Definition and Properties
The normal distribution (Gaussian distribution) is a continuous probability distribution that forms a symmetric bell-shaped curve centered on the mean. It is fully characterized by two parameters: the mean and standard deviation. The central limit theorem guarantees that the sum of many independent random variables approaches a normal distribution regardless of their original form.
The 68-95-99.7 Rule
In a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. This rule allows quick intuitive judgments about how unusual a value is.
For instance, a value more than two standard deviations above the mean income belongs to only about 2.5% of the population, immediately identifying it as an extreme observation.
When Normal Distribution Does Not Apply
Income distributions are closer to log-normal with a long right tail, so the normal assumption fails. Height and blood pressure approximate normality, but wealth, social media followers, and earthquake magnitudes follow power laws with fundamentally different behavior.
Application in MyRank
Each indicator in MyRank has a different distribution shape. For normally distributed metrics like height, percentile changes are gradual near the center. For skewed distributions like income, differences among top earners get compressed. Being aware of distribution shape helps you understand the true weight of your ranking position.