R

Descriptive Statistics in R

📘 Introduction

Descriptive statistics is the branch of statistics that summarizes, organizes, and describes the main characteristics of a dataset. Instead of making predictions or drawing conclusions about a population, descriptive statistics focuses on presenting data in a meaningful and understandable way using numerical measures and graphical summaries.

Information

R provides numerous built-in functions for calculating descriptive statistics, making it one of the most widely used tools for data analysis and statistical computing.

🎯 Why Learn Descriptive Statistics?

Understand the characteristics of a dataset.
Summarize large amounts of data efficiently.
Identify trends, patterns, and outliers.
Support decision-making using data.
Prepare data for advanced statistical analysis.

📊 Types of Descriptive Statistics

Descriptive Statistics

Measures of Central Tendency

Measures of Dispersion

Measures of Position

Frequency Distribution

Graphical Summaries

📝 Sample Dataset

Student Marks

marks <- c(
  78, 85, 92, 88, 76,
  95, 81, 89, 84, 90
)

print(marks)

📍 Measures of Central Tendency

Measures of central tendency describe the center or typical value of a dataset.

Measure	Description	R Function
Mean	Arithmetic average.	mean()
Median	Middle value after sorting.	median()
Mode	Most frequently occurring value.	No built-in function.

Calculating Mean and Median

mean(marks)

median(marks)

Output

Console Output

[1] 85.8
[1] 86.5

📍 Calculating the Mode

R does not include a built-in function for calculating the statistical mode, but it can be created using the following function.

Mode Function

getMode <- function(x) {
  uniqueValues <- unique(x)

  uniqueValues[
    which.max(
      tabulate(
        match(x, uniqueValues)
      )
    )
  ]
}

numbers <- c(
  2,4,4,6,7,4,8
)

getMode(numbers)

Output

Console Output

[1] 4

📏 Measures of Dispersion

Measures of dispersion describe how spread out the data values are.

Measure	Description	Function
Range	Difference between maximum and minimum values.	range()
Variance	Average squared deviation from the mean.	var()
Standard Deviation	Square root of variance.	sd()

Dispersion Measures

range(marks)

var(marks)

sd(marks)

📈 Finding Minimum and Maximum

Minimum and Maximum

min(marks)

max(marks)

📊 Quartiles and Percentiles

Quartiles divide data into four equal parts and help describe the distribution.

Quartiles

quantile(marks)

Output

Console Output

0%   25%   50%   75%  100%
76.0 81.75 86.50 89.75 95.0

📋 Summary Statistics

The summary() function provides a quick statistical overview of numerical data.

Using summary()

summary(marks)

Output

Console Output

Min.   :76.00
1st Qu.:81.75
Median :86.50
Mean   :85.80
3rd Qu.:89.75
Max.   :95.00

📊 Frequency Distribution

Frequency tables show how often each value occurs.

Frequency Table

grades <- c(
  "A","B","A","C",
  "B","A","B","A"
)

table(grades)

Output

Console Output

grades
A B C
4 3 1

📉 Cumulative Frequency

Cumulative Frequency

freq <- table(grades)

cumsum(freq)

Output

Console Output

A B C
4 7 8

📊 Descriptive Statistics for Data Frames

Student Dataset

students <- data.frame(
  Name = c(
    "Alice",
    "Bob",
    "Charlie",
    "David"
  ),
  Marks = c(
    85,
    72,
    91,
    78
  ),
  Age = c(
    20,
    21,
    20,
    22
  )
)

summary(students)

📈 Applying Statistics to Multiple Columns

Use the apply() function to calculate statistics across multiple columns.

Column Means

scores <- data.frame(
  Math = c(80,90,85),
  Science = c(75,88,92),
  English = c(78,81,89)
)

apply(
  scores,
  2,
  mean
)

📦 Using Built-in Datasets

R includes several built-in datasets for learning and analysis.

