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normal distribution

C2
UK/ˈnɔːm(ə)l dɪstrɪˈbjuːʃ(ə)n/US/ˈnɔːrməl dɪstrəˈbjuːʃ(ə)n/

Technical (scientific, academic, statistical)

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Definition

Meaning

A specific probability distribution for a continuous random variable, characterized by its symmetrical bell-shaped curve where data clusters around a central mean.

A fundamental statistical concept used to model errors, natural phenomena, and many measurable variables in fields from psychology to finance; also called the Gaussian distribution.

Linguistics

Semantic Notes

The term implies a theoretical, idealised model; real-world data is often described as 'approximately' or 'roughly' normally distributed.

Dialectal Variation

British vs American Usage

Differences

No significant lexical differences; spelling follows standard national conventions (e.g., analyse/analyze).

Connotations

Identical technical connotations in both variants.

Frequency

Equally high frequency in technical contexts in both regions.

Vocabulary

Collocations

strong
assume a normal distributionstandard normal distributionfollow a normal distribution
medium
approximate a normal distributionbell curve of a normal distributionparameters of a normal distribution
weak
data from a normal distributiontest for normal distributionproperty of normal distribution

Grammar

Valency Patterns

The [variable] follows a normal distribution.A normal distribution of [data] is observed.We assume [that] the data is normally distributed.

Vocabulary

Synonyms

Strong

bell curve

Neutral

Gaussian distribution

Weak

symmetrical distribution

Vocabulary

Antonyms

non-normal distributionskewed distributionbimodal distribution

Phrases

Idioms & Phrases

  • “The bell curve”

Usage

Context Usage

Business

Used in risk assessment, quality control (Six Sigma), and financial modeling to predict outcomes.

Academic

Core concept in statistics, psychology (test scores), natural sciences for analyzing experimental data.

Everyday

Rarely used precisely; occasionally referenced in discussions about test scores or population traits.

Technical

Precise mathematical definition with specific properties (68-95-99.7 rule, mean, standard deviation).

Examples

By Part of Speech

verb

British English

  • The data did not normally distribute.
  • We need to check if the residuals are normally distributed.

American English

  • The variable fails to be normally distributed.
  • We tested whether the sample was normally distributed.

adverb

British English

  • The data is approximately normally distributed.
  • The values are not normally distributed.

American English

  • The sample was nearly normally distributed.
  • The data was assumed to be normally distributed.

adjective

British English

  • The normal-distribution assumption is critical.
  • We used normal-distribution theory.

American English

  • The normal distribution model is applied.
  • He calculated the normal distribution parameters.

Examples

By CEFR Level

B1
  • The graph of a normal distribution looks like a bell.
  • Many things in nature follow this pattern.
B2
  • Test scores often follow a normal distribution around the average.
  • If the data is normally distributed, we can use specific statistical tests.
C1
  • The central limit theorem posits that the means of sufficiently large samples will approximate a normal distribution, regardless of the population's distribution.
  • Violations of the normal distribution assumption can invalidate the results of many parametric tests.

Learning

Memory Aids

Mnemonic

Picture a symmetrical bell: most data clusters in the middle (the mean), with tails tapering off evenly on both sides.

Conceptual Metaphor

DATA IS A SHAPED OBJECT (specifically, a smooth, symmetrical bell).

Watch out

Common Pitfalls

Translation Traps (for Russian speakers)

  • Прямой перевод "нормальное распределение" is correct and standard. Avoid confusing with general "regular distribution" (обычное распределение).

Common Mistakes

  • Using 'normal' to imply 'usual' or 'typical' instead of the specific statistical model. Incorrectly assuming all data is normally distributed.

Practice

Quiz

Fill in the gap
For many statistical tests, it is essential that the data a normal distribution.
Multiple Choice

Which property is NOT characteristic of a standard normal distribution?

FAQ

Frequently Asked Questions

No. While many natural phenomena approximate it, many datasets are skewed, multi-modal, or follow other distributions.

Two parameters: the mean (μ), which locates the center, and the standard deviation (σ), which controls the spread.

A standard normal distribution is a special case with a mean of 0 and a standard deviation of 1. Any normal distribution can be transformed into a standard normal distribution.

It is named after the German mathematician Carl Friedrich Gauss, who made significant contributions to its mathematical formulation.