Let's break down each calculation step by step:

Given scores:

$X = 6, 2, 4, 2$

1. Calculate $\sum X^2$

This is the sum of the squares of each score.

$\sum X^2 = 6^2 + 2^2 + 4^2 + 2^2$

$\sum X^2 = 36 + 4 + 16 + 4 = 60$

2. Calculate $(\sum X)^2$

First, we find the sum of all scores and then square the result.

$\sum X = 6 + 2 + 4 + 2 = 14$

Now, square this sum:

$(\sum X)^2 = 14^2 = 196$

3. Calculate $\sum (X - 2)$

Subtract 2 from each score and then sum the results.

$X - 2 = 6 - 2, 2 - 2, 4 - 2, 2 - 2$

$X - 2 = 4, 0, 2, 0$

$\sum (X - 2) = 4 + 0 + 2 + 0 = 6$

4. Calculate $\sum (X - 1)^2$

Subtract 1 from each score, square the result, and then sum all the squared results.

$(X - 1)^2 = (6 - 1)^2, (2 - 1)^2, (4 - 1)^2, (2 - 1)^2$

$(X - 1)^2 = 5^2, 1^2, 3^2, 1^2$

$(X - 1)^2 = 25, 1, 9, 1$

$\sum (X - 1)^2 = 25 + 1 + 9 + 1 = 36$

Summary of Values:

1. $\sum X^2 = 60$
2. $(\sum X)^2 = 196$
3. $\sum (X - 2) = 6$
4. $\sum (X - 1)^2 = 36$

Would you like a more detailed explanation on any of these calculations? Here are 5 questions related to this topic:

1. How would the calculations change if the scores were negative?
2. What is the difference between $\sum X^2$ and $(\sum X)^2$?
3. Can you calculate the mean and variance of this data set?
4. How would you calculate $\sum (X - 3)$ for the given scores?
5. What does each of these summation operations represent in statistics?

Tip: Always double-check the steps when working with multiple summations to ensure accuracy!