Relative Dispersion in Statistics
What is dispersion statistics or statistical dispersion?
If there is one integral way to predict the profits to be gained or the losses to be incurred from an investment, it is statistical dispersion. It is a key method to estimate probable volatility on a specific security. Thus, statistical dispersion (also known as spread in a variable, variability, statistical variability, variation, scatter, dispersion statistics and spread) is often defined as probability distribution.
In other words, dispersion statistics tells you how spread out the distribution of a data is. To calculate the exact measurement of a dispersion, key methods such as variance, standard deviation, interquartile range, range, mean difference, median absolute deviation, average absolute deviation (average deviation) and distance standard deviation are used.
Let’s read about these dispersion measure statistics in detail:
'Measure of Dispersion Statistics' – Examples and Properties
The measurement of a dispersion is always zero (real number) if its data is identical and it will increase on diversification. More importantly, the measurement is never negative. Another thing to remember is that a dispersion always has the same unit of measurement as its data. Some key ‘measures of dispersion statistics’ examples include:
1. Standard deviation: It is defined as the distance of a value from the mean. The standard deviation formula is—
Standard Deviation is denoted by sigma (σ). To calculate SD through the aforementioned formula, we must follow some basic steps, which are mentioned below:
a. First, calculate the mean.
b. Subtract all the values from the mean and square the results.
c. Add all the squared results and multiply the total by 1/N (N stands for numbers/values).
d. In the last step, get the square root of the result obtained after Step 3.
2. Interquartile range (IQR): refers to a dispersion statistics measurement wherein the differences between upper and lower quartiles are measured. Its formula is:
It is also called the midspread or middle fifty.
3. Range: It is described as the smallest interval comprising all the data that also gives an indication of dispersion statistics.
4. Mean difference: involves the calculation of the average absolute difference of two independent values obtained from a probability distribution.
5. Median absolute deviation (MAD): involves the calculation of the variability of a univariate sample of a quantitative data. It is also referred to as population parameter.
6. Average Deviation: It is the difference between an element and a given point. The formula for average deviation (absolute deviation or average absolute deviation) is:
7. Distance standard deviation: it is the square root of a distance variance, which is a unique case of two identical variables.
The aforementioned statistical dispersion measures are location-invariant and, obviously, linear in scale. This means that if any random variable X has a dispersion of Sx,linear transformation Y = aX + b for real a and b should have the dispersion Sy = | a | Sx.
On the contrary, there are dimensionless measures of dispersion that have no units. These dimensionless measures include:
a. Coefficient of variation
b. Quartile coefficient of dispersion
c. Relative mean difference
Other key measures of dispersion are:
a. Variance (Location-variance, yet not linear in scale)
b. Variance-to-mean ratio
Relative Dispersion in Statistics
Relative dispersion in statistics is referred to as a coefficient of variation, which is a statistical measurement of the dispersion of data points around the mean in a data series. It is calculated by dividing standard deviation by the mean. Thus, relative dispersion is dimensionless and often represented in percentage. So, the low value of a relative dispersion is indicative of lower standard deviation. For example, the result of a standard deviation of 6 cm for a mean of 4m will be 0.015, which is 1.5%. However, with a mean of 40 cm, the result will be 0.15, which is 15%.
Our experts have successfully answered the following questions on dispersion statistics:
Q What is the difference between absolute dispersion and relative dispersion in statistics?
Q Elaborate on statistical analysis methods for measures of dispersion.
Q What are dispersion statistics and prism deviation?
Q Explain the formula for calculating median
Q Explain the advantages and disadvantages of using standard deviation.
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