Normalization (Statistics) Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A student scored 75 in Math (ฮผ=65,ฯƒ=8\mu=65, \sigma=8) and 80 in English (ฮผ=78,ฯƒ=3\mu=78, \sigma=3). In which subject did they perform better relative to their class?

Solution

  1. 1
    Math z-score: z=75โˆ’658=108=1.25z = \frac{75-65}{8} = \frac{10}{8} = 1.25 standard deviations above mean
  2. 2
    English z-score: z=80โˆ’783=23โ‰ˆ0.67z = \frac{80-78}{3} = \frac{2}{3} \approx 0.67 standard deviations above mean
  3. 3
    Math z-score (1.25) > English z-score (0.67)
  4. 4
    The student performed better relative to their class in Math despite the lower raw score

Answer

Math z=1.25 > English z=0.67. The student performed better relatively in Math.
Z-scores enable fair comparison across different distributions. A raw score of 75 in Math (hard class) is relatively better than 80 in English (easy class) because it is more standard deviations above its respective mean.

About Normalization (Statistics)

Normalization rescales data to a standard range or distribution โ€” such as [0,1][0,1] or zero mean and unit variance โ€” to make different variables comparable.

Learn more about Normalization (Statistics) โ†’

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