Answer:
To determine who did relatively better between Isaac and Ian, we can calculate the Z-scores for both of their test grades. Z-scores help us compare individual data points to the mean and standard deviation of a dataset.
a) Calculate the Z-score for Isaac's test grade:
Z-score = (X - μ) / σ
Where:
X is the individual's test score (Isaac's score in Art History) = 77.3
μ is the mean of the Art History class = 73
σ is the standard deviation of the Art History class = 10.7
Z-score for Isaac = (77.3 - 73) / 10.7 ≈ 0.43
b) Calculate the Z-score for Ian's test grade:
Z-score = (X - μ) / σ
Where:
X is the individual's test score (Ian's score in English) = 62.9
μ is the mean of the English class = 66.8
σ is the standard deviation of the English class = 10.8
Z-score for Ian = (62.9 - 66.8) / 10.8 ≈ -0.36
Now, let's compare the Z-scores:
Isaac's Z-score is approximately 0.43.
Ian's Z-score is approximately -0.36.
Since Z-scores represent how many standard deviations a data point is from the mean, a higher Z-score indicates a relatively better performance compared to the class mean.
In this case, Isaac's Z-score of 0.43 is positive, indicating that his score in Art History is 0.43 standard deviations above the class mean. Ian's Z-score of -0.36 is negative, indicating that his score in English is 0.36 standard deviations below the class mean.
Therefore, Isaac did relatively better compared to Ian in their respective tests. So, the answer is: Isaac did relatively better.