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Related Concept Videos

How Data are Classified: Numerical Data00:59

How Data are Classified: Numerical Data

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Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data are the result of counting or measuring the attributes of a population. Amount of money, pulse rate, weight, number of people living in a town, and number of students who opt for statistics are examples of quantitative data.
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Numerical Calculations01:24

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In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
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Testing a Claim about Mean: Known Population SD01:11

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A complete procedure of testing the hypothesis about a population mean is explained here.
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Review and Preview01:10

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In statistics, several tools are used to interpret the data. Measures of central tendency represent the characteristics of the data, such as mean, median, and mode. Additionally, measures of variance like standard deviation and range are used to find the spread of data from the mean. Relative standing measures the distance between data locations. Commonly used measures of relative standings are percentile, z score, and quartiles.
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Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
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When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
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Updated: Mar 7, 2026

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
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Numerical abilities in fish: A methodological review.

Christian Agrillo1, Maria Elena Miletto Petrazzini1, Angelo Bisazza1

  • 1Department of General Psychology, University of Padova, Italy.

Behavioural Processes
|February 8, 2017
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Summary
This summary is machine-generated.

Fish possess numerical abilities comparable to other vertebrates. Studies reveal fish can discriminate quantities, similar to mammals and birds, using methods like spontaneous choice tests and learning procedures.

Keywords:
Continuous quantitiesFishNumerical cognitionOperant conditioningShoal choicesTraining procedure

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Area of Science:

  • Comparative cognition
  • Ethology
  • Animal behavior

Background:

  • Numerical competence is crucial for survival and reproduction in various ecological contexts.
  • Mammalian and avian numerical abilities are well-documented.
  • Recent research has begun exploring numerical cognition in fish.

Purpose of the Study:

  • To review and evaluate methods for studying numerical abilities in fish.
  • To compare fish numerical cognition with that of other vertebrate groups.

Main Methods:

  • Spontaneous choice tests: assessing preference for larger/smaller groups in ecologically relevant scenarios.
  • Discrimination learning procedures: training fish to distinguish quantities using abstract stimuli and rewards.
  • Review of existing literature on fish numerical cognition.

Main Results:

  • Two primary methods, spontaneous choice tests and discrimination learning, are systematically applied to fish.
  • Fish exhibit substantial similarities in numerical abilities compared to other vertebrates.
  • Methodological variations exist, but consistent findings emerge across studies.

Conclusions:

  • Fish demonstrate significant numerical discrimination capabilities.
  • The cognitive mechanisms underlying numerical abilities appear conserved across diverse vertebrate taxa.
  • Further research using standardized methods can deepen our understanding of fish numerical cognition.