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Estimation of the Physical Quantities01:05

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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Probability Histograms01:17

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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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Related Experiment Video

Updated: Oct 9, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Real-World Data Difficulty Estimation with the Use of Entropy.

Przemysław Juszczuk1, Jan Kozak2, Grzegorz Dziczkowski2

  • 1Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland.

Entropy (Basel, Switzerland)
|December 24, 2021
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Summary

This study uses entropy measure to identify crucial data features for better decision-making in big data environments. Selecting top data attributes improves classification accuracy, tackling information overload challenges.

Keywords:
classificationdecision tableentropy measurepreprocessingreal-world data

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Area of Science:

  • Data Science
  • Information Theory
  • Machine Learning

Background:

  • The Internet of Things and big data generate overwhelming information, challenging traditional data analysis methods.
  • Existing techniques struggle to efficiently extract non-redundant information, hindering effective decision-making.
  • Selecting optimal solutions from complex datasets remains a significant challenge for practitioners.

Purpose of the Study:

  • To investigate the utility of entropy measure as an indicator of data complexity and difficulty.
  • To develop a method for capturing non-redundant, non-correlated core information from diverse real-world datasets.
  • To enhance classification performance by leveraging entropy-based feature selection.

Main Methods:

  • Data preprocessing applied to diverse real-world datasets (markets, sports, fake news).
  • Entropy measure utilized to quantify data difficulty and identify core information.
  • Classification algorithms applied to assess solution quality before and after entropy-based feature selection.
  • Comparison of classification results using the best 25% of entropy-selected attributes versus initial preprocessing.

Main Results:

  • Entropy measure effectively indicates data difficulty and identifies key information.
  • Feature selection based on entropy significantly improves the quality of classification outcomes.
  • The proposed entropy-based approach successfully extracts non-redundant information from complex datasets.

Conclusions:

  • Entropy measure is a valuable tool for managing big data complexity and improving information extraction.
  • Entropy-based feature selection offers a robust method for enhancing machine learning model performance.
  • This approach provides a more efficient way to derive satisfactory solutions from large, complex datasets.