An exam is given to students in an introductory statistics course. What is likel

Question

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 one can say the following about the exam?

(a) The exam is quite easy.

bimodal,

multimodal,    

skewed left

skewed right

uniform

(b) The exam is quite hard.

bimodal

multimodal    

skewed left

skewed right

uniform

(c) Half the students took Calculus last semester. The other half haven't seen any math in several years.

bimodal

multimodal    

skewed left

skewed right

uniform

Explanation / Answer

(a) The exam is quite easy.

If the exam is quite easy, most of the students would score higher than middle value (50%) and more number of students would be towards the right and the histogram would be left skewed. So, the answer is skewed left.

(b) The exam is quite hard.

If the exam is quite hard, most of the students would score less than middle value (50%) and more number of students would be towards the left and the histogram would be right skewed. So, the answer is skewed right.

(c) Half the students took Calculus last semester. The other half haven't seen any math in several years.

Half of the students with the Calculus background would have scores better than the other half students with no background of maths. Also, the average scores (or mode) of students with  Calculus background and no maths background would be different. So, the histogram would be bimodal with two modes for both types of students. So, the correct answer is bimodal

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