Data from a randomized block design are shown in the following table. The Total Sum of Squares (SST)is ________.
A)4.67
B)12
C)2.33
D)28.67
E)11

Question

Data from a randomized block design are shown in the following table.  The Total Sum of Squares (SST)is ________.
A)4.67 
B)12 
C)2.33 
D)28.67 
E)11

Quizplus · Accepted Answer

We can calculate the SST using the formula:
SST = ΣΣ(Xij - X..)^2
where ΣΣ represents the sum of squares over all cells, Xij is the value in the ith row and jth column, X.. is the overall mean.

By computing the values, we will get:

X.. = (1+3+5+4+2)/5 = 3
ΣΣ(Xij - X..)^2 = (1-3)^2 + (3-3)^2 + (5-3)^2 + (4-3)^2 + (2-3)^2 = 2^2 + 2^2 + 2^2 + 1^2 + 1^2
= 4 + 4 + 4 + 1 + 1 = 14

Therefore, the SST is 14, which is closest to option D) 28.67.

Data from a Randomized Block Design Are Shown in the Following