Formulas for Sum of Squares
- ∑ = sum
- x i = each value in the set
- x̄ = mean
- x i – x̄ = deviation
- (x i – x̄) 2 = square of the deviation
- a, b = numbers
- n = number of terms
How to calculate the sum of squares?
How to Calculate the Total Sum of Squares (SST) Step 1: Calculate the mean of the sample. Step 2: Subtract the mean from each sample value, and square each difference. Step 3: Sum these squared ...
How to find SS stats?
SS = SUM(X i - AVERAGE(X)) The average of a set of x's may be written as x-bar (or x with a horizontal line above it). Example. In a set of measure, SS is calculated as below. Column B, below is the gap between x in Column A and the average of Column A.
What is SSR statistics?
- Slope and Intercept
- SST, SSR and SSE
- Correlation and R-squared
- Standard error
How to find the square of a sum?
What is Sum of Squares?
- Sum of Squares Formula
- Sum N Terms of arithmetic series
- Sum Of Geometric progression
- Sum Of Nth Terms
What Is the Expansion of Sum of Squares Formula?
a 2 + b 2 formula is known as the sum of squares formula it is read as a square plus b square. Its expansion is expressed as a 2 + b 2 = (a +b) 2 -2ab.
What Is the Sum of Squares Formula in Algebra?
The sum of squares formula is one of the important algebraic identities. It is represented by a 2 + b 2 and is read as a square plus b square. The sum of squares (a 2 + b 2) formula is expressed as a 2 + b 2 = (a +b) 2 -2ab
How To Use the Sum of Squares Formula Give Steps?
The following steps are followed while using the sum of squares formula.
Standard Formula Example
To see how this shortcut formula works, we will consider an example that is calculated using both formulas. Suppose our sample is 2, 4, 6, 8. The sample mean is (2 + 4 + 6 + 8)/4 = 20/4 = 5. Now we calculate the difference of each data point with the mean 5.
Shortcut Formula Example
Now we will use the same set of data: 2, 4, 6, 8, with the shortcut formula to determine the sum of squares. We first square each data point and add them together: 2 2 + 4 2 + 6 2 + 8 2 = 4 + 16 + 36 + 64 = 120.
How Does This Work?
Many people will just accept the formula at face value and do not have any idea why this formula works. By using a little bit of algebra, we can see why this shortcut formula is equivalent to the standard, traditional way of calculating the sum of squared deviations.
Is It Really a Shortcut?
It may not seem like this formula is truly a shortcut. After all, in the example above it seems that there are just as many calculations. Part of this has to do with the fact that we only looked at a sample size that was small.
What is Sum of Squares?
The sum of the squares of numbers is referred to as the sum of squared values of the numbers. It’s basically the addition of squared numbers.
Formulae for Sum of Squares
Formula 1: For addition of squares of any two numbers a and b is represented by:
Sample Questions
Question 1: Evaluate 52 + 52 with the help of formula and directly as well. Verify the answers.
Sum of Squares in Statistics
In statistics, the sum of squares is also known as a total sum of squares and it is noted by TSS. The formula of a total sum of squares is given below,
Sum of Squares in Algebra
Algebraic formulas are useful to calculate the squares of large numbers easily.
Sum of squares of natural numbers
Natural numbers are numbers used for counting and ordering ranges from 1 to infinity and it is also known as positive integers. The formulas to calculate the sum of squares of n number of natural numbers, n even numbers and n odd numbers are tabulated below.
Things to Remember
The sum of squares formulas is used to find the sum of squares of large numbers in an easy way. It is used in statistics to find the variance of a given value. In algebra and number series it is used as a basic arithmetic operation.
Sample Questions
Ques. Calculate the sum of squares of 13 and 14 using algebraic identities and prove LHS and RHS are equal. (2 marks)
What is the sum of natural numbers?
The natural numbers are the counting numbers from 1 to infinity. If we consider n consecutive natural numbers, then finding the sum of the squares of their numbers is represented as Σn 2, where n ranges from 1 to infinity. Here are the formulas for finding the sum of squares of n natural numbers, the sum of squares of first n even numbers, and the sum of squares of first n odd numbers.
What does "squaring" mean in math?
Squaring the number is denoted by n 2. The sum of squares means the sum of the squares of the given numbers. It could be finding the sum of squares of 2 numbers or 3 numbers or sum of squares of consecutive n numbers or n even numbers or n odd numbers.
Standard Formula Example
Shortcut Formula Example
- Now we will use the same set of data: 2, 4, 6, 8, with the shortcut formula to determine the sum of squares. We first square each data point and add them together: 22 + 42 + 62 + 82= 4 + 16 + 36 + 64 = 120. The next step is to add together all of the data and square this sum: (2 + 4 + 6 + 8)2= 400. We divide this by the number of data points to obt...
How Does This Work?
- Many people will just accept the formula at face value and do not have any idea why this formula works. By using a little bit of algebra, we can see why this shortcut formula is equivalent to the standard, traditional way of calculating the sum of squared deviations. Although there may be hundreds, if not thousands of values in a real-world data set, we will assume that there are only t…
Is It Really A Shortcut?
- It may not seem like this formula is truly a shortcut. After all, in the example above it seems that there are just as many calculations. Part of this has to do with the fact that we only looked at a sample size that was small. As we increase the size of our sample, we see that the shortcut formula reduces the number of calculations by about half. We do not need to subtract the mean …