# Sum of Squared Errors Calculator

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The sum of squared errors (SSE) measures the distance between each point and the mean of all points in a data set or group.

Calculate the sum of squared errors (SSE) with this calculator.

## What Is the Sum of Squared Errors SSE

The sum of squared errors is a measure of the spread of your data set. It is an alternative to the standard deviation or the mean absolute deviation. The sum of squared errors is calculated by summing the squared distance between each point and the mean of all points.

The sum of squared errors will always be positive because we square the distances between points and the mean. The squared error is the same as the absolute deviation squared.

## What Does the Sum of Squared Errors Tell You

A large sum of squared errors means there is a large variation and your data set. There might be a lot of values close to the mean, or there might be a few values a long way from the mean.

The sum of squared errors can be sensitive to outliers because it uses the error squared. This means that if you have a large sum of squared errors, it can be useful to see whether it is caused by a few large outliers or many points that are a small distance from the mean.

The sum of squared errors does not account for the number of data points in the group. This means that larger data sets can have a larger sum of squared errors, even if most values are close to the mean.

## What Is the Difference Between the Sum Of Squared Errors and the Mean Absolute Deviation

The sum of squared errors is similar to the mean absolute deviation.  Except,  the mean absolute deviation some the absolute distance between each point and the mean, while the sum of squared errors sums the square distance between each point and the mean in the data set.

The sum of squared errors is more sensitive to outliers than the mean absolute deviation. This is because the sum of squared errors uses the distance between each point and the mean squared, while the mean absolute deviation just uses the absolute value of the distance.

Since the sum of squared errors squares the distance terms, outliers become even larger. The effect of outliers becoming larger means that sum of squared errors values can become very large with a small number of outliers.

## Sum of Squared Errors Formula

The sum of squared errors can be calculated by finding the square distance between each point and the main and summing all of these values.

$SSE = \sum_{i=1}^n (x_i - \bar{x})^2 \newline \text{x_i are individual points of x}\newline \text{\bar{x} is the mean of all points x_i}$