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?

Use z-scores.

Formula:
z = (x - mean)/sd

For Math:
x = 70
mean = 67
sd = 9.58

For English:
x = 84
mean = 78
sd = 12.45

Find both z-scores, then compare.

.3131

z=(70-67)/9.58

z=0.31

z=(84-78)/12.45
z=0.48

What is the answer or how to get started

To determine on which exam the student did better, we need to compare the student's score with the mean scores for Math and English, taking into consideration the standard deviation as well.

Let's calculate the z-scores for the student's scores in Math and English. The z-score is a measure of how many standard deviations an individual score is from the mean.

For Math:
Z-score = (Student's Math score - Mean Math score) / Standard Deviation Math
= (70 - 67) / 9.58
= 0.31

For English:
Z-score = (Student's English score - Mean English score) / Standard Deviation English
= (84 - 78) / 12.45
= 0.48

The z-scores tell us how many standard deviations above or below the mean the student's scores are. In this case, the z-score for English is higher than the z-score for Math, indicating that the student's English score is further above the mean compared to the Math score.

Therefore, the student did better in English compared to Math.