Data from a randomized block design are shown in the following table. $\begin{array}{c}
\quad\quad\quad\text { Treatment Levels }\
\begin{array}{l}
\
\text {Block 1}\
\text {Block 2}\
\text {Block3}
\end{array}
\begin{array}{l}
1 \
8 \
6 \
7
\end{array}
\begin{array}{l}
2 \
5 \
6 \
8
\end{array}
\begin{array}{c}
3 \
10 \
9 \
8
\end{array}
\begin{array}{r}
4\
7\
5\
9
\end{array}
\end{array}$
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. $\begin{array}{c}
\quad\quad\quad\text { Treatment Levels }\
\begin{array}{l}
\
\text {Block 1}\
\text {Block 2}\
\text {Block3}
\end{array}
\begin{array}{l}
1 \
8 \
6 \
7 
\end{array}
\begin{array}{l}
2 \
5 \
6 \
8 
\end{array}
\begin{array}{c}
3 \
10 \
9 \
8 
\end{array}
\begin{array}{r}
4\
7\
5\
9
\end{array}
\end{array}$
 The Total Sum of Squares (SST)is ________.
A)4.67
B)12
C)2.33
D)28.67
E)11

Quizplus · Accepted Answer

The Total Sum of Squares (SST) is calculated by summing the squared differences between each observation and the overall mean of the data. First, calculate the overall mean: (1+8+6+7+5+6+8+10+9+8+7+5+9)/12 = 7. Then, calculate each squared difference and sum them: (1-7)^2 + (8-7)^2 + ... + (9-7)^2 = 28.67.

Data from a Randomized Block Design Are Shown in the Following