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Based on the researcher's calculation method, identify which measure of central tendency she is using and explain why this specific measure is necessary for her planned follow-up analyses (calculating z scores and performing inferential statistics).
Case context: A research psychologist conducts a study on memory retention. After testing 50 participants, she calculates a specific measure of central tendency for the memory scores, which she plans to use later to calculate z scores and perform inferential statistics like a t-test. In her notes, she writes that this measure is the sum of all memory scores divided by 50.
Question: Based on the researcher's calculation method, identify which measure of central tendency she is using and explain why this specific measure is necessary for her planned follow-up analyses (calculating z scores and performing inferential statistics).
Sample answer: The researcher is using the mean (). We know this because she calculated it by summing all the scores and dividing by the total number of scores. She must use the mean for her follow-up analyses because the mean possesses specific mathematical properties that make it exceptionally useful for conducting inferential statistics, and it is a required component for calculating both standard deviations and individual z scores.
Key points:
- The measure of central tendency calculated is the mean.
- The mean is identified by its calculation: dividing the sum of all scores by the total number of scores.
- The mean has statistical properties that make it valuable and necessary for doing inferential statistics.
Rubric: Full credit is awarded if the student correctly identifies the measure as the mean and explains its relationship to inferential statistics and standard deviations as outlined in the provided text.
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Research Methods in Psychology - 4th American Edition @ KPU
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Formula for the Mean
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