How to Compute Raw and Central Moments Using R

In this article, we are going to compute raw and central moments using R Programming Language. The moments of data used to describe the nature of the dataset are Variation, Skewness, and Kurtosis.

• Raw Moments – The moments about zero distribution are known as Raw moments.
• Central Moments – The moments about the mean of distribution are known as Central Moments.

Using R we can easily find the raw moments with the predefined package “moments”

In a moment’s package, we have all.moments() function which is used to calculate raw moments and central moments.

Syntax: all.moments(x,order.max,central=FALSE)

Where,

• x: a numeric vector of data
• order.max: the maximum order of the moments to be computed (default value is 2).
• Central: a logical value (FALSE for raw moments or TRUE for central moments)

Below is the implementation:

R

# install required packages
install.packages('moments')

# load installed package
library(moments)

# create a vector which represent marks
# of student marks
student_marks<-c(98,87,96,91,85,89,93,96,99,86)

# Raw Moments
print('Raw Moments')
print(all.moments(student_marks))

# Central Moments
print('Central Moments')
print(all.moments(student_marks,central=TRUE))

Output:

Explanation:

If we observe the above R code to calculate central moments we need to make sure the third attribute of all.moments() function should be set to True because by default it’s False.

Raw Moments:-

                         μ′₀ = 1.0 

                         μ′₁ = 92.0 

                         μ′₂ = 8487.8

Central Moments:-

                        μ₁ = 1.0

                        μ₂ = 0.0

                        μ₃ = 23.8