The** normal distribution** is the most commonly used distribution in statistics. This tutorial explains how to plot a normal distribution in R.

To plot a normal distribution in R, we can either use base R or install a fancier package like ggplot2.

**Using Base R**

Here are three examples of how to create a normal distribution plot using Base R.

**Example 1: Normal Distribution with mean = 0 and standard deviation = 1**

To create a normal distribution plot with mean = 0 and standard deviation = 1, we can use the following code:

#Create a sequence of 100 equally spaced numbers between -4 and 4 x <- seq(-4, 4, length=100) #create a vector of values that shows the height of the probability distribution #for each value in x y <- dnorm(x) #plot x and y as a scatterplot with connected lines (type = "l") and add #an x-axis with custom labels plot(x,y, type = "l", lwd = 2, axes = FALSE, xlab = "", ylab = "") axis(1, at = -3:3, labels = c("-3s", "-2s", "-1s", "mean", "1s", "2s", "3s"))

This generates the following plot:

**Example 2: Normal Distribution with mean = 0 and standard deviation = 1 (less code)**

We could also create a normal distribution plot without defining *x *and *y*, and instead simply using the “curve” function using the following code:

curve(dnorm, -3.5, 3.5, lwd=2, axes = FALSE, xlab = "", ylab = "") axis(1, at = -3:3, labels = c("-3s", "-2s", "-1s", "mean", "1s", "2s", "3s"))

This generates the exact same plot:

**Example 3: Normal Distribution with customized mean and standard deviation**

To create a normal distribution plot with a user-defined mean and standard deviation, we can use the following code:

#define population mean and standard deviation population_mean <- 50 population_sd <- 5 #define upper and lower bound lower_bound <- population_mean - population_sd upper_bound <- population_mean + population_sd #Create a sequence of 1000 x values based on population mean and standard deviation x <- seq(-4, 4, length = 1000) * population_sd + population_mean #create a vector of values that shows the height of the probability distribution #for each value in x y <- dnorm(x, population_mean, population_sd) #plot normal distribution with customized x-axis labels plot(x,y, type = "l", lwd = 2, axes = FALSE, xlab = "", ylab = "") sd_axis_bounds = 5 axis_bounds <- seq(-sd_axis_bounds * population_sd + population_mean, sd_axis_bounds * population_sd + population_mean, by = population_sd) axis(side = 1, at = axis_bounds, pos = 0)

This generates the following plot:

**Using ggplot2**

Another way to create a normal distribution plot in R is by using the ggplot2 package. Here are two examples of how to create a normal distribution plot using ggplot2.

**Example 1: Normal Distribution with mean = 0 and standard deviation = 1**

To create a normal distribution plot with mean = 0 and standard deviation = 1, we can use the following code:

#install (if not already installed) and load ggplot2 if(!(require(ggplot2))){install.packages('ggplot2')} #generate a normal distribution plot ggplot(data.frame(x = c(-4, 4)), aes(x = x)) + stat_function(fun = dnorm)

This generates the following plot:

**Example 2: Normal Distribution using the ‘mtcars’ dataset**

The following code illustrates how to create a normal distribution for the *miles per gallon* column in the built-in R dataset *mtcars*:

ggplot(mtcars, aes(x = mpg)) + stat_function( fun = dnorm, args = with(mtcars, c(mean = mean(mpg), sd = sd(mpg))) ) + scale_x_continuous("Miles per gallon")

This generates the following plot: