Chapter-3:- Histogram in R-programming

Example-1:- Generate random number by mean and standard deviation 

Code:- 

# Generate sample data

data <- rnorm(100, mean = 50, sd = 10)

# Create histogram with custom parameters

hist(data, 

     breaks = 10,               # Number of bins

     freq = FALSE,              # Density scale (needed for overlay)

     col = "lightblue",         # Fill color

     border = "darkblue",       # Border color

     main = "Histogram Example",# Title

     xlab = "Measurements",      # X-axis label

     xlim = c(20, 80),          # X-axis limits

     density=50, angle=30, label=TRUE)

# Overlay a density curve

lines(density(data), col = "red", lwd = 2, lty="dashed")

Solution:-

Explanation:- 

• In code we have to use "rnorm" if we have to generate random number, also use "mean" & "sd" because these are parameter 
• breaks= denote the number of bins if we put here 10 it means 10 bins, but always not 10 it can vary according to data may be +/- 5 

• freq=FALSE; if we use then it use density & freq=TRUE use frequency:-

• Use freq = FALSE (Density) when: 
• a) Comparing different sample sizes:- If you want to compare a survey of 100 people against a survey of 10,000 people, you cannot use counts because the larger survey's bars will tower over the smaller one. Density scales them both so they are comparable. 
• b) Overlaying a Density Curve: If you want to draw a smooth "bell curve" line over your histogram using lines(density(data)), you must use freq = FALSE. Otherwise, the line will be so small it looks like it's lying on the floor (at 0.0). 
• c) Probability analysis: You want the total area of the histogram to equal 1 (100%), which represents the probability distribution of the data. 

• 
  
• Use freq = TRUE (Frequency) when: 
• a) You need raw counts: You want to know exactly how many items fall into each bin (e.g., "Exactly 15 people are in the 20-30 age group"). 
• b) Simple reporting: You are presenting data to a general audience who finds "counts" easier to understand than "densities." 
• c) Single dataset: You are only looking at one group of data and don't need to compare it to a mathematical model. 
• d) Note: This is the default setting in R. 

• density=50 means bar color 50% area cover
• angle=30 means line draw in bar is at 30 degree angle
• lines is use to draw line but it use only when freq=FALSE otherwise in case of freq=TRUE it show flat line
• lwd=2 means thickness of line
• lty= show dashed line

All parameter of hist() :-

Data and Binning:-

x	The numeric data vector for the histogram
breaks	Defines the bins, accepting vectors, numbers, algorithms like “Sturges”, or function
nclass	An alternative to breaks for compatibility

Frequency vs Density:-

freq	If TRUE (default), plot counts; If FALSE, plot probability densities
probability	An alias for !freq

Bin Intervals:-

include.lowest	If TRUE, includes values equal to breakpoints in the first or last bin
right	If TRUE (default), intervals are right-closed (a,b)

Appearance:-

col	Color for the bars
border	Color for bar borders
density	Shading line density
angle	Angle of shading lines
labels	Adds labels on bars if not FALSE

Labels and Axes:-

main	Main title
xlab	X-axis label
ylab	Y-axis label (default to “frequency” if freq is true
xlim/ ylim	Axis limits
axes	If TRUE (default), axes are drawn

Behavior:-

plot	If TRUE (default), draws the histogram; if FALSE return only calculation
warn.unused	Warns about unused graphical parameters if plot=FALSE

Example-2:- How to write Histogram if we have given data:-

Code:-

data <- c(13,23,23,45,66,85,41,38,98,84,68) 

# Create histogram with custom parameters

hist(data, 

     breaks = 30,

     freq = FALSE,

     col = "lightblue",           # Fill color

     border = "yellow",           # Border color

     main = "Histogram Example",   # Title

     xlab = "Measurements",      # X-axis label

     xlim = c(10, 100),           # X-axis limits example here 20 to 80

     density=50,angle=30, label=TRUE)         

lines(density(data), col = "red", lwd = 2,lty="dashed")

Solution:-

Explanation:- Same as above example, only difference here we have given data, in previous we generate data