In one elementary school, 200 students are tested on the subject of Math and English. The table below shows the mean and standard deviation for each subject.
Mean SD
Math 67 9.58
English 78 12.45
One student’s Math score was 70 and the same individual’s English score was 84. On which exam did the student do better?
Compare in terms of a standard score (Z).
Z = (score-mean)/SD
Which Z score is greater?
To determine on which exam the student did better, we need to compare the student's scores in Math and English.
To do this, we can use the concept of z-scores. The z-score represents how many standard deviations a data point is from the mean.
To find the z-score for the Math score of 70, we use the formula:
z = (x - mean) / SD
where x is the score (70), mean is the mean for Math (67), and SD is the standard deviation for Math (9.58).
So, for the Math score:
z_math = (70 - 67) / 9.58 = 0.31
Similarly, we can find the z-score for the English score of 84 using the formula:
z_english = (84 - 78) / 12.45 = 0.48
Since the z-scores indicate the number of standard deviations from the mean, a higher z-score implies a better performance.
Comparing the z-scores, we can see that the student's z-score for English (0.48) is higher than the z-score for Math (0.31). Therefore, the student did better in English than in Math.