Summary of iris Dataset

summary(iris)

mean(iris$Sepal.Length)

sd(iris$Sepal.Length)

📊 Graphical Summaries

Graphs provide visual summaries of descriptive statistics.

Histogram

Box Plot

Histogram

hist(
  marks,
  col = "skyblue",
  main = "Distribution of Marks"
)

Box Plot

boxplot(
  marks,
  col = "orange",
  main = "Student Marks"
)

🌍 Real-World Example

A company wants to analyze monthly employee salaries to understand the overall salary distribution.

Employee Salary Analysis

salary <- c(
  42000,
  50000,
  47000,
  61000,
  58000,
  52000,
  49000
)

summary(salary)

mean(salary)

median(salary)

sd(salary)

range(salary)

🔄 Descriptive Statistics Workflow

Collect Data

Clean Data

Calculate Statistics

Measure Center

Measure Spread

Create Graphs

Interpret Results

📋 Common Statistical Functions

Function	Description
mean()	Calculates the average.
median()	Returns the middle value.
min()	Returns the smallest value.
max()	Returns the largest value.
range()	Returns minimum and maximum values.
var()	Calculates variance.
sd()	Calculates standard deviation.
quantile()	Calculates quantiles.
summary()	Displays summary statistics.
table()	Creates frequency tables.

⚠️ Common Mistakes

Mistake	Explanation	Solution
Ignoring missing values	Statistical functions may return NA.	Use na.rm = TRUE when appropriate.
Confusing mean and median	Mean is sensitive to outliers, while the median is more robust.	Choose the measure that best represents the data.
Expecting a built-in mode function	R does not provide one for statistical mode.	Create a custom function or use an external package.
Interpreting summary statistics without visualizing the data	Important patterns and outliers may be missed.	Use charts such as histograms and box plots alongside numerical summaries.

💡 Best Practices

Inspect data before performing statistical analysis.
Handle missing values appropriately.
Use both numerical summaries and graphical visualizations.
Choose statistical measures based on the characteristics of the dataset.
Document assumptions and analysis steps for reproducibility.

Best Practice

Descriptive statistics provide the foundation for understanding any dataset. Combining summary measures with visualizations helps reveal patterns, detect anomalies, and prepare data for more advanced statistical analyses.

📝 Summary

Descriptive statistics summarize and describe the key characteristics of a dataset using measures of central tendency, dispersion, position, and frequency. In this chapter, you learned how to calculate the mean, median, mode, range, variance, standard deviation, quartiles, and frequency distributions using Base R functions. You also explored summary statistics, graphical summaries, and descriptive analysis for data frames and built-in datasets. These techniques form the basis for effective data exploration and statistical analysis in R.

>>"Descriptive statistics turn raw data into meaningful information, providing the first step toward understanding and making informed decisions."

📘 Introduction

ℹ️Information

🎯 Why Learn Descriptive Statistics?

📊 Types of Descriptive Statistics

📝 Sample Dataset

Student Marks

📍 Measures of Central Tendency

Calculating Mean and Median

Output

Console Output

📍 Calculating the Mode

Mode Function

Output

Console Output

📏 Measures of Dispersion

Dispersion Measures

📈 Finding Minimum and Maximum

Minimum and Maximum

📊 Quartiles and Percentiles

Quartiles

Output

Console Output

📋 Summary Statistics

Using summary()

Output

Console Output

📊 Frequency Distribution

Frequency Table

Output

Console Output

📉 Cumulative Frequency

Cumulative Frequency

Output

Console Output

📊 Descriptive Statistics for Data Frames

Student Dataset

📈 Applying Statistics to Multiple Columns

Column Means

📦 Using Built-in Datasets

Summary of iris Dataset

📊 Graphical Summaries

Histogram

Box Plot

🌍 Real-World Example

Employee Salary Analysis

🔄 Descriptive Statistics Workflow

📋 Common Statistical Functions

⚠️ Common Mistakes

💡 Best Practices

⭐Best Practice

📝 Summary

Information

Best Practice