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: Concept Identification: The request is to provide the standard formula for calculating a Z-score. A Z-score quantifies how many standard deviations a raw score deviates from the distribution's mean. Step 2: Formula Derivation: The Z-score calculation involves determining the difference between a raw score and the mean, then scaling this difference by the standard deviation.
Calculate the score's deviation from the mean: $(X - M)$
Normalize this deviation into standard deviation units: $\frac{(X - M)}{SD}$
The resulting formula is: \[ Z = \frac{X - M}{SD} \] Step 3: Option Analysis:
(A) Z= (X-M)/SD: This formula accurately reflects the raw score minus the mean, divided by the standard deviation, and is the correct representation.
(B) Z= (X+M)/SD: This option is incorrect as it adds the mean.
(C) Z= (X-SD)/M: This option is incorrect, as it subtracts the standard deviation and divides by the mean.
(D) Z= (M-SD)/X: This formula is structurally incorrect.
Step 4: Conclusion: The definitive formula for converting a raw score into a Z-score is Z = (X-M)/SD.