Statistics
Normal Distribution
A continuous probability distribution characterized by a symmetric, bell-shaped curve where the mean, median, and mode are equal.
What is Normal Distribution?
The normal distribution is a specific theoretical distribution mathematically defined by its mean and standard deviation. Roughly 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three.
Why Normal Distribution Matters
Due to the Central Limit Theorem, the normal distribution is the foundation of classical parametric statistics, allowing researchers to make predictable probability estimates about sampling error.
Example
Standardized test scores are intentionally scaled and designed so that the population of test-takers forms a normal distribution.
Common Mistakes
- Believing that real-world data can be perfectly normal, when in fact the normal distribution is just a theoretical mathematical model.
- Assuming that variables like income or reaction times are normally distributed, when they are usually heavily skewed.