Calculate the Average, Variance and Standard Deviation in R Programming

16 Dec, 2021
R Programming Language is an open-source programming language that is widely used as a statistical software and data analysis tool. R generally comes with the Command-line interface. R is available across widely used platforms like Windows, Linux, and macOS. R language provides very easy methods to calculate the average, variance, and standard deviation.
Average a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number. The basic formula for the average of n numbers x1, x2, ......xn is
Example:
Suppose there are 8 data points,
2, 4, 4, 4, 5, 5, 7, 9
The average of these 8 data points is,
To compute the average of values, R provides a pre-defined function mean(). This function takes a Numerical Vector as an argument and results in the average/mean of that Vector.
Syntax: mean(x, na.rm)
Parameters:
x: Numeric Vector
na.rm: Boolean value to ignore NA value
Example 1:
R
# R program to get average of a list # Taking a list of elementslist = c(2, 4, 4, 4, 5, 5, 7, 9) # Calculating average using mean()print(mean(list))
 Output:
[1] 5
Example 2:
R
# R program to get average of a list # Taking a list of elementslist = c(2, 40, 2, 502, 177, 7, 9) # Calculating average using mean()print(mean(list))
 Output:
[1] 105.5714
Variance is the sum of squares of differences between all numbers and means. The mathematical formula for variance is as follows,
where,
N is the total number of elements or frequency of distribution. 
Example:
Let’s consider the same dataset that we have taken in average. First, calculate the deviations of each data point from the mean, and square the result of each,[Tex]variance = \frac{9 + 1 + 1 + 1 + 0 + 0 + 4 + 16}{8} = 4[/Tex]
One can calculate the variance by using var() function in R.
Syntax: var(x)
Parameters:
x: numeric vector
Example 1:
R
# R program to get variance of a list # Taking a list of elementslist = c(2, 4, 4, 4, 5, 5, 7, 9) # Calculating variance using var()print(var(list))
 Output:
[1] 4.571429
Example 2:
R
# R program to get variance of a list # Taking a list of elementslist = c(212, 231, 234, 564, 235) # Calculating variance using var()print(var(list))
 Output:
[1] 22666.7
Standard Deviation is the square root of variance. It is a measure of the extent to which data varies from the mean. The mathematical formula for calculating standard deviation is as follows,  
Example:
Standard Deviation for the above data,
One can calculate the standard deviation by using sd() function in R.
Syntax: sd(x)
Parameters:
x: numeric vector
Example 1:
R
# R program to get# standard deviation of a list # Taking a list of elementslist = c(2, 4, 4, 4, 5, 5, 7, 9) # Calculating standard# deviation using sd()print(sd(list))
 Output:
[1] 2.13809
Example 2:
R
# R program to get# standard deviation of a list # Taking a list of elementslist = c(290, 124, 127, 899) # Calculating standard# deviation using sd()print(sd(list))
 Output:
[1] 367.6076
kumar_satyam
R Data-science
R-Statistics
R Language
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