by the sample mean

USAGE SUMMARY

The phrase "by the sample mean" is correct and usable in written English.
It can be used in statistical contexts when referring to calculations or conclusions drawn from the average value of a sample. Example: "The results were adjusted by the sample mean to ensure accuracy in the analysis."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

20 human-written examples

parameterized by the sample mean μ i and sample covariance Σ i.

EURASIP Journal on Image and Video Processing

In practical situations, the population mean μ and standard deviation σ, if unknown, can be estimated by the sample mean and the sample standard deviation.

Journal of the Brazilian Computer Society

In the following, the lower bound (28) will be computed from the simulations by substituting Pb and var[F x)] by the sample mean and variance resulting from {F(x i )}, respectively.

EURASIP Journal on Wireless Communications and Networking

All velocities are normalised by the sample mean speed v 0 μ at γ ˙ = 0.

eLife

Missing values on these variables were replaced by the sample mean for men and women, respectively.

BMC Public Health

The coefficient of variation (CV) was calculated by dividing the sample s.d. by the sample mean.

British Journal of Cancer

Human-verified similar examples from authoritative sources

Similar Expressions

39 human-written examples

All samples were centered by subtracting the sample mean and scaled by dividing by the sample standard deviation.

Plosone

Results reported for the reporter algorithm (RA) in the Results section are raw z-scores per metabolite, normalized by subtracting the sample mean and dividing by the sample standard deviation.

Bioinformatics

Since the image features could have a variable dynamic range over all studies, each of the 286 features was normalized by subtracting the sample mean and dividing by the sample standard deviation before applying subsequent processing.

BioMed Research International

The corresponding sample mean and standard deviation were determined and these scores were normalized to z scores ss' ss and S bps by subtracting the sample mean and dividing by the standard deviation.

BMC Genomics

Internally derived sex specific SD scores were calculated for birth weight and BMI at age 14, by subtracting the sample mean from the individual mean and then by dividing by the sample standard deviation.

Plosone

Expert writing Tips

Best practice

When reporting statistical analyses, clearly state that adjustments or normalizations were performed "by the sample mean" to ensure transparency and reproducibility.

Common error

Avoid assuming the "sample mean" is always representative of the population mean. Always consider the sample size and potential biases before making generalizations.

Linguistic Context

The phrase "by the sample mean" functions primarily as an adverbial phrase, modifying a verb or adjective to specify how an action is performed or a state is achieved. As Ludwig AI confirms, it is grammatically correct and usable. Examples from Ludwig show its use in contexts like normalization and adjustment of data.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

The phrase "by the sample mean" is a grammatically correct and technically specific term primarily used in scientific and statistical contexts. It denotes that a calculation, adjustment, or normalization is performed using the average value calculated from a sample. As Ludwig AI confirms, it is considered reliable and usable. While not exceptionally common, its presence in academic and research-oriented sources underscores its importance in precise scientific communication. Related phrases such as "using the sample average" or "based on the sample mean" can provide alternative ways to convey the same meaning, depending on the specific nuance desired.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

using the sample average

Emphasizes the act of utilizing the average value from the sample for calculations or adjustments.

based on the sample mean

Highlights that certain conclusions or actions are grounded in the calculated average of the sample data.

calculated from the sample mean

Focuses on the origin of a value or result, specifying that it was derived from the sample mean.

determined by the sample mean

Suggests that the average value of the sample directly influences or sets a specific outcome or determination.

normalized by the sample mean

Implies a standardization process where values are adjusted relative to the sample's average.

adjusted by the sample mean

Indicates a modification to data or results, using the sample mean as a reference point.

scaled by the sample mean

Signifies a transformation of values where the sample mean serves as a scaling factor.

proportional to the sample mean

Highlights a direct relationship where one quantity varies in relation to the average value of the sample.

estimated using the sample mean

Focuses on the inference of a parameter or value, where the sample mean is a key input in the estimation process.

with respect to the sample mean

Suggests a consideration or analysis that is framed in the context of the average value of the sample.

FAQs

How is "by the sample mean" used in statistical analysis?

In statistical analysis, "by the sample mean" often refers to adjusting or normalizing data using the average value calculated from a sample. For example, data might be centered "by subtracting the sample mean" to remove bias.

What does it mean to normalize a dataset "by the sample mean"?

Normalizing "by the sample mean" involves adjusting data points relative to the average value of the sample. This can involve subtracting the sample mean from each data point or dividing by it to create a dimensionless ratio. It is done to compare different dataset or to make the data easier to analyze

When should I use "by the sample mean" instead of "by the population mean"?

Use "by the sample mean" when you only have access to a sample of the entire population and need to make inferences or adjustments based on that sample's characteristics. If the entire population is known, use "by the population mean".

Are there alternatives to saying "adjusted by the sample mean"?

Yes, you could say "adjusted using the sample average", "normalized by the sample mean", or "centered around the sample mean" depending on the specific context and the type of adjustment being made.