To calculate the Sum of Squares (SS) for a population, we can use the following formula:

$SS = \sum X^2 - \frac{(\sum X)^2}{N}$

Where:

• $\sum X^2$ is the sum of the squared scores.
• $\sum X$ is the sum of the scores.
• $N$ is the number of scores in the population.

Given:

• $\sum X = 12$
• $\sum X^2 = 54$
• $N = 6$

Substituting the values into the formula:

$SS = 54 - \frac{(12)^2}{6}$

$SS = 54 - \frac{144}{6}$

$SS = 54 - 24$

$SS = 30$

So, the Sum of Squares (SS) for this population is 30.

Would you like to see more details on this formula or other related calculations? Here are some additional questions you may find useful:

1. How do you calculate the variance for this population once you have the SS?
2. What is the difference between SS and variance?
3. How is the SS formula adapted for a sample instead of a population?
4. How does the sum of squares relate to the standard deviation?
5. What does the sum of squares tell us about the variability of the data?

Tip: Always ensure you're using the correct version of formulas for populations vs. samples, as the denominators differ (N for populations, N-1 for samples).