# Calculate Sum of Squared Deviations in R (2 Examples)

This tutorial explains how to **compute the sum of squares** (also called sum of squared deviations) in the R programming language.

Table of contents:

Let’s get started.

## Example Data

Consider the following example data:

x <- 11:20 # Create example vector x # Print example vector # [1] 11 12 13 14 15 16 17 18 19 20 |

x <- 11:20 # Create example vector x # Print example vector # [1] 11 12 13 14 15 16 17 18 19 20

The previous output of the RStudio console shows that our example data is a numeric vector containing a range from 11 to 20.

## Example 1: Compute Sum of Squares Using sum() & mean() Functions

The following R programming syntax illustrates how to calculate the sum of squared deviations of a numeric vector in R.

For this task, we can apply the sum and mean functions as shown in the following R code:

ss_1 <- sum((x - mean(x))^2) # Calculate sum of squares ss_1 # Print sum of squares # [1] 82.5 |

ss_1 <- sum((x - mean(x))^2) # Calculate sum of squares ss_1 # Print sum of squares # [1] 82.5

The previous output of the RStudio console shows the result: The sum of squares of our input vector is 82.5.

## Example 2: Compute Sum of Squares Using var() & length() Functions

In Example 2, I’ll show an alternative to the mean and sum functions that we have used in Example 1. In this example, we’ll use the var and length functions instead.

Have a look at the following R code:

ss_2 <- var(x) * (length(x) - 1) # Calculate sum of squares ss_2 # Print sum of squares # [1] 82.5 |

ss_2 <- var(x) * (length(x) - 1) # Calculate sum of squares ss_2 # Print sum of squares # [1] 82.5

As you can see, the RStudio console returns exactly the same result as the code in Example 1. For that reason, the code of Example 2 provides a good way to double-check your results.

## Video, Further Resources & Summary

In case you need more explanations on the R programming codes of this tutorial, you may want to have a look at the following video on the Statistics Globe YouTube channel. In the video, I’m explaining the R code of this article in a live session:

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Furthermore, you may have a look at some of the related articles on statisticsglobe.com. You can find a selection of tutorials below.

- Calculate (Root) Mean Squared Error
- Calculate Moving Average, Maximum, Median & Sum of Time Series
- Calculate Sum & Mean of Hours, Minutes & Seconds
- Introduction to R Programming

In summary: You have learned on this page how to **calculate the sum of squared deviations** in the R programming language. Let me know in the comments section, in case you have additional questions.

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