# Normal distribution

A normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability density function. It is the most prominent probability distribution in used statistics.

Normal distributions are a family of distributions with the same general symmetric bell-shaped curve, with more values concentrated in the middle than in the tails. Two parameters describe a normal distribution, the mean, and standard deviation. The mean is the central location (the peak), and the standard deviation is the dispersion (the spread). Skewness and excess kurtosis are zero for a normal distribution.

The normal distribution is the basis of much statistical theory. Statistical tests and estimators based on the normal distribution are often more powerful than their non-parametric equivalents. When the distribution assumption can be met they are preferred, as the increased power lets you use a smaller sample size to detect the same difference.

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Continuous distributions
- Univariate descriptive statistics
- Calculating univariate descriptive statistics
- Univariate plot
- Creating a univariate plot
- Frequency distribution
- Normality
- Normal distribution
- Normal probability (Q-Q) plot
- Creating a normal probability plot
- Normality hypothesis test
- Tests for normality
- Testing the normality of a distribution
- Central limit theorem and the normality assumption
- Inferences about distribution parameters
- Discrete distributions
- Study design
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023