Math Snap
PROBLEM
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline & \multicolumn{1}{|c|}{\text{Kafsha e laboratorit}} \\ \cline{2-10} \text{Anestezia} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text{A} & 0.28 & 0.50 & 0.68 & 0.27 & 0.31 & 0.99 & 0.26 & 0.35 & 0.38 & 0.34 \\ \hline \text{B} & 0.20 & 0.38 & 0.50 & 0.29 & 0.38 & 0.62 & 0.42 & 0.87 & 0.37 & 0.43 \\ \hline \text{C} & 1.23 & 1.34 & 0.55 & 1.06 & 0.48 & 0.68 & 1.12 & 1.52 & 0.27 & 0.35 \\ \hline \end{array}
STEP 1
1. We are given three groups of data labeled A, B, and C.
2. We need to calculate the sum of squares for each group.
STEP 2
1. Calculate the mean for each group.
2. Compute the squared deviation from the mean for each data point in each group.
3. Sum the squared deviations for each group.
STEP 3
Calculate the mean for group A:
STEP 4
Calculate the mean for group B:
STEP 5
Calculate the mean for group C:
STEP 6
Compute the squared deviations for group A:
\begin{align}
(0.28 - 0.436)^2 & = 0.024576, \\
(0.50 - 0.436)^2 & = 0.004096, \\
(0.68 - 0.436)^2 & = 0.059536, \\
(0.27 - 0.436)^2 & = 0.027556, \\
(0.31 - 0.436)^2 & = 0.015876, \\
(0.99 - 0.436)^2 & = 0.307216, \\
(0.26 - 0.436)^2 & = 0.031056, \\
(0.35 - 0.436)^2 & = 0.007396, \\
(0.38 - 0.436)^2 & = 0.003136, \\
(0.34 - 0.436)^2 & = 0.009216
\end{align}
STEP 7
Compute the squared deviations for group B:
\begin{align}
(0.20 - 0.446)^2 & = 0.060076, \\
(0.38 - 0.446)^2 & = 0.004356, \\
(0.50 - 0.446)^2 & = 0.002916, \\
(0.29 - 0.446)^2 & = 0.024556, \\
(0.38 - 0.446)^2 & = 0.004356, \\
(0.62 - 0.446)^2 & = 0.030276, \\
(0.42 - 0.446)^2 & = 0.000676, \\
(0.87 - 0.446)^2 & = 0.180276, \\
(0.37 - 0.446)^2 & = 0.005776, \\
(0.43 - 0.446)^2 & = 0.000256
\end{align}
STEP 8
Compute the squared deviations for group C:
\begin{align}
(1.23 - 0.86)^2 & = 0.1369, \\
(1.34 - 0.86)^2 & = 0.2304, \\
(0.55 - 0.86)^2 & = 0.0961, \\
(1.06 - 0.86)^2 & = 0.04, \\
(0.48 - 0.86)^2 & = 0.1444, \\
(0.68 - 0.86)^2 & = 0.0324, \\
(1.12 - 0.86)^2 & = 0.0676, \\
(1.52 - 0.86)^2 & = 0.4356, \\
(0.27 - 0.86)^2 & = 0.3481, \\
(0.35 - 0.86)^2 & = 0.2601
\end{align}
STEP 9
Sum the squared deviations for group A:
STEP 10
Sum the squared deviations for group B:
SOLUTION
Sum the squared deviations for group C:
The sums of squares for each group are:
- Group A:
- Group B:
- Group C:
