Percentiles_Presentation_Extended.pptxss

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1. Understanding Percentiles A Simple Guide for Beginners

2. What Are Percentiles? - Percentiles split data into 100 equal parts. - They help us see where a value stands in a group. - Example: A test score in the 80th percentile means it's higher than 80% of the other scores.

3. Why Are Percentiles Useful? - Used in test scores to compare students. - Help doctors understand health data (like height and weight percentiles). - Used in finance to analyze income or stock performance.

4. Formula for Percentiles To find the k-th percentile: Pₖ = (k/100) × (n + 1) Where: - k = the percentile you want to find - n = total number of values in the dataset

5. Steps to Calculate a Percentile (Part 1) 1️⃣ Arrange data in **ascending order**. 2️⃣ Choose **k**, the percentile you want (e.g., 30th percentile means k = 30). 3️⃣ Count the number of values (**n**) in the dataset.

6. Steps to Calculate a Percentile (Part 2) 4️⃣ Apply the formula: **Pₖ = (k/100) × (n + 1)** 5️⃣ The result gives the **position** in the ordered dataset. 6️⃣ Identify the value at that position.

7. Example: Finding the 30th Percentile Dataset: **45, 38, 35, 29, 54, 54, 43, 42, 38** 1️⃣ Arrange in order: **29, 35, 38, 38, 42, 43, 45, 54, 54** 2️⃣ Use the formula: (30/100) × (9 + 1) = **3rd position** 3️⃣ 30th percentile = **38**

8. Example: Finding the 50th Percentile (Median) Dataset: **10, 20, 30, 40, 50, 60, 70** 1️⃣ Arrange in order: **10, 20, 30, 40, 50, 60, 70** 2️⃣ Use the formula: (50/100) × (7 + 1) = **4th position** 3️⃣ 50th percentile = **40**

9. Common Percentiles & Their Meaning - **25th percentile** = 1/4 of the data is below this point. - **50th percentile (Median)** = Half of the data is below this point. - **75th percentile** = 3/4 of the data is below this point. - **100th percentile** = The highest value in the dataset.

10. Conclusion & Practice Questions ✔ Percentiles help compare values in a dataset. ✔ Use the formula **Pₖ = (k/100) × (n + 1)**. ✔ Practice with these questions: 1️⃣ Find the **40th percentile** of: **12, 18, 24, 30, 36, 42, 48**. 2️⃣ Find the **90th percentile** of: **5, 10, 15, 20, 25, 30, 35, 40, 45, 50**.