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Based on the shape of this distribution, explain how the relationship between the mean and median is affected, and explain which measure of central tendency the psychologist should choose to report as the center of the distribution and why.
Case context: A developmental psychologist collects data on the reaction times of children performing a computer-based attention task. When plotting the scores, they observe that while most children respond quickly (creating a high peak on the left), a few children take an exceptionally long time to respond, creating a long tail extending to the right.
Question: Based on the shape of this distribution, explain how the relationship between the mean and median is affected, and explain which measure of central tendency the psychologist should choose to report as the center of the distribution and why.
Sample answer: The presence of a long right tail indicates a skewed distribution. In a skewed distribution, the mean is pulled in the direction of the longer tail (the skew), which will cause the mean to differ from the median (it will be higher/pulled to the right). The psychologist should choose the median to report as the center of the distribution. This is because, in a highly skewed distribution, the mean is pulled so far by extreme scores that it becomes an inaccurate representation of the center, making the median the preferred measure of central tendency.
Key points:
- Identify the distribution as skewed (with a long right tail).
- Explain that skewness pulls the mean in the direction of the longer tail, causing it to differ from the median.
- Select the median as the preferred measure of central tendency.
- Explain that the median is preferred because the mean becomes an inaccurate representation of the center in highly skewed data.
Rubric: The answer must demonstrate comprehension by: 1) identifying that the distribution is skewed and explaining that the mean is pulled toward the longer tail, causing it to differ from the median; 2) concluding that the median is the preferred measure of central tendency; and 3) explaining that the median is chosen because the mean becomes an inaccurate representation due to the extreme scores in the tail.
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Research Methods in Psychology - 4th American Edition @ KPU
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