Histogram Plots in R

 

Histogram Plots in R

Introduction

A histogram is a graphical representation of the frequency distribution of continuous numerical data. It divides the data into intervals called bins or classes and displays the number of observations in each interval using adjacent bars.

Unlike bar charts, the bars in a histogram touch each other, indicating that the data is continuous.

Histograms are useful for:

  • Understanding data distribution.
  • Identifying skewness.
  • Detecting outliers.
  • Examining spread and central tendency.
  • Visualizing frequency distributions.

Syntax

hist(x,
     breaks,
     main,
     xlab,
     ylab,
     col,
     border,
     freq)

where

  • x : numeric vector.
  • breaks : number of bins or class intervals.
  • main : title.
  • xlab : x-axis label.
  • ylab : y-axis label.
  • col : bar color.
  • border : border color.
  • freq : TRUE (frequency), FALSE (density).

Example 1: Simple Histogram

Suppose the marks of students are:

marks <- c(45,50,55,60,62,65,67,70,
           72,75,78,80,82,85,90)

hist(marks)

This produces a histogram showing the frequency distribution of marks.



Example 2: Adding Title and Labels

hist(marks,
     main="Distribution of Marks",
     xlab="Marks",
     ylab="Frequency")

Example 3: Changing Color

hist(marks,
     col="lightblue")

Example 4: Changing Border Color

hist(marks,
     col="yellow",
     border="red")



Example 5: Specifying Number of Bins

hist(marks,
     breaks=5,
     col="green")

Here, the data is divided into 5 intervals.



Example 6: Explicit Class Intervals

hist(marks,
     breaks=c(40,50,60,70,80,90,100),
     col="orange")

Intervals:

40-50
50-60
60-70
70-80
80-90
90-100



Example 7: Random Normal Data

x <- rnorm(1000)

hist(x,
     col="skyblue",
     main="Normal Distribution")

This approximates a bell-shaped curve.



Example 8: Density Histogram

x <- rnorm(1000)

hist(x,
     probability=TRUE,
     col="lightgreen")

or

hist(x,
     freq=FALSE)

The y-axis represents probability density instead of frequency.



Example 9: Overlaying Density Curve

x <- rnorm(1000)

hist(x,
     probability=TRUE,
     col="lightblue")

lines(density(x),
      col="red",
      lwd=3)

This superimposes a smooth density curve.



Example 10: Overlaying Normal Curve

x <- rnorm(1000)

hist(x,
     probability=TRUE,
     col="lightgray")

curve(dnorm(x,
            mean=mean(x),
            sd=sd(x)),
      add=TRUE,
      col="blue",
      lwd=3)



Example 11: Monthly Rainfall Distribution

rainfall <- c(120,150,90,80,70,200,
              250,220,180,160,140,110)

hist(rainfall,
     col="cyan",
     main="Rainfall Distribution",
     xlab="Rainfall")

Example 12: Histogram from Data Frame

student <- data.frame(
Marks=c(55,60,65,70,75,80,85,90,95)
)

hist(student$Marks,
     col="pink")

Example 13: Add Mean Line

x <- rnorm(1000)

hist(x,
     col="yellow")

abline(v=mean(x),
       col="red",
       lwd=3)

The vertical red line represents the mean.



Example 14: Compare Different Bin Sizes

5 bins

hist(x,
     breaks=5)


20 bins

hist(x,
     breaks=20)


More bins reveal finer details of the distribution.

Example 15: Histogram with Rug Plot

x <- rnorm(100)

hist(x,
     col="lightblue")

rug(x)

The rug plot shows individual observations along the x-axis.



Example: Distribution of Student Marks

marks <- c(45,55,60,62,65,68,70,
           72,74,76,78,80,82,85,88,90)
hist(marks,
     breaks=5,
     col="skyblue",
     border="black",
     main="Marks Distribution",
     xlab="Marks",
     ylab="Frequency")


Histogram of Normal Distribution

x <- rnorm(1000)
hist(x,
     breaks=30,
     col="lightgreen",
     main="Normal Distribution")

The histogram resembles a bell-shaped curve.



Important Parameters

ParameterPurpose
breaks    Number of bins
main    Title
xlab    x-axis label
ylab    y-axis label
col    Color
border    Border color
freq    Frequency scale
probability    Density scale

Common Distributions

Normal Distribution

Symmetric bell shape.

