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Diagnose how the single score of impacts the range calculation. Clarify what false impression the resulting range of gives about the group, and describe the actual consistency of the majority of the students.
Case context: A psychology instructor analyzes the exam scores of a class. The majority of the students scored between and , which would yield a narrow range of . However, one student scored a . Calculating the range for the entire class results in a value of . The instructor wants to understand why this range value is misleading.
Question: Diagnose how the single score of impacts the range calculation. Clarify what false impression the resulting range of gives about the group, and describe the actual consistency of the majority of the students.
Sample answer: The score of acts as an outlier that dramatically increases the range from to . This inflated range of is misleading because it gives the false impression that the entire class's scores are highly variable. In reality, the class is highly consistent, as almost all students scored between and , with only a single student deviating from the rest.
Key points:
- The score of acts as an outlier that distorts the range.
- The range is inflated from to due to this single score.
- The range of falsely suggests the entire class's scores are highly variable.
- The majority of the class scored consistently between and .
Rubric: The response must identify the score of as an outlier that inflates the range. It must explain that this inflated range incorrectly suggests high variability among the entire class, whereas the majority of the class actually performed consistently within a narrow range.
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Research Methods in Psychology - 4th American Edition @ KPU
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