Normalization (Statistics) Math Example 1

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

Example 1

easy
City A has 500 crimes with population 100,000. City B has 300 crimes with population 50,000. Which city is safer? Calculate crime rates per 100,000 people.

Solution

  1. 1
    City A crime rate: 500100,000×100,000=500\frac{500}{100,000} \times 100,000 = 500 per 100,000
  2. 2
    City B crime rate: 30050,000×100,000=600\frac{300}{50,000} \times 100,000 = 600 per 100,000
  3. 3
    City B has fewer total crimes (300 < 500) but a HIGHER crime rate (600 > 500 per 100,000)
  4. 4
    Safer city by rate: City A (500 per 100,000) — normalization reveals the true comparison

Answer

City A: 500/100K rate; City B: 600/100K rate. City A is safer despite having more total crimes.
Normalization (rate = count/population) allows fair comparison across groups of different sizes. Raw counts favor larger cities (more of everything); rates per capita give a meaningful comparison. Always normalize when comparing populations of different sizes.

About Normalization (Statistics)

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

Learn more about Normalization (Statistics) →

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