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 scores -2.00. Therefore, David has the higher standardized score.
B)David's standardized score is -1.64 and Steven's standardized scores -2.00. Therefore, Steven has the higher standardized score.
C)David's standardized score is 1.64 and Steven's standardized scores 2.00. Therefore, Steven has the higher standardized score.
D)Cannot be determined with the information provided.

Question

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 scores -2.00. Therefore, David has the higher standardized score.
B)David's standardized score is -1.64 and Steven's standardized scores -2.00. Therefore, Steven has the higher standardized score.
C)​David's standardized score is 1.64 and Steven's standardized scores 2.00. Therefore, Steven has the higher standardized score.
D)​Cannot be determined with the information provided.

Quizplus · Accepted Answer

To find the standardized score, we use the formula: z = (x - mean) / standard deviation. 
For David, z = (52 - 70) / 11 = -1.64 
For Steven, z = (52 - 64) / 6 = -2.00 
Since a higher standardized score indicates a score farther from the mean, Steven has the higher standardized score with a score of -2.00 compared to David's score of -1.64. Therefore, the answer is choice B.