Normal distribution

How it is used

Also called the Gaussian distribution or the bell curve. Many tests assume that the data, or the residuals, are 'normally distributed', so analysts check normality with plots or tests such as Shapiro–Wilk. Roughly 68%, 95% and 99.7% of values fall within one, two and three standard deviations of the mean.

Example sentences

1. A Shapiro–Wilk test showed that the data did not follow a normal distribution.

2. Adult height roughly follows a normal distribution within each sex.

Common collocations

• follow a normal distribution
• standard normal distribution
• approximately normal
• bell-shaped curve
• test for normality

Related terms

• distributionThe pattern showing which values a variable takes and how often each one occurs, often pictured as a histogram or a curve.
• z-scoreA value showing how many standard deviations an observation lies above or below the mean, found by subtracting the mean and dividing by the standard deviation.
• central limit theoremThe result that the distribution of sample means gets closer to a normal distribution as the sample size grows, whatever the shape of the population distribution, as long as its variance is finite.
• standard deviationA measure of how spread out values are around the mean; a small value means the data sit close to the mean, a large one means they are widely scattered.
• assumptionA condition that must hold, at least approximately, for a statistical test or model to give valid results, such as normality, equal variances or independent observations.

More terms: Probability Distributions

• skewed
• binomial distribution
• Poisson distribution