Question
A statistics teacher gives a multiple-choice exam with 20 questions. The teacher wants to discourage guessing on the exam, so for each question the student
A statistics teacher gives a multiple-choice exam with 20 questions. The teacher wants to discourage guessing on the exam, so for each question the student earns 1 point for a correct answer, 0 points for no answer, and -1 point for a wrong answer. Consequently, if a student answered every question incorrectly the student would earn a score of -20 on the exam. However, if a student answered every question correctly, the student would earn a score of 20 on the exam. After the exam, the teacher distributes the list of test scores and asks the class to calculate the standard deviation. The first student to finish the calculations says that the standard deviation is -1.8.
Other students respond with the following comments. Which comment is definitely correct?
- The standard deviation was calculated incorrectly.
- Most students guessed on too many problems and earned negative scores.
- Most students scored below the mean.
- There is an outlier that has a negative value close to -20.
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