Bell-shaped CurveMeredith and I have been discussing the fiasco with Gluten-Free Cheerios not being really gluten free –some of the time. So today I thought I would give everyone a quick visual tutorial and what the fuss is all about and why we are not happy with General Mills’ response.

First of all, I would draw your attention to the image at the top of this post. Any time you take samples from a large population, the average of the samples will plot as a bell-shaped curve thanks to something called the Central Mean Theorem. Either take my word for it or look it up on Wikipedia.

There are two terms you must understand – mean and standard deviation. Mean is usually called the average although there are really three different terms that can be called average – the mean, mode and median. I’ll let you look up the difference, but today we will use

Mean = Average = Sum of all samples/Number of samples

The standard deviation is simply a measure of how wide the bell-shaped curve is. It is also known that 67% of all samples will be within one standard deviation of the middle of the curve, 95% will be within two standard deviations and 99.73% will be within three standard deviations.

What this all means is that once you have the mean and the standard deviation, you can predict how many samples will fall where on the ranges of values that you are measuring.

Our Problems with General Mills’ Measuring Process

1. The process mean

Accepted practice during product production validation is to

  1. Take samples from the production process
  2. Measure each sample
  3. Calculate the mean of all the samples
  4. Calculate the range of the largest measurement from the smallest measurement
  5. Plot the mean and the range on charts
  6. Repeat steps 1-5 until you have a sufficient number of data points (generally 30 or more – more being better)
  7. Calculate the process mean (the mean of all the sample means taken) and the process standard deviation.

General Mills instead took the samples, ground them up, mixed them together, ground the mix again, then took multiple samples out of the same pot and calculated the mean of all those samples which they say is 10-13 parts per million (ppm) ) – the FDA limit is 20 ppm.

Their process was equivalent to taking 11 homeless people and Bill Gates, putting all their worldly goods into one pot and dividing it equally to say that homeless have enough wealth, on average, to buy mansions to live in. It doesn’t provide a realistic view of the real situation.

2. They don’t provide a measure of the process’ variance

It is known that at least one package had a gluten level of 90 ppm– but General Mills insists on saying that every package meets the FDA limit. Which is true on average. But celiac people don’t eat Cheerios on average – they eat from a box of Cheerios. The question they have to ask is THAT BOX gluten free as defined by the FDA?

Let’s say that General Mills’s stated average (10 ppm) is correct (not likely) and they have a standard deviation of 5 ppm. We can then calculate how many boxes of Gluten-free Cheerios are really gluten-free and how many are not.

Bell-Shaped Curve with FDA Limit for Gluten FreeAs shown in the chart, there could be between 2-5% of the boxes of Gluten-free Cheerios that wouldn’t meet the FDA limit. What does this mean? If a celiac person eats just one box of Gluten-free Cheerios a month, they have a 20 to nearly 50% chance of eating Cheerios that is not gluten free in a year. For my granddaughter, that means that she’ll wake up covered in diarrhea, crying because of stomach pains, growth being slower, weight loss.

Of course the above is hypothetical because General Mills is not disclosing the data that they should to convince those who need gluten free that their Gluten-free Cheerios is really gluten free.

For those who haven’t heard our podcasts on the General Mills Gluten free fiasco, here’s links to the podcasts:

Listen or Download via iTunes here
Listen or Download via Podomatic here

A physicist by trade, author by choice, a born teacher, a retired veteran, and an adamant problem solver, Frank has helped the White House, federal agencies, military offices, historical museums, manufacturers, and over 250 technology startups get stuff done, communicate effectively, and find practical solutions that work for them. In his spare time, he makes sawdust and watches Godzilla movies.