mean square: meaning, definition, pronunciation and examples

C1/C2
UK/ˌmiːn ˈskweə/US/ˌmin ˈskwɛr/

Formal, Technical, Academic

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Quick answer

What does “mean square” mean?

A statistical measure: the average of the squares of a set of numbers or values.

Audio

Pronunciation

Definition

Meaning and Definition

A statistical measure: the average of the squares of a set of numbers or values.

Primarily used in mathematics, statistics, physics, and engineering to quantify variance, error, or the average squared deviation from a central point (like the mean or zero). The term is most commonly encountered in the phrase 'root mean square' (RMS), which is the square root of the mean square and represents a kind of average magnitude.

Dialectal Variation

British vs American Usage

Differences

No significant lexical or syntactic differences. Pronunciation of 'mean' may follow regional vowel patterns.

Connotations

Purely technical and mathematical in both variants.

Frequency

Equally frequent in technical/academic contexts in both regions. Virtually non-existent in everyday conversation.

Grammar

How to Use “mean square” in a Sentence

The mean square of [set of values/errors]to calculate/find the mean squarethe mean square is defined as...mean square error (MSE) between X and Y

Vocabulary

Collocations

strong
root mean squaremean square errormean square deviationcalculate the mean square
medium
mean square valuemean square ofresidual mean squareexpected mean square
weak
overall mean squaremean square approximationmean square estimate

Examples

Examples of “mean square” in a Sentence

adjective

British English

  • The mean-square deviation was calculated for the dataset.
  • We need the mean-square error metric for the model validation.

American English

  • The mean-square error was calculated for the dataset.
  • They reported the mean-square convergence rate.

Usage

Meaning in Context

Business

Rare. Might appear in advanced analytics, econometrics, or quality control reports discussing forecast errors.

Academic

Very common in statistics, mathematics, physics, engineering, and data science papers and textbooks.

Everyday

Extremely rare. Unlikely to be used outside of educational or highly technical discussions.

Technical

Core terminology. Essential in signal processing (RMS voltage), statistical modelling (MSE), and experimental science.

Vocabulary

Synonyms of “mean square”

Neutral

average of squaresquadratic mean (when referring to RMS context)

Weak

second moment (around the mean, specific statistical context)

Watch out

Common Mistakes When Using “mean square”

  • Using 'mean square' as an adjective (e.g., 'a mean square value' is correct, but 'the result was mean square' is not).
  • Confusing 'mean' in this context with other meanings (verb or adjective).
  • Omitting 'root' when intending to refer to the more commonly used 'root mean square' (RMS).

FAQ

Frequently Asked Questions

No. The mean square of deviations from the mean is the 'variance'. The standard deviation is the square root of the variance (i.e., the root mean square deviation).

Almost never. It is a specialised term confined to technical, scientific, and mathematical contexts.

RMS stands for 'Root Mean Square'. It is the square root of the mean square and is used to express an effective average magnitude, common in electrical engineering (e.g., RMS voltage) and physics.

Squared values make all deviations positive (eliminating cancellation of positive and negative differences), and it gives more weight to larger deviations, which is often desirable in error and variance analysis.

A statistical measure: the average of the squares of a set of numbers or values.

Mean square is usually formal, technical, academic in register.

Mean square: in British English it is pronounced /ˌmiːn ˈskweə/, and in American English it is pronounced /ˌmin ˈskwɛr/. Tap the audio buttons above to hear it.

Learning

Memory Aids

Mnemonic

Think of a number 'squaring up' (multiplying by itself), and then several such squared numbers having a 'mean' (average) meeting. It's the **average of the squared troops**.

Conceptual Metaphor

MEASURE OF SPREAD IS AREA. Squaring deviations turns them into 'areas', and averaging them gives a typical 'area' of deviation from the center.

Practice

Quiz

Fill in the gap
To assess the accuracy of the forecast, the analyst calculated the error of the predictions.
Multiple Choice

In the phrase 'mean square', what part of speech is 'mean'?