Performing Weibull analysis requires that Median Percents be used. A brief explanation of Median Percents followed by a Table of Median Percents is presented below.
What are Median Percents & How Many Are There?
A population is a group of "things" being studied. The "things" might be the size of men's feet, or severity of earthquakes. A data set is a collection of values, measured by a scientist that serves as a "snap shot view" of population. A data-set may have 14 or 5 or any other number of measured data-points.
When a data-set contains 9 data points, there will be a "Median Percent" associated with each data point. When only 5 data points represent a population, there will be exactly 5 Median Percents. The size of a data-set always determines the number of Median Percents.
For 5 data-points, the Median Percents are ALWAYS the following sequence:
If we imagine a forest with exactly 100 trees, and a scientist who measures 5 random samples shown below:
The "most likely" distribution of tree sizes in the forest would be:
Unfortunately, these estimates are "rather sloppy" and almost never accurately characterize the forest. While 13 trees 6 inches and smaller is a better guess than any other, it is likely not accurate.
How are Median Percents Used?
Weibull Analysis uses Median Percents to create a Weibull Plot that estimates the "typical" x size for the population and the "β parameter" that defines population shape. While Median Percents are often poor estimates, the Weibull Plot is a method for "squeezing" good results out of mediocre data. Details of why this works and how to perform the analysis is explained by The Weibull Bible.
Median Percents are routinely used during Weibull Analysis; however, they are a fundamental property of data theory, and are not unique to Weibull.
How Can We Know the Median Percents for a Sample?
Every Weibull Analysis requires knowing the Median Percents for each data point. One way of determining each Median Percent is to use the table below; but, there are other methods.
Tables of Median Percent:
Each column displays Median Percents for a particular number of data-points. For 5 data-points, the table below lists exactly the 1st through 5th Medians shown above. The values in the table below are quite accurate.
Copyright 2022 by Paul F. Watson
Questions? Contact paul-watson@sbcglobal.net