An instructor finds that the standard deviation for undergraduates on a statistics test is 16. On the same exam, the standard deviation for an equal number of graduate students is 8. On the basis of these data alone, he concludes that average performance for graduate students is higher than that for undergraduates. Identify what is wrong with his conclusion and why. What can he correctly conclude?
What will be an ideal response?
Correct Answer:
He cannot conclude that the performance of the graduate students is better or worse than that of the undergraduate students without knowing the means of the distributions. He can correctly conclude that the performance of the graduate students varies less than that of the undergraduate students.
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