Case Study

Explain the conceptual difference between a unimodal distribution and a bimodal distribution in this context, and explain why the student's histogram represents the former.

Case context: A student researcher is examining a histogram of self-esteem scores collected from a sample of undergraduate students. The student notes that the histogram has one prominent peak in the middle of the graph and slopes downward toward both the higher and lower ends. However, the student is confused about why this graph is classified as unimodal rather than bimodal.

Question: Explain the conceptual difference between a unimodal distribution and a bimodal distribution in this context, and explain why the student's histogram represents the former.

Sample answer: A unimodal distribution is defined by having only one distinct peak, where the data is concentrated around a single central value and tails off in both directions. In contrast, a bimodal distribution has two distinct peaks, representing two different high-frequency regions. Because the student's self-esteem histogram displays only one prominent peak in the middle, it is classified as unimodal.

Key points:

  • Unimodal distributions have a single, distinct peak.
  • Bimodal distributions contain two distinct peaks.
  • The self-esteem histogram matches a unimodal distribution due to its single peak.

Rubric: The response must explain that a unimodal distribution has one distinct peak (30%), a bimodal distribution has two distinct peaks (30%), and apply these definitions to show that the self-esteem histogram with one central peak fits the unimodal classification (40%).

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Updated 2026-05-27

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Research Methods in Psychology - 4th American Edition @ KPU

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