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Related Concept Videos

Standard Deviation01:10

Standard Deviation

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The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
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Mean Absolute Deviation01:13

Mean Absolute Deviation

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The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to...
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Variation: Normal Distribution, Range, and Standard Deviation02:32

Variation: Normal Distribution, Range, and Standard Deviation

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In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
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The Wave Nature of Light02:12

The Wave Nature of Light

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The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms and was able to demonstrate that white light consists of the individual colors of the rainbow combined together. Newton explained his optics findings in terms of a "corpuscular" view of light, in which light was composed of streams of extremely tiny particles traveling at high speeds according to Newton's laws of motion.
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Standard Deviation of Calculated Results01:14

Standard Deviation of Calculated Results

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Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency.
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
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Calculating Standard Deviation01:08

Calculating Standard Deviation

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The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. Further, the standard deviation is always a positive value or zero.
The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high...
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Related Experiment Video

Updated: Feb 15, 2026

Investigating the Relationship between Sea Surface Chlorophyll and Major Features of the South China Sea with Satellite Information
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Rogue waves and large deviations in deep sea.

Giovanni Dematteis1,2, Tobias Grafke1,3, Eric Vanden-Eijnden4

  • 1Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.

Proceedings of the National Academy of Sciences of the United States of America
|January 18, 2018
PubMed
Summary
This summary is machine-generated.

Rogue waves in the deep sea can be predicted by identifying specific wave patterns. This method uses the modified nonlinear Schrödinger equation and large deviations theory for early detection of these extreme events.

Keywords:
JONSWAP spectrumLaplace methodMonte Carlointermittencyperegrine soliton

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Area of Science:

  • Oceanography
  • Applied Mathematics
  • Physics

Background:

  • Rogue waves are unpredictable and dangerous phenomena in the deep sea.
  • Understanding their formation is crucial for maritime safety and offshore engineering.
  • Existing models often struggle to accurately predict the probability of extreme wave events.

Purpose of the Study:

  • To develop a method for reliably estimating the probability distribution of sea surface elevation, particularly extreme values.
  • To identify precursors and enable early detection of rogue waves.
  • To provide a transferable approach for systems with random initial conditions.

Main Methods:

  • Utilizing the modified nonlinear Schrödinger (MNLS) equation in one spatial dimension.
  • Employing normally distributed random initial conditions with a spectrum approximating realistic sea states.
  • Combining Monte Carlo sampling with large deviations theory to solve an optimization problem for precursor identification.

Main Results:

  • Demonstrated reliable estimation of sea surface elevation probability distributions, including extreme tails.
  • Identified specific, regular wave patterns as precursors to rogue waves.
  • Showcased that rogue waves occur due to unlikely configurations triggering large surface disturbances.

Conclusions:

  • The proposed method effectively predicts rogue wave occurrences by analyzing wave precursors.
  • The approach offers a computationally efficient way to study extreme events in nonlinear systems.
  • This methodology is adaptable to other complex systems with inherent randomness.