mean squared deviation

USAGE SUMMARY

The phrase "mean squared deviation" is correct and usable in written English.
It is typically used in statistics to refer to a measure of the average of the squares of the deviations from the mean. Example: "To assess the accuracy of our predictions, we calculated the mean squared deviation of the forecasted values."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

50 human-written examples

The so-obtained geometries were filtered by an algorithm explicitly considering topological symmetry with a root mean squared deviation cut-off of 0.5 Å (ref. 65).

Nature

Overall, the two prokaryotic TRICs are very similar, with a root mean squared deviation (r.m.s.d). of 1.39 Å when 188 Cα atoms are superimposed.

Nature

Solutions typically involve minimizing the mean squared deviation between the experimental data and the data predicted from a theoretical model of the structure.

Nature

The new correlation equation and other existing ones are fitted to the data optimizing the root mean squared deviation.

Fluid Phase Equilibria

According to the model accuracy predictor MetaMQAP22, the predicted global root mean squared deviation of the modelled CMTr21 423 catalytic domain with respect to the (currently unknown) structure is ~2.3 Å, which indicates good overall quality of the model.

Nature

The folded structures have root mean squared deviation of 2.0 Å with respect to the NMR structures considering all heavy atoms.

Biophysical Chemistry

Human-verified similar examples from authoritative sources

Similar Expressions

10 human-written examples

The K345A subunit of the heterodimer is in the loop-closed conformation; its Cα carbon atoms closely match those of the corresponding subunit of wild-type enolase (root-mean-squared deviation of 0.23 Å).

Journal of Molecular Biology

As shown in [6], the linear objective function reflects the mean-squared deviation of from, that is, the model error in the TF domain.

EURASIP Journal on Advances in Signal Processing

Furthermore, the MBTD1 can also be well superimposed with L3MBTL2 with a root-mean-squared deviation of 0.697 Å.

Plosone

Superposition of the three MBT repeats of L3MBTL1 with those of MBTD1 and L3MBTL2 shows a good structural alignment of Cα positions with a root-mean-squared deviation (RMSD) of 2.345 Å and 2.168 Å, respectively.

Plosone

These models were checked for acceptable Cα root-mean-squared deviation (rmsd) using three different programs that perform pairwise structure alignment and provide a global rmsd.

Biochemistry

Expert writing Tips

Best practice

When reporting "mean squared deviation", specify the context or model to which it applies. For example, state "the mean squared deviation of the predicted values from the observed values" to provide clarity.

Common error

Avoid using "mean squared deviation" interchangeably with "standard deviation". The former measures the average of squared differences from the mean, while the latter measures the spread of data around the mean. Choose the metric that best fits your analytical needs.

Linguistic Context

The phrase "mean squared deviation" functions as a statistical term used to quantify the average of the squared differences between observed values and their mean. As Ludwig AI states, this phrase is correct and usable in written English, typically appearing in scientific and technical contexts.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

The term "mean squared deviation" is a statistical measure indicating the average of the squared differences between data points and their mean. As indicated by Ludwig AI, the phrase is grammatically correct and commonly used in scientific contexts. Related terms include "mean squared error" and "root mean square deviation" (RMSD). It's essential to distinguish "mean squared deviation" from standard deviation and to specify the context when reporting its value for clarity. Use it to assess model accuracy, data dispersion, and to make comparisons.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

average squared difference

Replaces "deviation" with "difference" offering a slightly more direct phrasing while retaining the core concept of quantifying the average of squared differences.

mean of squared errors

Substitutes "deviation" with "errors", framing the concept in terms of error measurement, which is common in predictive modeling and regression analysis.

average of squared residuals

Uses "residuals" instead of "deviation", specifically highlighting the differences between observed and predicted values in a model.

root mean square deviation

Refers to the square root of the mean squared deviation, providing a value in the original units of the data, which can be more interpretable.

average squared variation

Emphasizes the variability being quantified, swapping "deviation" for "variation" to focus on the spread of data points.

quadratic mean deviation

Replaces "squared" with "quadratic", which is a mathematically equivalent term that may be preferred in some contexts.

mean squared error

Replaces "deviation" with "error" and is commonly used for evaluating the performance of forecasting models.

expected squared distance

Frames the measure in terms of distances, useful in geometric or spatial statistics contexts where distances from a central point are being considered.

second moment about the mean

Uses a more theoretical statistical term referring to the second central moment, which is mathematically equivalent to the mean squared deviation.

average of the squares of differences from the mean

Expands the phrase to fully describe the calculation being performed, providing clarity at the expense of conciseness.

FAQs

How is "mean squared deviation" calculated?

The "mean squared deviation" is calculated by finding the average of the squared differences between each data point and the mean. This involves subtracting the mean from each data point, squaring the result, summing all the squared differences, and then dividing by the number of data points.

What does a high "mean squared deviation" indicate?

A high "mean squared deviation" indicates that the data points are widely spread out from the mean, suggesting high variability or large errors in a predictive model. Conversely, a low value indicates that the data points are clustered closely around the mean.

What are some alternatives to "mean squared deviation"?

Alternatives to "mean squared deviation" include "mean squared error", "root mean square deviation" (RMSD), and variance. The choice depends on the specific context and the desired properties of the metric.

How does "mean squared deviation" differ from "mean absolute deviation"?

"Mean squared deviation" squares the differences from the mean before averaging, giving more weight to larger deviations. "Mean absolute deviation", on the other hand, takes the absolute value of the deviations before averaging, treating all deviations equally. MSD is more sensitive to outliers.