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Based on the example of exam scores, explain how a single outlier affects the calculation of the range and why the resulting value is misleading.
Question: Based on the example of exam scores, explain how a single outlier affects the calculation of the range and why the resulting value is misleading.
Sample answer: In an exam where most students score between and , the range is . If a single student scores a , the range suddenly increases to . This inflated value is misleading because it suggests the entire class's scores are highly variable, when in reality only one student deviated significantly while the rest scored very consistently.
Key points:
- Most students scored between and , resulting in a narrow range of .
- A single student scoring a causes the range to jump to .
- The outlier inflates the range, giving a false impression of high variability.
- The actual performance of the rest of the class remains highly consistent.
Rubric: The response must describe how the range changes from to due to a single student scoring when the rest scored between and . It should explain that this outlier inflates the range and creates a false impression of high variability for the class as a whole.
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Research Methods in Psychology - 4th American Edition @ KPU
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