Comparative Statistics Math Example 2

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Example 2

medium
Three products have customer satisfaction scores. Product A: mean=4.2, SD=0.5 (n=50). Product B: mean=3.8, SD=1.2 (n=50). Explain which product is preferable and why SD matters.

Solution

  1. 1
    Center: Product A has higher average satisfaction (4.2 > 3.8)
  2. 2
    Spread: Product A has much lower SD (0.5 vs 1.2) — more consistent ratings
  3. 3
    Product A interpretation: most customers rate it similarly around 4.2 (consistent quality)
  4. 4
    Product B interpretation: wide SD means some customers rate it 5 (excellent) while others rate it 1 (terrible) — unpredictable quality
  5. 5
    Preference: Product A — higher center AND more consistent (lower SD)

Answer

Product A: higher mean (4.2) and more consistent (SD=0.5). Product B is inconsistent (SD=1.2) despite some high ratings.
Comparing products or groups requires both center and spread. High mean + high SD means occasionally excellent but sometimes terrible. For quality-sensitive decisions, low variability is often as important as high average performance.

About Comparative Statistics

Comparative statistics involves using statistical measures to compare two or more groups, data sets, or distributions.

Learn more about Comparative Statistics →

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