# Sum of Squares Calculator

Created by Mariamy Chrdileli
Reviewed by Rijk de Wet
Last updated: May 31, 2023

Welcome to the sum of squares calculator, a simple tool to help you assess the dispersion of your data.

Whether you work in finance or data analytics, you've likely encountered the concept of variability in your data. If you're searching for a way to measure this variability accurately, our sum of squares calculator can help.

In this article, we'll delve deep into everything you need to know about the sum of squares, such as:

• What is the sum of squares in statistics?
• How do I calculate the sum of squares?
• What is the sum of squares formula?
• How does the sum of squares calculator work? And more! 👩🏻‍🏫

🙋 While you're here, you can visit our standard deviation calculator to learn about another important statistical measure related to the sum of squares.

## What is the sum of squares in statistics?

In statistics, the sum of squares (or the sum of squared deviations) indicates the variability or dispersion among the data points. The value is utilized in numerous statistical concepts, including:

• Determining the variance — a measure of the variability of the values in a dataset.

• Evaluating model fit in regression analysis — how well the model explains the observed variability in the outcome variable. In simple words, how well your statistical model predicts the real data. You can learn more about the concept with Omni's coefficient of determination calculator.

• Detecting outliers — data points located at an abnormal distance from other values.

Keep reading to find out how to find the sum of squares and get to know the sum of squares equation.

## How do I calculate the sum of squares?

The sum of squares formula is as follows:

$\text{SS} = \sum_{i=1}^{n}(y_{i}-\bar{y})^{2}$

where:

• $\text{SS}$ — Sum of squares;
• $y_i$ — The ith value in the sample;
• $\bar{y}$ — Mean value of the sample; and
• $y_i - \bar{y}$ — Deviation of each data point from the mean.

To better understand the formula, let's discuss an example. Suppose you're trying to calculate the sum of squared deviations of the following data points: $20$, $22$, and $18$. To determine the value, you can follow the next steps:

1. Determine the mean of your data:

$ȳ = \frac 13 (20 + 22 + 18) = 20$

2. Subtract the mean from each value in the data and square the result:

• $(20-20)^2 = 0$

• $(22-20)^2 = 2^2 = 4$

• $(18-20)^2 = (-2)^2 = 4$

3. Calculate the total of all the squared differences:

$0 + 4 + 4 = 8$

That's all! The sum of squares, in this case, equals 8. The interpretation of your result will depend on the context, although in general, a higher sum of squares indicates higher variability.

## How does the sum of squares calculator work?

If all the calculations above look cumbersome, don't worry, our sum of squared deviations calculator will handle the number crunching. All you have to do is enter numbers in your data set, and the tool will determine the sum of squares for you.

Note that you need at least two values to calculate the sum of squares, and our tool allows you to enter a whopping 50 values!

## FAQ

### What is the sum of squares used for?

The sum of squares (SS) determines the variability within a dataset, and statisticians often use the value to determine variance and assess general linear hypotheses. The latter utilizes three types of sums of squares: the sum of squares of errors (SSE), the regression sum of squares (SSR), and the total sum of squares (SST).

### How do I find the sum of squares?

To find the sum of squares (SS), you can follow these steps:

1. Determine the mean of the values your dataset.
2. Calculate each deviation from the mean by subtracting the mean from each value.
3. Square all the individual values obtained in step 2.
4. Add up all the squared values calculated in step 3.

That's all! You now know how to calculate the sum of squares.

### Is sum of squares the same as standard deviation?

Although related, the sum of squares (SS) and standard deviation (SD) are different. Standard deviation indicates how far each score lies from the mean, and the sum of squares displays the overall variance of the dataset.

### What is the SS value if datapoints are 30, 33, and 35?

The sum of squares value (SS) if data points are 30, 33, and 35 is approximately 12.667. Generally, the higher the sum of squares, the higher variability is detected — although the interpretation of the value depends on the context.

Mariamy Chrdileli
SS = ∑(yi - y)

Enter up to 50 y-values below. Empty rows are not considered.
The sum of squares cannot be calculated yet.
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