**Re: MSA Manual 4th Edition, Page 100 - What is wrong in the graph?**

I don't have the manual, so I don't fully understand your question. I can explain what "bimodal" means - see if this helps that part of your question.

If you have a bunch of data, there are 3 different ways to look at an "average" - mean, median, and mode.

Mean is the arithmetic mean - you add the values, divide by the number of data points you have. This is the most common type of average.

Median is the "middle value" - you line up the data from smallest to largest, and the median is the middle value. If you have an even number of data points, take the two middle values, add together, and divide by two (note - you're taking the mean of the two middle values, right?). Median is commonly used for instances where you want to know the "average value", but the data contains extreme high or low values which would significantly impact the mean. Example - housing prices. There are a few multi-million dollar homes. If included in the calculation, they have a significant impact. Median gives you a better idea of what happens to the market, in general.

Mode is the most common value. You make a bar graph, and the mode is the highest point. Often you get something that looks sort of like a bell curve, with one high point. If you put the numbers in your data onto balls, mixed them up and drew one, the mode would be the most likely one to pick (you have more of them in the ball box than the other numbers.)

Sometimes your data is "bimodal" - if you make a graph, it has 2 modes. It looks like two mountains close to each other - each with a peak (mode). This usually suggests you are not looking at one population of data, but TWO mixed together.

I once had an upset customer showing me data which told him that we had a real problem - his yields were either good, or trash. I looked at the graph and data. The graph looked like a textbook example of a bimodal distribution. Looking at the data in more detail, I saw that many lots were in both humps of the graph - that lot appeared to be yielding low and high. It told me that there was some other cause for the two humps. Further study of the data revealed that the customer had two manufacturing lines - one yielded well, the other poorly. The real difference in the humps was not our product, but his manufacturing line. I worked through this with the customer very diplomatically, and he left knowing our products were fine, and he appreciated the help I provided.

Mike