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Explain why adding the eighth score of changes the calculation method for finding the median, and describe how the new median is determined using the scores and .
Case context: A psychology student is calculating the median for a set of seven scores: . After ordering the sequence to , the student identifies the median as . Later, a peer suggests adding an eighth score of to the dataset.
Question: Explain why adding the eighth score of changes the calculation method for finding the median, and describe how the new median is determined using the scores and .
Sample answer: Adding the eighth score of increases the total number of scores to an even number (eight). In an even dataset (), there is no longer a single middle score. The student must instead identify the two middle scores, which are and , and calculate the value halfway between them, resulting in a new median of .
Key points:
- Explain that the dataset shifts from an odd number of scores to an even number of scores
- Identify and as the two middle scores in the new ordered set
- Demonstrate comprehension that the median is the value halfway between these two middle scores
Rubric: The response must explain: 1) That adding the score of makes the number of scores even. 2) That an even dataset requires using the two middle scores. 3) That the halfway value between the middle scores of and is calculated, yielding .
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Research Methods in Psychology - 4th American Edition @ KPU
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