🎯 R Percentiles – Calculate, Interpret, and Apply with Code Examples

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🧲 Introduction – Understanding Percentiles in R

Percentiles divide your dataset into 100 equal parts, helping you understand the distribution and ranking of data. They’re widely used in exam scores, sales reports, outlier detection, and risk analysis.

In R, percentiles are calculated using the versatile quantile() function.

🎯 In this guide, you’ll learn:

• How to calculate percentiles in R
• Use quantile(), ecdf(), and percentile-based logic
• Interpret results for practical data analysis

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🔢 1. What Is a Percentile?

A percentile tells you the value below which a given percentage of observations fall.

📌 Example:
If the 90th percentile of exam scores is 85, then 90% of students scored ≤ 85.

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📐 2. Basic quantile() Usage

x <- c(45, 67, 89, 72, 53, 91, 84, 60, 70, 88)

quantile(x, probs = 0.9)

🔍 Explanation:

• probs = 0.9 means you want the 90th percentile
• Output: 90% of the values are less than or equal to the result

🧾 Sample Output:

90% 
89.7 

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🎯 3. Calculate Multiple Percentiles

quantile(x, probs = c(0.25, 0.5, 0.75, 0.9))

🔍 Explanation:

• 25% → Q1 (lower quartile)
• 50% → Q2 (median)
• 75% → Q3 (upper quartile)
• 90% → 90th percentile

🧾 Output:

25%  50%  75%  90% 
60.0 72.0 88.0 89.7 

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📊 4. Percentile Rank of a Value

Want to find the percentile rank of a specific number?

val <- 72
ecdf_func <- ecdf(x)
ecdf_func(val)

🔍 Explanation:

• ecdf() creates a cumulative distribution function
• ecdf_func(val) tells you the proportion of values ≤ val

🧾 Output:

0.6  # 60th percentile rank

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📘 5. Visualize Percentiles with Boxplot

boxplot(x, main = "Boxplot with Percentiles")
abline(h = quantile(x, probs = c(0.25, 0.5, 0.75)), col = c("blue", "red", "blue"), lty = 2)

🔍 Explanation:

• Blue lines: Q1 & Q3
• Red line: Median (Q2)

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🔍 6. Percentiles on a Real Dataset (mtcars$mpg)

quantile(mtcars$mpg, probs = seq(0, 1, 0.1))  # Deciles (every 10%)

🧾 Output (partial):

  0%  10%  20%  30% ... 100% 
10.4 ...       ...     33.9 

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📌 Summary – Recap & Next Steps

Percentiles help rank values, detect outliers, and assess data spread. R’s quantile() and ecdf() functions make percentile calculations simple and flexible.

🔍 Key Takeaways:

• Use quantile(x, probs = p) to get percentiles
• ecdf(x) returns percentile rank of any value
• Combine percentiles with boxplots for powerful insights
• Use seq(0, 1, 0.01) for full percentile breakdown (1st–99th)

⚙️ Real-World Relevance:
Percentiles are crucial in education analytics, business benchmarking, health risk assessment, and financial scoring.

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❓ FAQs – Percentiles in R

❓ How do I find the 95th percentile in R?
✅ Use:

quantile(x, 0.95)

❓ What is the difference between percentile and quantile in R?
✅ No difference in functionality—quantile() calculates percentiles (0–100) based on proportions (0.0–1.0).

❓ How to get all percentiles (1% to 99%)?
✅ Use:

quantile(x, probs = seq(0.01, 0.99, by = 0.01))

❓ How do I get percentile rank of a number?
✅ Use empirical CDF:

ecdf(x)(value)

❓ Can percentiles be used to detect outliers?
✅ Yes. Values below the 1st or above the 99th percentile are often considered extreme outliers.

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