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Related Concept Videos

Weighted Mean00:57

Weighted Mean

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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...
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Arithmetic Mean01:08

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The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the data set, divided by the total number of elements. It is sometimes loosely referred to as the “average.”
When all the values in a data set are not unique, the sum in the numerator can be calculated by multiplying each distinct value by its frequency.
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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.
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Harmonic Mean01:09

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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.
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Geometric Mean01:15

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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.
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Regression Toward the Mean01:52

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Related Experiment Video

Updated: Apr 29, 2026

Investigating the Deployment of Visual Attention Before Accurate and Averaging Saccades via Eye Tracking and Assessment of Visual Sensitivity
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Obligatory averaging in mean size perception.

Jüri Allik1, Mai Toom2, Aire Raidvee3

  • 1Department of Psychology, University of Tartu, Estonia; Estonian Academy of Sciences, Tallinn, Estonia.

Vision Research
|May 27, 2014
PubMed
Summary

Perceiving ensemble characteristics, like mean circle size, bypasses attention limits. This study shows the brain automatically processes average size before individual details are consciously known.

Keywords:
Ensemble characteristicsFocused attentionObligatory averagingPerception of the mean sizePerceptual awareness

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Area of Science:

  • Cognitive Psychology
  • Visual Perception
  • Psychophysics

Background:

  • Focused attention and working memory have limited capacity, typically handling only a few objects.
  • Ensemble perception is a proposed mechanism to overcome these attentional limitations.

Purpose of the Study:

  • To investigate the associative law of summation in ensemble perception.
  • To determine if ensemble size judgments rely on explicit knowledge of individual elements or automatic pooling.

Main Methods:

  • Observers estimated the mean size of four circles against a reference circle.
  • Stimuli were presented briefly, preventing detailed scrutiny of individual circles.
  • Judgments were made with size changes applied to one, two, or all four circles.

Main Results:

  • Observers accurately discriminated mean size differences regardless of how many circles were modified.
  • Judgments of individual circle sizes were less accurate than mean size judgments.
  • Size information was pooled obligatorily before conscious awareness.

Conclusions:

  • Ensemble perception of size is an automatic process, not reliant on explicit individual element analysis.
  • The brain prioritizes processing of summary statistics (mean size) over individual element data.
  • This automatic pooling mechanism aids in overcoming cognitive limitations in attention and working memory.