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Dispersion

The word "dispersion" literally means "spread" or "scatter". Statistically, dispersion of a distribution reflects how the data is scattered. Dispersion indicates the degree variation of the values of a sample taken from a population.
Measures of Dispersion

The degree of dispersion can be calculated. It is a real non-negative number which is higher when the data is more dispersed and is lower when the data is shrinks towards the center.
Following are the important measures of dispersion:

  • Standard deviation: It is an important measure of dispersion. It measures the variability of the data. It indicates the variation of the data from its central tendency.
  • Interquartile Range: Interquartile range measures a range in which the most of the data appears. It defines the variables that are most close to central tendency.
  • Range: Range is also a measure of dispersion of data. It is defined as the difference between biggest and smallest values in a distribution.
  • Absolute Mean Difference: It is the measure of absolute value of difference of each observation from the mean of the sample.
  • Mean Deviation: Mean deviation indicates the deviation of the values of a data from its average or mean.
  • Median Absolute Deviation: It measures the statistical dispersion of given data by measuring absolute deviation of the variables from their median or the middlemost value.
Indirect Measures of Dispersion
There are other indirect measures of dispersion which do not measure dispersion directly, but are derived from other measures of dispersion.
These are given below:
  • Variance : It is the indirect measure of dispersion, since it is the square of standard deviation which measures the degree dispersion.
  • Variance to Mean Ratio : It is abbreviated as VMR and is expressed as the ratio of variance and mean. i.e. 
  • VMR = $\frac{\sigma^{2}}{\bar{x}}$.
Dimensionless Measures of Dispersion
Other measures of dispersion are also available that are dimensionless which means they have no unit, no matter if their variables have units.
 These are as follows:
  • Coefficient of Variation : It is abbreviated as CV. Coefficient of variation is the ratio of standard deviation and mean, i.e. 
  • CV = $\frac{\sigma}{\bar{x}}$. It is also known as relative standard deviation.
  • Quartile Coefficient of Dispersion : It is expressed as the ratio in the form of first and third quartiles or $Q_{1}$ and $Q_{3}$, i.e.
  • QCD = $\frac{Q_{3}-Q_{1}}{Q_{3}+Q_{1}}$.

 

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