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Sum of Squares Calculator

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The online sum of squares calculator helps you to calculate the algebraic and statistical sum of squares of the given sample data values. In statistical terms, an online sum of squared deviations calculator enables you to find the sum of squared deviation for the given set of numbers. Well, remember that finding the sum of squares is very helpful in the field of applied mathematics, physics, and electronics, etc. So, it’s better to have an exact idea about the sum of squares before using this tool.

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. In algebra, the sum of squares 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 squared deviations 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 squares = 𝚺  ( Xi -X̄)2

Where,

Xi = Statistical Data

X̄ = Statistical 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

Where,

n = total numbers in expression for which you want to calculate sum of squares

The Relationship between sum of squares and simple 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 sum of squares(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 simple 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, this 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 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.

About Sum of Squares Calculator:

The total sum of squares calculator examines dataset values and calculate the sum of squares statistics and algebraic within a fraction of seconds. This calculator displays the steps by steps calculation of both statistical and algebraic calculations. You can use this sum of squared deviations calculator to calculate the sum of squared differences from the mean.

How to find sum of squares With Sum of squared deviations calculator:

This calculator for sum of squares is 100 free that will works efficiently in the calculating sum of squares accurately. Just follow the given points for calculating sum of squares.

Read on!

Inputs:

  • First of all, you have to select the standard from which the numbers are separated from the dropdown of this tool.
  • Then, enter the numbers below in the designated field.
  • Lastly, hit the calculate button.

Outputs:

When you enter all the fields, the online calculator will show you,

  • Sum of the squares for statistical.
  • Sum of the squares for algebraic.
  • Step-by-step statistical calculations.
  • Step-by-step algebraic calculations.

How to calculate sum of squares manually (Step-by-Step)?

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

Swipe on!

Example:

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

This sum of squares calculator generates results according to these calculations.

Frequently Ask Questions:

What is the sum of squares within?

It is termed as “sum of squares within the groups(SSwithin). The formula for the SSwithin is the degree of freedom of each group multiplied by the squared standard deviation of each group.

What does the total sum of squares mean?

It is defined as “sum of all squared differences between the observation and means”. In statistical data analysis, the sum of squares (SS) is a standard way of representing the results.

Why do we calculate the sum of squares?

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 etc.

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:

Remember that sum of squares is typically used in calculating statistics including variance, standard deviation, and standard error. 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 online sum of squares calculator to find sum of squares of any group of data (statistically & algebraically).

References:

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

From the source of thoughtco: Sum of Squares Formula Shortcut, Is It Really a Shortcut?

From the source of accendoreliability: The Sum of Squares Concept, Regression Analysis and Errors