Question

The formula for changing a raw score to a Z score is:
Where X= Raw Score, M=Mean, SD= Standard Deviation

• A. Z= (X-M)/SD
• B. Z= (X+M)/SD
• C. Z= (X-SD)/M
• D. Z= (M-SD)/X

Hint:

Think of a Z-score as answering the question: "How far is my score from the average, and how significant is that distance?" Subtracting the mean \((X-M)\) gives you the distance. Dividing by the standard deviation \((/SD)\) tells you how many "standard" steps that distance is.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question asks for the standard formula to calculate a Z-score. A Z-score (or standard score) indicates how many standard deviations an individual raw score is from the mean of the distribution.
Step 2: Key Formula or Approach:
The logic of the Z-score is to find the difference between the raw score and the mean, and then scale that difference by the standard deviation.
Find the deviation of the score from the mean: \((X - M)\)
Express this deviation in terms of standard deviation units by dividing by the standard deviation: \(\frac{(X - M)}{SD}\)
So, the formula is: \[ Z = \frac{X - M}{SD} \] Step 3: Detailed Explanation:
Let's analyze the given options:
(A) Z= (X-M)/SD: This correctly represents the raw score minus the mean, divided by the standard deviation. This is the correct formula.
(B) Z= (X+M)/SD: This incorrectly adds the mean.
(C) Z= (X-SD)/M: This incorrectly subtracts the standard deviation and divides by the mean.
(D) Z= (M-SD)/X: This formula is incorrect in its structure.
Step 4: Final Answer:
The correct formula for changing a raw score to a Z-score is Z = (X-M)/SD.