Sum of Squares Calculator

Sum of Squares Calculator:

Use this sum of squares calculator to locate the algebraic & statistical sum of squares for the given datasets. It also suggests how to clear up the sum of squares step by step.

what's Sum of Squares?

Statistics:

• The sum of squares (SS) measures the range of a dataset. It's calculated with the aid of locating the squared deviations of each records factor from the imply cost and summing all of them up. A better SS suggests greater spread in the within the given dataset.

Algebra:

• It refers to the addition of several phrases that have been squared and now not necessarily involve deviations from the mean.

what's the Sum of Squares system?

For Statistical Calculation:

The sum of squares equation for statistical statistics is as follows:

(Xi -X̄)2

Where:

• Xi = Statistical Data
• X̄ = Statistical mean

You can use our sum of squares calculator to calculate the sum of squared deviations from the suggest.

For Algebraic Calculation:

The formula for the calculation of sum of squares for algebraic calculation is as follows:

\(\ (n_1)^{2} +(n_2)^{2}+(n_3)^{2}.....(n_n)^{2}\)

Where:

• n = total numbers in expression

The connection between Sum of Squares and pattern Variance:

The Sum of Squares (SS):

• It represents the full squared deviation of the dataset values from the imply
• The sum of squares represents the range of the records points

Sample Variance (s²):

• It calculates the average squared deviation from the suggest in a pattern
• Sample variance facilitates to degree the populace variant/li>

Pattern variance helps you to estimate the populace variance (version of the whole populace from which the sample is drawn). The sum of squares (SS) is the numerator inside the sample variance (s²) method. As you can see beneath:

\(\ S^{2} =\frac{S.S}{n-1}\)

Where:

• s² is the sample variance
• S.S is the sum of squares
• n is the sample size

What are the restrictions of the usage of The Sum of Squares?

Boundaries of the Sum of Squares (SS):

• Sensitivity to Outliers: The intense facts points can make the statistics appear greater unfold out than it is. it may lead to overestimation of facts variability
• Assumption of Normality: The sum of squares works first-rate with the typically distributed facts(a bell-fashioned curve). If the facts isn't always commonly disbursed then the sum of squares won't let you have the variance and wellknown deviation
• Constrained records: The sum of squares best tells you approximately the overall variation of the dataset (how spread out the facts factors are from the mean). It doesn't provide records approximately the path or shape of the distribution (e.g., skewed or symmetrical)

How to Calculate Sum of Squares?

Follow these steps:

• Locate the imply (average)
• Now subtract the imply fee from the given records factors
• Take the square of the differences and upload them together

Example:

Suppose you have a dataset as 6,9,3,17,19,23 find the sum of squares?

Solution:

(For Statistical):

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

Total numbers = 6

Total sum = 77

Statistical mean = 77 / 6 = 12.833

By putting vlaues in the sum of squares formula:

= (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

(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

Other than guide calculations, use the total sum of squares calculator to simplify calculations for any dataset (statistically & algebraically) grade by grade!

References:

From the source of Wikipedia: Sum of squares, data, Algebra and algebraic geometry, and plenty extra!

From the source of sciencing.com: a way to Calculate a Sum of Squared Deviations from the imply (Sum of Squares)