Problem
Attempts Score / 2 3. Sum of Squares for the Treatment Group A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression. Treatment Group \[ \begin{array}{l} 14141415151717181819 \\ 20202021222323232426 \\ 26262627272828293030 \\ \text { Control Group } \\ 15151719192021222223 \\ 24242424242525252626 \\ 27272729292930313132 \\ 3434 \end{array} \] What is the sum of squared deviations for the Treatment Group?
Solution
Step 1 ：Create a list of the scores for the Treatment Group: [14, 14, 14, 15, 15, 17, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 23, 24, 26, 26, 26, 26, 27, 27, 28, 28, 29, 30, 30].
Step 2 ：Calculate the mean of these scores. The mean is \(22.06896551724138\).
Step 3 ：Calculate the squared deviation for each score by subtracting the mean from each score, squaring the result, and then summing up all these squared values. The sum of squared deviations is \(759.8620689655173\).
Step 4 ：The final answer is the sum of squared deviations for the Treatment Group, which is \(\boxed{759.8620689655173}\).
