Comparative Statistics Math Example 4

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Example 4

hard
Men: mean height = 70", SD = 3". Women: mean height = 64", SD = 2.5". A person is 67" tall. Calculate their z-score in each distribution and determine which group they are more extreme in.

Solution

  1. 1
    z-score in men's distribution: z=67−703=−33=−1.0z = \frac{67-70}{3} = \frac{-3}{3} = -1.0
  2. 2
    z-score in women's distribution: z=67−642.5=32.5=1.2z = \frac{67-64}{2.5} = \frac{3}{2.5} = 1.2
  3. 3
    In men: 1 SD below average (shorter than typical man)
  4. 4
    In women: 1.2 SD above average (taller than typical woman)
  5. 5
    More extreme in women's distribution (|1.2| > |1.0|)

Answer

Men z=-1.0; Women z=+1.2. The person is more extreme (unusual) relative to the women's distribution.
Z-scores enable comparison across different distributions. The person is 'more unusual' in women's heights (further from that mean in SD units). This cross-distribution comparison is only possible after standardization.

About Comparative Statistics

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

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