How to Calculate Total Sum of Squares (TSS or SST)?

Short tutorial on how to calculate total sum of squares (TSS or SST).

Total Sum of Squares (TSS or SST)

Total Sum of Squares (TSS or SST) is defined as the sum of over all observations, of the squared differences of each observation from the overall mean.
This short tutorial will help you explain how to calculate the total sum of squares (TSS or SST) with a neat and simple example.

Formula:
Total Sum of Squares TSS or SST = Σ (X_i - X̄)
where,
X = Statistical Data
X̄ = Statistical Mean

Example:
Consider a statistical data 1,2,3,4,5. Calculate Total Sum of Squares (TSS or SST).
Step 1:
Statistical Data = 1,2,3,4,5
Total Data = 5

To Find:
Total Sum of Square TSS or SST
Step 2:
Applying the values in the formula,
Total Sum of Squares TSS or SST = Σ (Xi - X̄)
Total Sum of Squares (TSS or SST) = (1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²
= (-2)² + (-1)² + (0)² + (1)² + (2)²
= 4 + 1 + 0 + 1 + 4
= 10

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