3. 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?
Calculate the Z scores for both tests. Which is larger?
To determine on which exam the student did better, we can compare the scores in Math and English using z-scores.
The z-score measures how many standard deviations a score is from the mean. A positive z-score indicates a score above the mean, while a negative z-score indicates a score below the mean.
To calculate the z-score, we can use the formula:
z = (x - μ) / σ
Where:
- x is the individual score
- μ is the mean of the subject
- σ is the standard deviation of the subject
Let's calculate the z-scores for the Math and English scores:
For Math:
x = 70 (individual score)
μ = 67 (mean score for Math)
σ = 9.58 (standard deviation for Math)
z_math = (70 - 67) / 9.58
For English:
x = 84 (individual score)
μ = 78 (mean score for English)
σ = 12.45 (standard deviation for English)
z_english = (84 - 78) / 12.45
Now, let's calculate the z-scores:
z_math = (70 - 67) / 9.58 = 0.314
z_english = (84 - 78) / 12.45 = 0.483
Since the z-score for English (0.483) is higher than the z-score for Math (0.314), the student did better in English compared to Math.
In summary, the student performed better in the English exam than in the Math exam.