Five students are enrolled in an advanced course in psychology. Two quizzes are given early in the semester, each worth a total of 10 points. The results are as follows:

(a) Compute each of the following:

ΣX = ________ (ΣX)2 = ________ Σ(X ˆ’ Y) = ________
ΣY = ________ (ΣY)2 = ________ ΣX ˆ’ ΣY = ________
ΣX2 = ________ Σ(X + Y) = ________ ΣXY = ________
ΣY2 = ________ ΣX + ΣY = ________ ΣX ΣY = ________

(b) Using the results of part (a), show that each of the following rules listed in this chapter is true:

Rule 1: ________ = ________
Rule 2: ________ = ________
Rule 3: ________ ‰  ________
Rule 4: ________ ‰  ________ (X data)
________ ‰  ________ (Y data

(c) After some consideration, the instructor decides that Quiz 1 was excessively difficult and decides to add 4 points to each student's score. This can be represented in symbols by using k to stand for the constant amount in question, 4 points. Using Rule 6, compute

Compute

(Note that this result is different from the preceding one.)
Now add 4 points to each student's score on Quiz 1 and obtain the sum of these new scores.

(d) Had the instructor been particularly uncharitable, he might have decided that Quiz 2 was too easy and subtracted 3 points from each student's score on that quiz. Although this is a new problem, the letter k can again be used to represent the constant; here, k = 3.

Using Rule 7, compute

Compute

(Note that this result is different from the preceding one.)

Now subtract 3 points from each student's score on Quiz 2 and obtain the sum of these new scores.

(e) Suppose that the instructor decides to double all of the original scores on Quiz 1. Using Rule 8, compute

Now double each student's score on Quiz 1 and obtain the sum of these new scores.

Student Quiz 1 (X)|Quiz 2 (Y) 4 3 2. 2. 2. 3. + ) - L+, %3D