To determine which test the student performed better on relative to the other students in each class, we can use z-scores. The z-score measures how many standard deviations a particular score is away from the mean. A higher z-score indicates a better performance compared to the class.
Let's calculate the z-scores for both test scores:
For the statistics class:
Mean (μ) = 79
Standard Deviation (σ) = 4.5
Student's Score (x) = 64
Z-score formula: z = (x - μ) / σ
z = (64 - 79) / 4.5
z ≈ -3.333
For the calculus class:
Mean (μ) = 69
Standard Deviation (σ) = 3.7
Student's Score (x) = 60
Z-score formula: z = (x - μ) / σ
z = (60 - 69) / 3.7
z ≈ -2.432
A more negative z-score means the student's score is further below the mean. In this case, the z-score for the calculus test is less negative, indicating that the student's performance on the calculus test was relatively better compared to other students in the calculus class, compared to their performance on the statistics test in relation to other students in the statistics class.