The sum of squares practice exercises

The sum of squares

The sum of squares or SS is a term on the ANOVA summary table. It is the sum of squared deviation of scores from the mean.

The problem

A high school teacher gave a history exam to her class of ten students. She graded the papers and recorded the score of each student. She then calculated the mean of these scores. Later she wanted to see how far from the mean the scores were located..

$X$
19
20
18
13
16
17
20
28
16
18

The formula of the sum of squares

$$\sum{(X-\bar{X})^2}$$

We read this as The sum of each score from the mean squared.

Step by step calculation of the sum of squares

Step1. To calculate the mean we add up all the scores and divide by the number of scores. Here is the formula for the mean.
$$\bar{X} ={\sum{X} \over {n}}$$ $$mean={sum of scores \over number of scores}$$

Step 2. Next she subtracted each score from the mean, to have the the degree of deviation of each score from the mean.
$$X-\bar{X}$$

Step 3. Next she squared these deviations $${(X-\bar{X})^2}$$

Step 4. Finally, she added up these squared deviation. This is the sum of squared deviations, or SS.
$$\sum{(X-\bar{X})^2}$$

The solution

Post below.