average squared deviation

USAGE SUMMARY

The phrase "average squared deviation" is correct and usable in written English.
It is typically used in statistical contexts to refer to the mean of the squared differences between each data point and the mean of the data set. Example: "To calculate the variance, we first need to find the average squared deviation of the data points from the mean."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

12 human-written examples

The LPSD is therefore the square root of the average squared deviation, conditional on a negative outcome (late arrival).

European Transport Research Review

In addition, Δ r values, defined as the square root of the average squared deviation of the estimated genetic correlations [ 17, 14], were calculated to indicate the differences in the estimates of the genetic correlations between each tested fit and the reference model (PC19) for comparison.

Genetics, Selection, Evolution

a Akaike's information criterion, expressed as deviation from highest value b Maximum Log Likelihood, expressed as deviation from highest value c Derived from the variance due to common factors d Eigenvalues 1 to 12 of LL T, expressed as proportion (in %) of total e Genetic correlations: minimum, maximum and mean values f Square root of the average squared deviation of the genetic correlations.

Genetics, Selection, Evolution

It's just the average squared deviation from the mean.

Yale University

Estimation of the goodness-of-fit of the FRAP data to the various analytical expressions (Figures 4 and 5) was performed by calculating the Average Squared Deviation (ASD) value of each fit.

Plosone

‡Measure of prediction accuracy that is, the average squared deviation between predicted and observed risk; a lower score represents greater accuracy.

British Medical Journal

Human-verified similar examples from authoritative sources

Similar Expressions

48 human-written examples

The mathematical expectation of the average squared deviations from the mean.

Duke University

Variance is the average squared deviations of the mean.

Journal of Industrial Engineering International

These measures are either based on the RMSD (root mean squared deviation: average squared distance between homologous alpha carbons) or the dRMSD (distance RMSD: average square difference of distances between equivalent pairs of amino acids) like the DALI score (Holm and Sander, 1995), APDB (O'Sullivan et al., 2003) or the iRMSD (Armougom et al., 2006a).

Bioinformatics

The protomers in the PhoQW104C-A128C PD structure are highly similar to each other, with an average root mean squared deviation (r.m.s.d). of 0.3.

eLife

Our dataset has an average maximum root mean squared deviation (RMSD) between conformers of 2.51 Å and an average number of conformers per protein of 8.6.

BMC Genomics

Expert writing Tips

Best practice

When reporting "average squared deviation", specify the context (e.g., from the mean) to ensure clarity and avoid ambiguity. This provides readers with a clear understanding of what baseline is used.

Common error

Avoid directly equating "average squared deviation" with standard deviation. While related, standard deviation is the square root of the variance (which is calculated using the average squared deviation).

Linguistic Context

The phrase "average squared deviation" primarily functions as a descriptive statistical term. It quantifies the spread of data points around a central value (typically the mean). According to Ludwig AI, this term correctly represents the mean of squared differences.

Expression frequency: Rare

Frequent in

Science

75%

Academia

25%

News & Media

0%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "average squared deviation" is a statistically significant term that finds frequent application in scientific and academic contexts. As confirmed by Ludwig AI, it's grammatically correct and essential for measuring the spread or dispersion of data around its mean. Related terms include "mean squared deviation" and "variance", the latter of which represents a broader concept built upon the average squared deviation. Usage tips emphasize specifying context and distinguishing it from standard deviation to ensure accuracy and clarity in reporting. Although relatively rare in general usage, its precise meaning makes it indispensable in technical and analytical discussions.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

mean squared deviation

Changes "average" to "mean" for direct synonymy; "mean" emphasizes central tendency calculation.

expected squared deviation

Replaces "average" with "expected", emphasizing predictive statistical outcome.

average of squared differences

Focuses on the differences being squared rather than the resulting deviation.

mean of squared differences

Combines "mean" for central tendency with squared differences for variance focus.

root mean squared deviation (RMSD)

Adds a square root transformation to the mean squared deviation, resulting in a different statistical measure.

squared error loss

Replaces "deviation" with "error loss", emphasizes prediction accuracy.

brier score

Specifically a measure of accuracy, average squared difference between predicted and observed values.

variance

This is a single term that encompasses the average squared deviation from the mean.

mean absolute deviation

Uses absolute values instead of squaring, changing the type of deviation measured.

sum of squared deviations

Focuses on the sum before averaging, changing the emphasis and scale.

FAQs

How does "average squared deviation" relate to variance?

The "average squared deviation" is the core component of variance. Variance is calculated as the average of the squared differences from the mean, essentially quantifying the spread of data points around the average.

What's a simple explanation of "average squared deviation"?

It measures how far a set of numbers are spread out from their average value. Each value's distance from the average is squared, and then these squared distances are averaged.

In what fields is "average squared deviation" most commonly used?

"Average squared deviation" is frequently used in statistics, data analysis, and machine learning to assess the dispersion of data and evaluate the performance of models. You can find it often used in science and academia.

What are some other terms similar to "average squared deviation"?

Other terms that are closely related include "mean squared deviation", "variance", and "mean squared error". All of them share the meaning of quantifying the difference between values.