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Based on the visual pattern in the histogram, diagnose the shape of the sleep duration distribution. Specifically, explain how the number of peaks and the symmetry of the tails characterize this distribution's shape.
Case context: A developmental psychologist measures the sleep durations of a sample of infants and plots these scores on a histogram. The resulting histogram shows two separate, prominent peaks. In addition, the tails of the distribution fall off in an uneven manner, with the right tail extending much further than the left tail.
Question: Based on the visual pattern in the histogram, diagnose the shape of the sleep duration distribution. Specifically, explain how the number of peaks and the symmetry of the tails characterize this distribution's shape.
Sample answer: The distribution's shape is characterized as bimodal because the histogram contains two distinct peaks. Furthermore, the shape is skewed because the tails fall off unsymmetrically, with the right tail trailing out further than the left.
Key points:
- Diagnose the shape as bimodal because there are two distinct peaks.
- Explain that the shape is skewed (non-symmetrical) because the tails fall off unevenly.
- Use the visual features of the histogram (peaks and tails) to characterize the distribution shape.
Rubric: The response must correctly diagnose the distribution as bimodal due to the two distinct peaks, and describe it as skewed (or non-symmetrical) because the tails fall off unevenly (with one tail trailing further).
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Research Methods in Psychology - 4th American Edition @ KPU
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Symmetrical Distribution
Unimodal Distribution
Bimodal Distribution
Skewed Distribution
Impact of Distribution Shape on Central Tendency
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