Measures of Dispersion

Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measureshave allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean.Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standarddeviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of this paper was to model a geometric measure of variation about the population mean which could overcome the weaknesses of the existing measures of variation about the population mean. The study was able to formulate the geometric measure of variation about the population mean that obeyedthe algebraic laws behind absolute numbers, which was capable of further algebraic manipulations as it could be used further to estimate the average variation about the mean for weighted datasets, probability mass functions and probability density functions. Lastly, the measure was not affected by outliers and skewed datasets. This shows that the formulated measure was capable of solving the weaknesses of the existing measures of variation about the mean

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Measures of Dispersion for Interval Data

Advances in Intelligent Systems and Computing - Uncertainty Modelling in Data Science ◽

10.1007/978-3-319-97547-4_13 ◽

2018 ◽

pp. 91-98 ◽

Cited By ~ 1

Author(s):

Przemyslaw Grzegorzewski

Keyword(s):

Interval Data ◽

Measures Of Dispersion

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Measures of Dispersion

Quantitative and Statistical Approaches to Geography ◽

10.1016/b978-0-08-024295-8.50009-5 ◽

1981 ◽

pp. 24-33

Author(s):

JOHN A. MATTHEWS

Keyword(s):

Measures Of Dispersion

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Biostatistics 1: Basic Concepts

Mayo Clinic Preventive Medicine and Public Health Board Review ◽

10.1093/med/9780199743018.003.0001 ◽

2010 ◽

pp. 3-11

Author(s):

M. Hassan Murad ◽

Qian Shi

Keyword(s):

Odds Ratio ◽

Sampling Error ◽

Interval Estimation ◽

Point Estimation ◽

Descriptive Data ◽

Sample Size Calculations ◽

Measures Of Dispersion ◽

Basic Concepts ◽

Error Bias

Chapter 1 reviews basic concepts of biostatistics. Topics include descriptive data, probability and odds, estimation and sampling error, hypothesis testing, and power and sample size calculations. The discussion of descriptive data includes types of data (discrete vs continuous and nominal vs ordinal), central tendency (mean, median, and mode), skewed distributions, and measures of dispersion (range, variance, standard deviation). Probability and odds are broken down into laws of probability, odds, odds ratio, relative risk, and probability distribution. The examination of estimation and sampling error covers concepts such as random error, bias, standard error, point estimation, and interval estimation.

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