How to Calculate Total Sum of Square

How to Calculate Total Sum of Square - Tutorial

Definition:

Total sum of square is a statistical method which evaluates the sum of the squared difference between the actual X and the mean of X, from the overall mean.

Formula:

Total Sum of Square TSS or SST = Σ (Xi - X̄)
where,
X = Statistical Data X̄ = Statistical Mean

Example :

If the statistical data are 1,2,3,4,5 then calculate the total sum of square

Given :

Statistical Data = 1,2,3,4,5

To Find :

Total Sum of Square TSS or SST

Solution :

Step:1

Statistical Data = 1,2,3,4,5

Total data = 5

Let us first calculate the value of Statistical Mean,

Statistical Mean (X̄) = (1 + 2 + 3 + 4 + 5) / 5
= 3
Step:2

Let us now calculate the Total sum of square value.

Total Sum of Square TSS or SST = Σ (Xi - X̄)

Total Sum of Square = (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

Result :

Total Sum of Square (TSS or SST) is 10.

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