Net Weight 3.0 Pounds

The other day I was picking up some onions in my local grocery store. There was the usual bin of the usual three-pound bags in their usual place in the back of the produce department. I grabbed one, absently put it in my cart, and marched off looking for the next item on my list.

But then, I had a fit of curiosity and decided to weigh this bag of onions. No idea why. I guess I was just curious to see if it really weighed three pounds. So, I went over to one of the several digital scales in the produce section, put the bag of onions on it, and read... 2.99 pounds.

Huh, not bad. Certainly close enough for government work. So I grabbed several other "three pound bags" of onions and weighed them. Just out of curiosity of course. The heaviest one I could find weighed 3.14 pounds. And if you're wondering: that's the one I bought.

So, readers, a question: Why in the world would there be an extra 0.14 pounds of free onions in a three pound bag?

I'll confess: My first thought was "Big Food is trying to make us all fat by deliberately overfeeding us onions!"

But hold on a minute. Wasn't I just fitting an existing conspiracy-based narrative onto a new set of facts? Could there perhaps be... some other reason?

As it turns out, there actually is another reason why a "three pound bag" of onions could weigh anything from 2.99 to 3.14 pounds. It's the real reason. And, oddly enough, I actually took a course in business school on this very topic in all kinds of (fascinating?) detail.

Whenever you sell something in volume--whether it's bottles of soda, jugs of olive oil, or bags of produce--you'll have some degree of randomness in quantities across your output. For example, let's say you have a large machine that simultaneously fills hundreds of 20-ounce plastic bottles with soda. Even if this machine is extremely accurate, there will still likely be some smallish variance above or below 20 ounces in many of the bottles, simply due to sheer randomness. And we can measure this variance and its effects using statistics.

Let's assume our soda machine's standard deviation (this is one measure of variance across a sample) is small, just a sixteenth of an ounce. Further, you can assume that about 99.7% of your output will be within three standard deviations of your mean. There's lots of math in here that I'm skipping over (much of which I confess I barely remember how to do any more), but essentially, you can be highly confident in our example that almost all the soda bottles from this machine will contain between 19.8125 ounces and 20.1875 ounces, which is plus or minus three standard deviations. Not bad.

But what if you want to be extra extra sure you sure you don't give any customer meaningfully less than 20 ounces? In this case, you can tweak your mean "fill quantity" slightly, to say 20.22 ounces. Doing this practically guarantees* that every bottle will have at least 20 ounces of soda. Even the most extreme-extreme outliers you'd likely ever see from this factory will still contain something like 19.97 ounces of soda. And of course, 19.97 ounces is close enough to 20 ounces for you to sell it legally as "20 ounces" just like a 2.99 pound bag of onions can be legally sold as "three pounds."

* [For the stats geeks out there: in our hypothetical factory, assuming a normal distribution, a mean fill of 20.22 ounces, and a standard deviation of 0.0625 ounces, a bottle of soda with less than 19.97 ounces would therefore be a five sigma event, meaning it might occur once every 1.7 million bottles.]

Okay. That's soda. We're talking onions, a product from nature that comes in random, unpredictable sizes. So, unless your onion packaging company wants to spend all day finding perfect groupings of varying-sized onions until every bag weighs three pounds with a tiny standard deviation, we're going to have to tolerate larger variances than we saw with our hypothetical soda machine.

Put in this context then, a range of say 2.99 pounds to 3.14 pounds (a mere 5% variance) is perfectly reasonable and explainable by the vagaries of random onion sizes and the onion packager-processor's best efforts at getting very close to 3.00 pounds into each bag.

And now I find myself pathologically weighing onions every time I buy them.

Readers, the next time you're buying three pound bags of onions or five pound bags of potatoes, head over to the produce scales and weigh them. What weights did you find?


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