Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

Measure of Dispersion or Variability

The measure of location or averages or central tendency is not sufficient to describe the characteristics of a distribution, because two or more distributions may have averages which are exactly alike, even though the distributions are dissimilar in other aspects, and on the other hand, measure of central tendency represents the typical value of the data set. To give a sensible description of data, a numerical quantity called measure of dispersion/ variability or scatter that describe the spread of the values in a set of data have two types of measures of dispersion or variability:

  1. Absolute Measures
  2. Relative Measures

A measure of central tendency together with a measure of dispersion gives adequate description of data as compared to use of measure of location only, because the averages or measures of central tendency only describes the balancing point of the data set, it does not provide any information about the degree to which the data tend to spread or scatter about the average value. So Measure of dispersion is an indication of the characteristic of the central tendency measure. The smaller the variability of a given set, the more the values of the measure of averages will be representative of the data set.

  1. Absolute Measures
    Absolute measures defined in such a way that they have units such as meters, grams etc. same as those of the original measurements. Absolute measures cannot be used to compare the variation/spread of two or more sets of data.
    Most Common absolute measures of variability are:

    • Range
    • Semi-Interquartile Range or Quartile Deviation
    • Mean Deviation
    • Variance
    • Standard Deviation
  2. Relative Measures
    The relative measures have no units as these are ratios, coefficients, or percentages. Relative measures are independent of units of measurements and are useful for comparing data of different natures.

    • Coefficient of Variation
    • Coefficient of Mean Deviation
    • Coefficient of Quartile Deviation
    • Coefficient of Standard Deviation

Different terms are used for measure of dispersion or variability such as variability, spread, scatter, measure of uncertainty,deviation etc.

References:
http://www2.le.ac.uk/offices/careers/ld/resources/numeracy/variability

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Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics. Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan. Like Applied Statistics and Mathematics and Statistical Computing. Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis etc.

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