What You Need to Know About Absolute Measure of Dispersion in Project Management

There are a few different statistics included in the Lean Six Sigma Green Belt training and Online Six Sigma courses that students should be familiar with. One is The Measures of Central Tendency, which works to locate the center of distribution in a project but does tell us where the points are distributed in relation to the center.

In order to comprehend the distribution of the data, project management professionals must be familiar with both the absolute measures of dispersion, as well as the relative. This frequency distribution can be understood as a simple “dispersion.” This refers to a lack of similarities in shapes, sizes, and amounts of items in a group. This is a smart and effective way to show how data is distributed in relation to the center points of data in a project set.

In this article, we will explore the absolute measure of dispersion and how it can be best utilized by project managers.

Understanding Both Dispersion and Uniformity in a Data Set

Items and observations are not often the same in data sets. There is typically a lack of uniformity and presence of variation amongst the value set. The amount of variation is determined by relative and absolute measures of dispersion. If a data set shows small dispersion, this can signify great uniformity of items, and large dispersion alludes to a lack of uniformity.

Exploring Both Absolute and Relative Measures of Dispersion – What is the Difference?

The two kinds of dispersion we will focus on are:

- The absolute measure of dispersion in a data set
- The relative measure of dispersion in a data set

When referring to absolute measure of dispersion, it is crucial to evaluate the degree of variation in a value set. For instance, when snowfall data is released after winter, it is available for different days in millimeters, while absolute measures of dispersion give a variation of snowfall in mm. Relative measures of dispersion do not have units of measurements of observations, as they are pure numbers. They are used to analyze the difference in variation of two or more data sets. Both of these measures are very useful to project management teams, so understanding them fully is crucial.

Understanding The Absolute Measure of Dispersion

Wondering about the absolute measure definition? The absolute measure of dispersion can be understood as:

- Mean deviation
- Standard deviation
- Quartile deviation
- Range

Range – How Do We Calculate It?

The range is the easiest to understand, so this is where we will start! Range is the amount of change between the smallest and largest values of a data set. The formula can be understood as largest minus smallest value. The formula reads as L minus S, which you can see displayed in the graphic below. The biggest value is 11, and the smallest is 4. So, the range can be calculated by performing a simple math equation of 11 subtracted by 4, which equals 7. The outcome is a great way for project managers to understand how wide the data set is and make appropriate recommendations based on this analysis.

COPIED FROM GRAPHIC

Measures of dispersion and range:

- Range – the difference between the largest and smallest variable.
- The formula for Range is: Largest value – Smallest value (L-S)
- Example: 7,9,6,8, 11, 10, 4 = (11-4) = 7

What Are Quartiles? Understanding Quartile Deviation

Next, we will explore what quartiles are and how they can be used to understand measures of dispersion. Quartiles separate data into four parts, where each section holds an equal amount of data. There are three quartiles. The first one is labeled Q1 and is known as the lower quartile. It holds 25% of items distributed below and 75% of items larger than it. The second quartile is labeled Q2 and is the median of the data. It holds 50% of values below and 50% of values above. The third quartile is Q3 and is known as the upper quartile, holding 75% of the distribution items below and 25% of the items above it. Q1 and Q3 are the two limits within the central 50% of data in the set. The third quartile minus the first quartile is equal to the medium.

Calculating For Quartile Deviation

Quartile deviation equals half the change between the first and third quartiles; it is also called the semi-inter quartile range due to the fact that quartile deviation is equivalent to half of the inter-quartile range. The absolute measures of dispersion can also be called quartile deviation.

How to Calculate the 3 Quartiles in a Data Set

Q1, or the first quartile, is equivalent to the amount of N+1 divided by 4. The third quartile, Q3, is calculated by multiplying Q1 times 3. The formula for the quartile deviation is Q3 minus Q1 divided by 2.

Calculating the second quartile is done the same way in which we solve for the median. The value of Q1 and Q3 can be found by using the formula shown below, where N equals the number of observations in the data set.

Understanding the Calculation Of the Three Quartiles

When calculating the quartile deviation as part of finding absolute measures of dispersion, remember that the absolute measures of dispersion can be calculated with software to make things easier. However, it is always good practice to know the underlying math involved to ensure the values you calculate make sense. This way, you can check the software you and your team use and be sure there were no malfunctions on the technology’s side.

In the image below, you will notice the values are arranged in order. You will first have to solve for the position of Q1 to start. The formula for this is Q1 plus 1 divided by 4. 10 plus 1 divided by 4 will be equal to 2.75, meaning the position of Q1 is equal to the value of 2.75th position.

Here is the formula:

Q1 equals the value at the 2nd position, plus .75 of the difference between the 2nd and 3rd values. The value at the 2mnd and 3rd position is 391 and 407. Our equation will equal 391 plus .75 of the difference between 391 and 407, which equates to 403. So, the Q1 value is 403.

Solving For the position of Q3

Next, we will solve for Q3. First, we will need to multiply the equation for finding Q1 by 3, as the position of Q3 is equal to the value at the 8.25th position. Q3 will equate to the value at the 8th position plus .25 of the difference between the 9th and 8th value. The 8th and 9th value positioning is 777 and 1490. Thus, our equation will be 777 plus .25 of the difference between 1490 and 777. The answer for this problem will be 955.25, which equals Q3.

Next, we will solve for the quartile deviation. The formula is Q3 – Q1 divided by 2. Our Q3 and Q1 equals 955.25 and 403. So, the answer will be 276.125, which is equal to the quartile deviation.

How to Calculate Standard Deviation & What This Value Means

Standard deviation is the positive square root of the mean of the square deviations taken from the mean of the data. It is used heavily in the study of data variation and can be relied on to help analyze data for statistical variations.

The formula can be seen as:

The square root of the sum of square x minus x-var over the bracket of n – 1.

These measures of dispersion are used when understanding how data is aligned relative to the center point. The center of data can tell an analyst a lot about a data set. However, knowing how the spread of data aligns with the total picture can help to complete a total understanding of a data set. Thus, you as a project manager will be able to better understand how to read data sets and can make recommendations based on your findings. This is all part of strengthening your craft and becoming a more trusted individual in the business. Six Sigma teams analyze data in the Measure phase.