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Use this sum of squares calculator to find the algebraic & statistical sum of squares for the given datasets. It also shows how to solve the sum of squares step by step.

**Statistics:**

- The sum of squares (SS) measures the variability of a dataset. It's calculated by finding the squared deviations of each data point from the mean value and summing them all up. A higher SS indicates more spread in the within the given dataset.

**Algebra:**

- It refers to the addition of several terms that have been squared and not necessarily involve deviations from the mean.

The sum of squares equation for statistical data 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 mean.

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 Sum of Squares (SS):**

- It represents the total squared deviation of the dataset values from the mean
- The sum of squares represents the variability of the data points

**Sample Variance (s²):**

- It calculates the average squared deviation from the mean in a sample
- Sample variance helps to measure the population variation

Sample variance helps you to estimate the population variance (variation of the entire population from which the sample is drawn). The sum of squares (SS) is the numerator in the sample variance (s²) formula. As you can see below:

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

Where:

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

**Sensitivity to Outliers:**The extreme data points can make the data seem more spread out than it is. It can lead to overestimation of data variability**Assumption of Normality:**The sum of squares works best with the normally distributed data(a bell-shaped curve). If the data is not normally distributed then the sum of squares may not let you have the variance and standard deviation**Limited Information:**The sum of squares only tells you about the total variation of the dataset (how spread out the data points are from the mean). It doesn't provide information about the direction or shape of the distribution (e.g., skewed or symmetrical)

Follow these steps:

- Find the Mean (Average)
- Now subtract the mean value from the given data points
- Take the square of the differences and add them together

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

Apart from manual calculations, use the total sum of squares calculator to simplify calculations for any dataset (statistically & algebraically) step by step!

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

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

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