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Geometric Mean01:15

Geometric Mean

3.4K
The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
3.4K
Harmonic Mean01:09

Harmonic Mean

3.1K
The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...
3.1K
Weighted Mean00:57

Weighted Mean

5.2K
While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
5.2K
Trimmed Mean01:10

Trimmed Mean

2.9K
While measuring the mean of a data set, care needs to be taken when associating the mean to its central tendency. The same goes for the arithmetic mean, the geometric mean, or the harmonic mean. This is because the presence of a single outlier data value can significantly affect the mean. That is, the mean is sensitive to fluctuations in the data set.
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the...
2.9K
Design Example: Aggregate Gradation01:24

Design Example: Aggregate Gradation

120
The right type and quality of aggregates are crucial for concrete as they significantly influence its properties, mix proportions, and cost-effectiveness. If different sources are available for sand, the commonly used fine aggregate in concrete, the selection of sand is primarily based on its gradation.
The grading, or particle-size distribution, of sand is determined using sieve analysis, with standard sizes ranging from 150 μm to 10 mm (ASTM No. 100 sieve to 3⁄8 in. sieve). Sand is...
120
Color Vision01:24

Color Vision

613
Color perception begins in the retina, the light-sensitive layer at the back of the eye. Two main theories explain how colors are seen: the trichromatic theory and the opponent-process theory. The trichromatic theory, proposed by Thomas Young in 1802 and extended by Hermann von Helmholtz in 1852, suggests that color vision is based on three types of cone receptors in the retina. These cones are sensitive to different but overlapping ranges of wavelengths corresponding to red, blue, and green.
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Related Experiment Video

Updated: Jul 19, 2025

Visualizing Visual Adaptation
04:43

Visualizing Visual Adaptation

Published on: April 24, 2017

9.0K

Weighted Geometric Mean (WGM) method: A new chromatic adaptation model.

Che Shen1, Mark D Fairchild1

  • 1Munsell Color Science Laboratory, Rochester Institute of Technology, Rochester, New York, United States of America.

Plos One
|August 14, 2023
PubMed
Summary

This study introduces the Weighted Geometric Mean (WGM) model for chromatic adaptation, improving color perception stability under changing light. The WGM model accurately predicts sensory and cognitive adaptation, offering a significant advancement in color vision research.

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Area of Science:

  • Vision Science
  • Computational Neuroscience
  • Color Physics

Background:

  • Human color perception relies on chromatic adaptation to maintain stable color constancy under varying illumination.
  • Chromatic adaptation encompasses sensory (automatic visual system adjustments) and cognitive (knowledge-based) processes.
  • The geometric mean is hypothesized as a key mathematical principle in peripheral sensory adaptation.

Purpose of the Study:

  • To propose and validate the Weighted Geometric Mean (WGM) model for chromatic adaptation.
  • To assess the WGM model's ability to predict incomplete adaptation along the Planckian or Daylight locus.
  • To compare the WGM model's performance against existing models like CAT16 and vK20.

Main Methods:

  • Development of the Weighted Geometric Mean (WGM) chromatic adaptation model.
  • Testing the WGM model using various corresponding color datasets.
  • Comparative analysis against the CAT16 and vK20 chromatic adaptation models.

Main Results:

  • The WGM model demonstrated significant improvements over CAT16 and vK20.
  • The WGM model accurately predicts the degree of both sensory and cognitive adaptation.
  • The model's predictions are physiologically plausible, aligning with human visual system capabilities.

Conclusions:

  • The WGM model offers a more accurate and physiologically plausible approach to chromatic adaptation.
  • This model advances our understanding of how the human visual system achieves stable color perception.
  • The WGM model provides a valuable tool for research in color vision and visual perception.