Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. Nash's test. Which student has the higher standardized score?
A)David's standardized score is -1.64 and Steven's standardized score is -2.00. Therefore, David has the higher standardized score.
B)David's standardized score is -1.64 and Steven's standardized score is -2.00. Therefore, Steven has the higher standardized score.
C)David's standardized score is 1.64 and Steven's standardized score is 2.00. Therefore, Steven has the higher standardized score.
D)Cannot be determined with the information provided.

Question

Quizplus · Accepted Answer

Standardized score (z-score) can be calculated using the formula: z = (x - μ) / σ, where x is the raw score, μ is the mean score, and σ is the standard deviation. 
For David, z-score = (52 - 70) / 11 = -1.64 
For Steven, z-score = (52 - 64) / 6 = -2.00 
Since standardized scores are measured in terms of number of standard deviations from the mean, a lower standardized score indicates a lower relative standing in the distribution. Therefore, Steven has the higher standardized score (i.e., the lower z-score).