What is Percentiles?

S3-SA3-0307

Grade Level:

Class 8

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Percentiles tell us what percentage of values in a dataset are below a certain value. If you score in the 90th percentile, it means 90% of the people scored less than you.

Simple Example

Quick Example

Imagine your friend scored 85 marks in a math test. If their score is in the 70th percentile, it means 70% of the students who took the test scored less than 85 marks.

Worked Example

Step-by-Step

Let's say 10 students took a science test and their scores (out of 100) are: 40, 55, 60, 65, 70, 75, 80, 85, 90, 95. We want to find the percentile for a student who scored 70.
---Step 1: Arrange the scores in ascending order. (Our scores are already arranged).
---Step 2: Count how many scores are less than or equal to 70. Scores less than or equal to 70 are: 40, 55, 60, 65, 70. There are 5 such scores.
---Step 3: Use the formula: Percentile = (Number of values <= X / Total number of values) * 100.
---Step 4: Substitute the values: Percentile = (5 / 10) * 100.
---Step 5: Calculate: Percentile = 0.5 * 100 = 50.
---Answer: A student who scored 70 is in the 50th percentile.

Why It Matters

Percentiles are super useful! In data science, they help understand data distribution, like how income is spread across a country. In AI/ML, they're used to set performance benchmarks. Even in sports, like cricket, analysts use percentiles to compare player performance, helping coaches make better team decisions.

Common Mistakes

MISTAKE: Confusing percentile with percentage. | CORRECTION: Percentage is your score out of a total (e.g., 80% marks). Percentile tells you how many people you scored better than (e.g., 80th percentile means you scored better than 80% of test-takers).

MISTAKE: Not arranging data in ascending order before calculating. | CORRECTION: Always sort your data from smallest to largest first. This is crucial for correctly counting values below a certain point.

MISTAKE: Forgetting to multiply by 100 in the formula. | CORRECTION: The formula gives a fraction or decimal, multiply by 100 at the end to express it as a percentile (a percentage).

Practice Questions

Try It Yourself

QUESTION: In a class of 20 students, 15 students scored less than your marks. What is your percentile? | ANSWER: 75th percentile

QUESTION: The heights of 8 friends in cm are: 145, 150, 152, 155, 160, 162, 165, 170. What is the percentile for a friend who is 155 cm tall? | ANSWER: 50th percentile

QUESTION: A mobile game records the highest scores of 10 players: 100, 120, 130, 150, 160, 180, 190, 200, 210, 220. What is the percentile of a player who scored 190? How many players scored better than this player? | ANSWER: 70th percentile. 3 players scored better.

MCQ

Quick Quiz

If your income is in the 80th percentile in your city, what does it mean?

80% of people in your city earn more than you.

Your income is 80% of the highest income in the city.

80% of people in your city earn less than or equal to you.

You earn exactly 80,000 rupees.

The Correct Answer Is:

The 80th percentile means 80% of the values (in this case, incomes) are at or below your value. So, 80% of people earn less than or equal to you.

Real World Connection

In the Real World

When you get your exam results for competitive tests like JEE or NEET, your result often includes your percentile score. This helps you understand how well you performed compared to all other students who took the exam, not just your raw marks. It's a key factor for college admissions in India!

Key Vocabulary

Key Terms

PERCENTAGE: A part of a whole expressed as a number out of 100. | DATASET: A collection of related data. | ASCENDING ORDER: Arranging numbers from smallest to largest. | MEDIAN: The middle value in a sorted dataset (which is the 50th percentile).

What's Next

What to Learn Next

Now that you understand percentiles, you can explore other measures of position like quartiles and deciles. These concepts build on percentiles and help you divide data into even more specific groups, making data analysis even more powerful!