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Measures of Central Tendency

Measures of Central Tendency

The "center" of a data set is also a way of describing location. The two most widely used measures of the "center" of the data are the mean (average) and the median. The words "mean" and "average" are often used interchangeably. The substitution of one word for the other is common practice. The technical term is "arithmetic mean" and "average" is technically a center location. However, in practice among non-statisticians, "average" is commonly accepted for "arithmetic mean."

Review and Preview

Review and Preview

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.
Percentiles are a type of fractile that partition data into...

Skewness

Skewness

The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency are...

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...

One-Way ANOVA: Unequal Sample Sizes

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:

Friedman Two-way Analysis of Variance by Ranks

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...

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Heterogeneity Mapping of Protein Expression in Tumors using Quantitative Immunofluorescence

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Measuring richness and evenness.

¹School of Environmental & Evolutionary Biology, University of St Andrews, St Andrews, Fife, UK KY16 9TS.

Trends in Ecology & Evolution

|January 18, 2011

Summary

This book provides comprehensive methods for surveying natural populations, essential for ecological research and biodiversity assessment. It covers statistical techniques and practical applications for field studies.

Area of Science:

Ecology
Environmental Science
Statistical Biology

Background:

Ecological research relies on accurate data from natural populations.
Effective population surveying is crucial for conservation and management.
Existing methodologies may lack comprehensive integration of statistical and practical field approaches.

Purpose of the Study:

To present a unified and detailed guide to surveying natural populations.
To offer robust statistical frameworks for ecological data analysis.
To equip researchers with practical tools for field surveys.

Main Methods:

Detailed statistical methodologies for population estimation.
Field techniques for data collection in diverse ecosystems.

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Last Updated: Jun 5, 2026

Heterogeneity Mapping of Protein Expression in Tumors using Quantitative Immunofluorescence

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Published on: October 25, 2011

Automatic Image Processing to Determine the Community Size Structure of Riverine Macroinvertebrates

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Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data

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Case studies illustrating the application of surveying methods.

Main Results:

Provides a framework for rigorous natural population assessment.
Enhances understanding of ecological sampling design.
Offers solutions for common challenges in biodiversity surveys.

Conclusions:

Effective natural population surveying requires integrated statistical and field expertise.
This work serves as a foundational resource for ecologists and conservationists.
Accurate surveying underpins informed environmental decision-making.