Practice Normalization (Statistics) in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

Converting to a standard reference so you can compare apples to apples.

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.

Example 2

medium
Test scores: Raw score 85/100. Class mean=70, SD=10. Z-score normalize this score and explain what it means relative to classmates.

Example 3

easy
Country A has 1000 hospital beds; Country B has 5000. Country A's population is 500,000; Country B's is 10,000,000. Calculate beds per 1000 people for each country and compare.

Example 4

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