Measures of dispersion are often used in finance as a proxy for risk:
Measures of dispersion are generally used to describe the variability in sample. The three commonly used measures of dispersion are as follows,
- Interquartile range - Difference between the [tex]25^{th}[/tex] and [tex]75^{th}[/tex] percentile (also known as the [tex]1^{st}[/tex] and [tex]3^{rd}[/tex] quartile). The formula is [tex]\bold{\text{Interquartile range = Q3 - Q1}}[/tex]
- Range - Difference between the largest and smallest observation. The formula is [tex]\bold{\text{Range = maximum value - minimum value}}[/tex]
- Standard deviation - SD is the square root of sum of squared deviation from the mean divided by the number of observations. The formula is as follows, [tex]\bold{\sigma=\sqrt{\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}}}[/tex]
Appropriate usage of measures of dispersion:
Median and interquartile range is used for skewed numerical data, ordinal data or mean. When mean is utilized as a measure of central tendency or symmetric numerical data, SD is used.
Usage in finance:
In finance, the Regression analysis technique helps in explaining the dispersion of dependent variable, that is measured by its variance, with the help of one or more independent variables each of which has positive dispersion. This proves to be a proxy for risk.