        ***
      *******
    ***********
      *******
        ***

Right Skewed Distribution

Long tail to the right.

*******
*****
***
**
*

Left Skewed Distribution

Long tail to the left.

*
**
***
*****
*******

Uniform Distribution

Almost equal frequencies.

******
******
******
******

Bimodal Distribution

Two peaks.

***      ***
*****  *****
*************

Difference Between Histogram and Bar Plot

HistogramBar Plot
Continuous data    Categorical data
Bars touch each other    Bars separated
Shows distribution    Shows comparison
x-axis contains intervals    x-axis contains categories
Uses hist()    Uses barplot()

Applications of Histograms

  • Examining marks distribution.
  • Population studies.
  • Rainfall analysis.
  • Quality control.
  • Machine learning data exploration.
  • Statistical analysis.
  • Detecting skewness and outliers.
  • Understanding probability distributions.

Useful Functions with Histograms

Density Curve

lines(density(x))

Normal Curve

curve(dnorm(x,mean(x),sd(x)), add=TRUE)

Mean Line

abline(v=mean(x))

Rug Plot

rug(x)

Conclusion

A histogram is one of the most important statistical plots used to understand the distribution of continuous numerical data. The hist() function in R provides numerous options for customizing bins, colors, labels, and probability scales. Histograms are fundamental tools in statistics, machine learning, and exploratory data analysis.

Comments

Post a Comment

Popular posts from this blog

Statistical Methods Lab ( R Language) PCCBL308 Semester 3 KTU BTech CB and CU 2024 Scheme - Dr Binu V P

  About Me Statistical Methods Lab ( R Language) PCCBL308 Course Details and Syllabus Introduction to R Download R Download R Studio Tutorial Experiments      1. Familiarization of R environment and R Studio. Installing and using packages.      2.Practice basic R input/output commands and create simple R programs                        using variables/mathematical operations. R Variables Basic Data Types in R Basic Input and Output Functions in R Keywords in R Operators in R Sample Programs Basic Programs to Try - Assignment-1      3.Learn Control Statements Decision-Making Statements in R ( if , if else, switch) Iterative  statements ( for , while , repeat ) Sample Programs using Control Statements Programs to Try using control satements - Assignment-2      4.Write R programs using functions ( Functions, Recursive Functions) Functions  in...
Read more

Programs in R - using control statements - Assignment 2

 Program List 1.Read a mark ( out of 100) and print the corresponding grade. Percentage Range Grade >=90 O >=85 and <90 A+ >= 80 and <85 A > =70 and <80 B+ > =60 and <70 B > =50 and <60 C >=45 and <50 P <45 F 2.Write a program to check the quadrant of a given point(x,y) 3.Write a program that accepts the length of three sides of a triangle as input and determine whether or not the triangle is a right triangle.( university question) 4.Given three points (x1,y1 ) ,(x2,y2) and (x3,y3), check whether they form a triangle. 5.Generate the series 1 2 4 7 11 16....n ( use while...read n) 6.Generate the Fibonacci series 0 1 1 2 3 5 8…..n ( use while..read n) 7.Check whether the given 3 digit number is an Armstrong number. (use while Eg:153,370,371,407) 8.Find the factors of a number ( use for) 9.Find the GCD or HCF of two numbers ( use Euclid algorithm and repeat loop) 10.Check whether the given number is a Krishnamurti number( Krishnamurthy Number...
Read more

Basic R Programs to Try - Assignment 1

 Program List 1.Area of the circle given center point (x1,y1) and one point on the perimeter (x2,y2).(Hint: input the two points and compute the distance between them as radius) 2.Area and perimeter of a right angled triangle given width(w) and height(h).(area=1/2.0*w*h .use Pythagoras theorem to find the hypotenuse then add the three sides to find the perimeter) 3.Marks in n subjects of a student are stored in a file .Find the total, average and percentage.(use scan() store the marks in marks.txt) 4.An Employee's total weekly pay equals the hourly wage multiplied by the total hours worked plus any overtime pay.Overtime pay equals the total overtime hours multiplied by 1.5 times the hourly wage.Write an R script that takes as inputs hourly wage, total regular hours and total overtime hours and displays an employee's total weekly pay. 5.Display the current date using lubridate package.( learn to install and use packages) 6.The customer requests a program that computes a person’s...
Read more