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Sum of Squares Calculator

Enter sample values and the calculator will determine the sum of their squares, with calculations shown.

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The total sum of squares calculator helps you to calculate the algebraic and statistical sum of squares of the given sample data values. In other words, when it comes to statistical terms, an online sum of squared deviations calculator allows you to find the sum of squared deviation (X-Xbar)2 for the data set. The calculator will show you the step-by-step calculations for both statistical and algebraic calculations. Well, remember that finding the sum of squares is very helpful in the field of applied mathematics, physics, and electronics, etc.

Well, let’s begin with the basics!

What is Sum of Squares?

Basically, the sum of squares for a sample of data usually refers to the sum of squared deviations with respect to the mean. While, in algebra, this term is helpful to calculate the sum of two or more square terms. If an expression or equation having two square terms with addition operator then, the sum of squares formula is used.

Our sum of squares calculator performs calculations and displays the outputs according to the following formulas!

Try this 100% free covariance calculator that provides an estimation of covariance between 2 random variables X and Y in probability & statistics experiments.

What is The Sum of Squares Formula?

For Statistical Calculation:

The sum of squares equation for statistical data is as follow,

Total sum of the squares = 𝚺  ( Xi -X̄)2


Xi = Statistical Data

X̄ = Statistical mean

You can use this sum of squared deviations calculator to calculate the sum of squared differences from the mean.

For Algebraic Calculation:

The formula for the calculation of sum of squares for algebraic calculation is as follow,

Total sum of squares = 12+22+32+…….+n2


n = total numbers in expression

The Relationship Between Sum of Squares and Sample Variance:

The sum of square is strongly related to the simple variance.It can be seen by the following formula,

S2 = S.S / n-1

Here, S2 is the sample variance, S.S is the sum of squares and n is the sample size.

The sum of square is a great sign of the level of the variability of a sample. So, if you calculate the (SS), then divided by one minus sample size produces a result of the simple variance.

This sum of square deviation calculator assists you in the calculation of sample variance by finding the sum of squares.

What are The Limitations of Using The Sum of Squares?

An analyst may have to do a lot of work with huge data to know with higher certainty how the asset has low or high variability. As the data becomes larger, the sum of squares(SS) becomes larger and data will be more spread out.

The commonly used measurement for variation is standard deviation and variance. As, we discussed below formula for the variance the sum of square must be first calculated also in the calculation of the standard deviation sum of squares(SS) is helpful. The formula for the standard deviation is,

σ²  =√ S.S / n-1

It doesn’t matter whether you want to enter a series of positive or negative integers, the sum of squares calculator find the sum of group data accurately.

How to Find the Sum of Square in Excel?

To determine the sum of the squares in excel, you should have to follow the given steps:

  • Put your data in a cell and labeled the data as ‘X’.
  • Then, calculate the average for the sample and named the cell as ‘X-bar’.
  • Next, subtract each value of sample data from the mean of data.
  • Use the next cell and compute the (X-Xbar)^2.
  • Finally, add up the values of (X-Xbar)^2 to obtain the sum of squares.

How to Calculate Sum of Squares Manually (Step-by-Step)?

The formula used for statistical and algebraic calculations of the sum of the squares is discussed below. Let’s elaborate each calculation with the help of an example.

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If you have numbers 6,9,3,17,19,23 then find the sum of squares of numbers?

Solution (For statistical):

Statistical data = (6,9,3,17,19,23)

Total numbers = 6

Total sum = 77

Statistical mean = 77 / 6

= 12.833

Total sum of the square = 𝚺  ( Xi -X̄)2

= (6-12.833)2 + (9-12.833)2 + (3-12.833)2 + (17-12.833)2 + (19-12.833)2 + (23-12.833)2

= 46.6944 + 14.6944 + 96.6944 + 17.3611 + 38.0277 + 103.3611

= 316.8333

Solution (For algebraic):

Total sum of the square = (6)2 + (9)2 + (3)2 + (17)2 + (19)2 + (23)2

= 36 + 81 + 9 + 361 + 529

= 1305

Frequently Ask Questions:

What is the sum of the squares of the differences between each data value and the mean?

The formula for the variance is the sum of squared differences between each data and their mean, divided by total numbers. By this, you can also find out the standard deviation of the data points.

What is the sum of squared differences?

The sum of squared differences (X-Xbar)^2 also called the sum of squared deviations or simply SS. It represents the sum of squared differences from the mean.

What are two squares with a sum of 100?

The two squares that add and give output 100 are 36 and 64.

How do I get the sum of a column in Excel?

To get the sum of a column, follow the given steps!

  • Click at the first cell and drag to select the range of cells you want to calculate.
  • Click on the Autosum.
  • Then click Sum.
  • Tap the checkmark.

Wrapping it up:

Sum of squares is helpful in telling you how much variation in data, also assists you to find out other statistical measures like variance, standard deviation, standard error etc. Also, it is considered in performing ANOVA (or analysis of variance) that is taken into account to tell if there are differences between multiple groups of data. So, consider our sum of squares calculator to calculate the sum of the squares of any group of data (statistically & algebraically).


From the source of Wikipedia: Sum of squares, Statistics, Algebra and algebraic geometry, and much more!