Relative Measures of Dispersion: Types And Definitions, According To Six Sigma
Six Sigma is a methodology determined by or dependent on the collection or analysis of data. As a result, Six Sigma experts who have completed the Lean Six Sigma program or some other Lean Six Sigma Green Belt training are aware that their teams are presented with a wide variety of data sources in various units of measurement. Metrics of the variance of a set of values, independent of the system of measurement, are referred to as relative measures of dispersion. That means that the dispersion of two sets of data with different measurements may be easily compared using relative dispersion measures. This information is particularly important during the DMAIC method’ Measure and Analyze stages.
The 4 Measures Of Dispersion
Dispersion can be measured in 4 different ways: coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, and coefficient of variation. All of the relative measures of dispersion have the word coefficients in them. For this article, we will focus on the first 3: coefficients of range, coefficient of quartile deviation, and coefficient of variation.
1.- Coefficient Of Range
This relative measure of dispersion is dependent on the value of range. The ‘Range Coefficient of Dispersion’ is an example of one of the relative measures of dispersion. The coefficient of range is determined by dividing the greatest value minus the lowest value by the highest value, adding the lowest value.
Let’s look at two different sets of facts. Set A includes 7 students’ Geometry marks out of the possible 25 points, whereas set B has the same amount of students’ Math scores out of a possible 100 points. We’ll have to figure out the spectrum of grades in each discipline. The absolute range in Geometry would be 11, whereas the absolute range for Math is 26. All of that is founded on absolute dispersion measurements rather than relative measures of dispersion, however, the fact is that the 2 subjects cannot be directly compared since their bases are not all the same. When we transform these 2 numbers into coefficients of range, then we can observe that Geometry has a higher coefficient of range over Mathematics. As a result, Geometry has more dispersion or variety than Mathematics. Students’ Mathematics grades are more consistent than their Geometry grades. This is discovered through the use of relative dispersion metrics.
2.- Coefficient of Quartile Deviation
In order to learn how to calculate the coefficient of quartile deviation, let’s take a look at this example:
In order to learn how to calculate the coefficient of quartile deviation, let’s use the same example regarding the geometry and math marks to show the distribution of data in terms of quartiles using relative measures of dispersion. Let’s estimate the coefficient of quartile deviation for both math and geometry through the quartile deviation formula, Q3 – Q1 / Q3 + Q1, and discover that the coefficient of quartile deviation seems to be equal for both of them. In the case of both Math and Geometry, the score is 0.5. As a result, the implication is that participants’ grades or marks for both disciplines suggest similar median efficiency.
Neither of the topics had better or worse average score uniformity than the others. Keep in mind the basic rule concerning relative measurements of dispersion in this situation. Whenever the coefficient of quartile deviation gets smaller, it suggests a high level of consistency or a basic rule concerning relative measurements of dispersion.
Only when the coefficient of quartile deviation is low, it suggests strong uniformity, or a modest variance of the central fifty percent of elements, or strong uniformity towards a median result. On the other hand, if the coefficient of quartile deviation is large, it suggests there is a lot of variance in the central fifty percent of the elements, or there is less consistency in the median result. That would be the 2nd relative measure of dispersion.
3.- Coefficient of Variation
It’s time to talk about the final relative measure of dispersion we will be discussing in this blog. The “Coefficient of Variation” is the sort of relative measure of dispersion which correlates to standard anomaly. It is generally represented in terms of percentage and it is one of the most often utilized relative measures of dispersion. Because relative measures of dispersion exist independently from the units where the data is represented, they may be contrasted among groups of different measurement units.
Assumptions We Can Base On Coefficient Of Variance
Let’s discuss the process and method that can be used to draw an inference. The coefficient of variation can be used to evaluate and examine the variability of multiple groups or sets of information. The group that possesses the larger coefficient of variation suggests that perhaps it is more changeable, less steady, less uniform, less constant, or less equal. The smaller the coefficient of variation, the less changeable, steady, regular, reliable, or homogenous the group becomes. A coefficient of variation is calculated using the following formula: sample standard deviation / sample mean x 100.
Let’s try and make a simple example for this information that will start with two companies, let’s call them Company 1 and Company 2. Company 1 and Company 2 have hired 476 & 524 employees, respectively. Company 1 and Company 2 workers get a median weekly income of 34.5 USD and 28.5 USD, correspondingly. For Company 1 and Company 2, the standard deviation in individual wages was 5 USD and 4.5 USD, accordingly.
The questions that we should be able to answer now would be “Which company spends a bigger amount for their average weekly salaries?” and “Which company has a more significant variability when it comes to paying each singular wage?”.
First Question: Which company spends a bigger amount on their average weekly salaries?
First, let’s determine which of the two companies offers a higher weekly salary. We know the first one employs 476 people, and they have a median weekly income of 34.5 USD, with a standard deviation of 5 USD. As a result, the overall sum of average weekly salaries made by Company 1 would be 34.5 USD x 476, bringing it to a grand total of 16,422 USD. The second company employs 524 people, with a median weekly income of 28.5 USD and a standard deviation of 4.5 USD. As a result, the sum of Company 2’s weekly wages would be 28.5 USD x 524, giving us a total of 14,934 USD. With this information, we can now very clearly see that Company 1 offers a higher weekly pay than Company 2.
Second Question: Which company has a more significant variability when it comes to paying each singular wage?
The second question wonders which of the two companies has a bigger variability in paying each individual wage. To understand and answer this, we’ll need to figure out the coefficient of variation that relates to each company. A coefficient of variation is calculated using the following formula: a sample standard deviation / sample mean x 100. As a result, Company 1’s and Company 2’s coefficients of variation are 14.49 & 15.79, correspondingly. Company 1 has a smaller coefficient of variation over Company 2, hence this is the result. Company 1 also pays a much higher weekly average salary than Company 2. Company 2’s coefficient of variation is greater than Company 1’s. As a result, there is a lot of variation in the distribution of individual salaries. Company 2 offers a lower percentage of average salaries per week than Company 1.
Inferences Or Deductions You Can Make From This Data
Due to internal anomalies, corporate rules, or other factors, it is projected that a small group of employees in Company 2 takes a bigger part of the pay. There’s a good likelihood that not all employees at Company 2 earn the median salary. That might not be the situation with Company 1, though. And that was the very last one of the relative measures of dispersion.
We hope this quick example demonstrates the way relative measures of dispersion, such as the coefficient of variation, could be utilized to draw inferences regarding information and data, even when this one was measured in multiple units. Because Six Sigma teams may be presented with multiple data sets with various units of measure, relative measures of dispersion can be very important. Relative measures of dispersion, similar to absolute measures of dispersion, can be useful for examining the spread of information in a database.