at a given percentage
- Percentile Rank = Percentage of students below a score
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