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Chapter 3: Problem 30

An exam is given to students in an introductory statistics course. What is likely to be true of the shape of the histogram of scores if: a. the exam is quite easy? b. the exam is quite difficult? c. half the students in the class have had calculus, the other half have had no prior college math courses, and the exam emphasizes mathematical manipulation? Explain your reasoning in each case.

Short Answer

Expert verified
a) The histogram of scores will be skewed to the left due to high scores across the board. b) The histogram will be skewed to the right due to lower scores for most students. c) We would see a bimodal distribution in the histogram because half of the students will do well (those who had calculus) and the half will likely score lower (those without prior college math courses).

Step by step solution

01

Analyze the effect of an easy exam

If an exam is very easy, most students will score high marks. Hence the distribution of scores will be clustered towards the high end of the score range. The histogram, as a result, would be skewed to the left (known as negatively skewed).
02

Analyze the effect of a difficult exam

If the exam is hard, most students will score low marks. The histogram, in this case, would be skewed to the right (known as positively skewed) because most scores would accumulate at the lower end of the score range.
03

Analyze the effect of students' mathematical backgrounds

When half of the students are experienced with calculus and half are not, and the exam emphasizes mathematical manipulation, the scores are likely to have a bimodal distribution. This means the histogram would have two peaks. One peak would correspond to the high scores from students who have had calculus, and another peak would correspond to the lower scores of the students with no prior college math courses.

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