📐 R – Max, Min, Mean, Median, Mode (with Code Explanation)

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🧲 Introduction – Core Descriptive Statistics in R

When analyzing data in R, it’s essential to start with the five most basic statistics:

• Maximum, Minimum: Identify extreme values
• Mean, Median: Measure central tendency
• Mode: Identify most frequent value

R provides simple functions for all of these—making it easy to summarize and explore your datasets efficiently.

🎯 In this guide, you’ll learn:

• How to calculate min, max, mean, median, and mode in R
• How to use them on numeric vectors or columns in data frames
• Understand when each metric is useful

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🔢 1. Minimum and Maximum in R

x <- c(12, 7, 19, 4, 11)

min(x)     # Output: 4
max(x)     # Output: 19

🔍 Explanation:

• min(x): Returns the smallest value in the vector
• max(x): Returns the largest value in the vector

Use it on data frames:

min(mtcars$mpg)
max(mtcars$mpg)

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📏 2. Mean (Average)

mean(x)    # Output: 10.6

🔍 Explanation:

• Calculates arithmetic average
• Useful when data has no major outliers

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🎯 3. Median

median(x)   # Output: 11

🔍 Explanation:

• Finds the middle value after sorting
• Robust to outliers, ideal for skewed data

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🔁 4. Mode in R (Custom Function)

R does not have a built-in mode() function for numeric vectors. Here’s how you define one:

get_mode <- function(v) {
  uniq_vals <- unique(v)
  uniq_vals[which.max(tabulate(match(v, uniq_vals)))]
}

get_mode(x)     # Output: most frequent value

🔍 Explanation:

• unique() extracts distinct values
• tabulate() counts how often each appears
• which.max() identifies the highest frequency

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📋 5. Summary on Real Dataset (mtcars)

data(mtcars)

mean(mtcars$hp)       # Mean horsepower
median(mtcars$hp)     # Median horsepower
min(mtcars$hp)        # Min horsepower
max(mtcars$hp)        # Max horsepower
get_mode(mtcars$cyl)  # Most common cylinder count

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📊 6. Compare All Stats Together

x <- mtcars$mpg

cat("Min:", min(x), "\n")
cat("Max:", max(x), "\n")
cat("Mean:", mean(x), "\n")
cat("Median:", median(x), "\n")
cat("Mode:", get_mode(x), "\n")

🧾 Sample Output:

Min: 10.4  
Max: 33.9  
Mean: 20.1  
Median: 19.2  
Mode: 21

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📌 Summary – Recap & Next Steps

These five statistics form the backbone of data profiling. Use them as a first step in any data analysis to understand range, center, and repetition in your dataset.

🔍 Key Takeaways:

• min() and max() give the range
• mean() is the average, sensitive to outliers
• median() is more robust to skewed values
• mode() requires a custom function but shows repetition
• Combine all to form a complete summary

⚙️ Real-World Relevance:
Used in data cleaning, quality checks, summary reports, dashboards, and statistical modeling.

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❓ FAQs – Descriptive Stats in R

❓ Why doesn’t R have a built-in mode function?
✅ R supports categorical modes, but numeric vectors require a custom function using match() and tabulate().

❓ What happens if there are multiple modes?
✅ The function shown returns the first most frequent value. You can enhance it to return all tied modes.

❓ What is the difference between mean and median?
✅ Mean is the average, affected by outliers. Median is the middle value—great for skewed distributions.

❓ How to apply these functions to multiple columns?
✅ Use sapply():

sapply(mtcars[, c("mpg", "hp")], mean)

❓ Can I visualize these statistics?
✅ Yes. Use:

boxplot(mtcars$mpg)
hist(mtcars$mpg)

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