Short note on Absolute Value of Dispersion

Dispersion is a statistical term that describes the size of the expected distribution of values for a given variable. It can be measured using a variety of statistics, including range, variance, and standard deviation. Dispersion is a term used in finance and investing to describe the range of possible investment returns. It can also be used to assess the level of risk associated with a specific security or investment portfolio.

The degree of uncertainty, and thus risk, associated with a particular security or investment portfolio is often interpreted as dispersion.

The volatility and risk associated with holding an asset are represented by the dispersion of return on that asset. The riskier or more volatile an asset is, the more variable its return is.

Thousands of potential securities are available to investors, and there are numerous factors to consider when deciding where to invest. The risk profile of the investment is one factor high on their list of considerations. Dispersion is one of many statistical measures used to put things in context.

Absolute dispersion

Absolute dispersion measures the amount of variation in a set of values expressed in units of observations. Any absolute measures of dispersion, for example, give the variation in rainfall in mm when rainfall data is made available in mm for different days. Relative measures of dispersion, on the other hand, are independent of the units used to measure the observations. They are nothing but numbers. They’re used to compare variation between two or more sets of observations with different units of measurement. Six Sigma teams can use both relative and absolute measures of dispersion.

The following are the absolute measures of dispersion

• Range
• Deviation from the median
• Deviation in the mean
• Deviation from the mean

Range

The difference between the largest and smallest absolute measures of dispersion is the simplest of the absolute measures of dispersion.

Quartile Deviation is an absolute measure of dispersion.

What are Quartiles, and how do you use them?

Quartiles are measures that divide data into four equal parts, with an equal number of observations in each.

Deviation in the Quartiles

Quartile deviation is half of the difference between the first and third quartiles, Q1 and Q3, in terms of absolute measures of dispersion. Because quartile deviation is equal to half of the inter-quartile range, it’s also known as the semi-inter quartile range.

Deviation from the mean

The standard deviation is the most important metric for analyzing data variation. It is critical for data analysis and various statistical inferences.

The standard deviation is the positive square root of the variance. Please keep in mind that the standard deviation is based only on the basis of the mean or average.

Dispersion Measurement in Relative Terms

When comparing the distribution of two or more data sets, relative measures of dispersion are used. This metric compares values without the use of units. The following are some examples of common relative dispersion methods:

• Coefficient of Variation
• Coefficient of Variation (CV) is a measure of how much something changes over time.
• Standard Deviation Coefficient
• Quartile Deviation Coefficient
• Mean Deviation Coefficient

Example

Assume you were given the task of comparing dispersion measures for two data sets. Items 97,98,99,100,101,102,103 are in data set A, while items 70,80,90,100,110,120,130 are in data set B. You can probably tell by looking at the data sets that the means and medians are the same (100), which are statistically known as “measures of central tendency.”

When comparing data sets A and B, the range (which indicates how to spread out the entire set of data is) for data set B (60) is much larger (6). In fact, nearly all measures of dispersion for data set B would be ten times higher, which makes sense given the tenfold larger range. Take a look at the standard deviations, for example

for the two sets of data:

2.160246899469287 is the standard deviation for A.

21.602468994692867 is the standard deviation for B.

Data set B has a figure that is exactly ten times that of data set A.

Conclusion

The range of possible investment outcomes based on the historical volatility of returns is referred to as dispersion.

The higher the dispersion, the riskier an investment is, and vice versa. Is the state of becoming dispersed or spread, as measured by alpha and beta, which measure risk-adjusted returns and returns relative to a benchmark index, respectively. The extent to which numerical data is likely to vary around an average value is referred to as statistical dispersion.