Percentiles and Quartiles

Statistics · Axiom Academy

LESSON Percentiles and Quartiles Understanding how data is divided and what percentiles tell us What are percentiles? Percentiles are values that divide a dataset into 100 equal parts. They help us understand where a particular value stands relative to the entire dataset. What are quartiles? Quartiles are special percentiles that divide data into four equal parts. They're essential for understanding data distribution and identifying outliers. In this lesson, you'll learn how to calculate and interpret percentiles and quartiles using real-world examples. A percentile tells you what percentage of the data falls below a certain value. For example, if you score in the 75th percentile on a test, you performed better than 75% of all test-takers. Real-World Example: Test Scores 100 students take a math test. Your score of 85 is at the 70th percentile. This means 70% of students scored below 85, and 30% scored at or above 85. To find the Pth percentile in a dataset: Sort the data in ascending order Calculate the position: i = (P/100) × (n + 1) , where n is the number of values If i is a whole number, the percentile is the value at position i If i is not whole, interpolate between the values at floor(i) and ceiling(i) Example Calculation: Finding the 60th Percentile Data: 12, 15, 18, 20, 22, 25, 28, 30, 35, 40 Step 1: n = 10 values (already sorted) Step 2: Position i = (60/100) × (10 + 1) = 6.6 Step 3: Interpolate between 6th value (25) and 7th value (28)

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