## Wednesday, February 17, 2010

### Eggzactly what am I buying?

Math is focused on quantity. How much? How large? How heavy? Specific units of measure enable us to define how much we are getting when we buy something. Then we can calculate cost per unit.

We buy fuel in gallons or liters. We buy paper by the ream (500 sheets) or the case. We buy produce in ounces, pounds, kilos or individual items. But when we buy eggs ... well what are we getting?

I suppose a carton of one dozen, large, grade A eggs is the normal unit of purchase. But it gets complicated from there!

The US Department of Agriculture monitors what happens in the poultry business in our country. Some of the standards they've set are voluntary. Egg producers have to pay extra to have the USDA seal on their packages. Other producers can save some money by complying only with state regulations, not Federal guidelines. The USDA has established standards for eggs that include:

• Grade: from AA, A, B then to (industrial use only) cracked or dirty
• Size: from PeeWee, Small, Medium, Large, Extra-Large to Jumbo
• Source: Caged, Free-Range
• Feed: Vegetarian, Organic, Omega-3, etc.
I was most interested in learning about the sizes of eggs. Why? Well because we bought some from an egg ranch last week and the eggs looked enormous. See for yourself:

You can see four grade AA Large eggs from the store at the left side of the carton. The four Egg Ranch Jumbo eggs at the right. Here's another look. The size difference is very apparent:

Now you might be wondering HOW BIG are those JUMBO eggs?

It turns out that the size is not really graded by the USDA regulations. It's the weight of a dozen eggs combined that determine how they are "sized". The scale looks like this:

Jumbo = 30 oz         (30/12=2.5)
Ex-Large = 27 oz     (27/12=2.25)
Large = 24 oz          (24/12=2.0)
Medium = 21 oz       (21/12=1.75)
Small = 18 oz           (18/12=1.5)
PeeWee = 15 oz       (15/12=1.25)

(I did an average in the parentheses, but it's not required that every egg match that size)

I read that there is a high likelihood of getting double-yolks in Jumbo eggs. In fact, the BBC news had an article talking about probabilities, saying it was millions to one against getting multiple double-yolk eggs in a dozen. That was just doing the simple mathematics.

The Daily Mail reports that the chances of finding a double-yolked egg is one tenth of 1%. So imagine how Fiona Exon felt when she started to make scrambled eggs for Sunday's breakfast. The first one had two yolks. The second had two yolks. And as the Mail says, she called her husband when the third also turned out to have a double yolk. When all six in the box were the same, she admits to being astonished. Experts say the chances of it happening are one trillion to one.

A reader went one step further and called a local egg ranch. The manager said, Oh yes, when we grade the eggs we put all the double-yolk ones into cartons for ourselves. Once in awhile we have too many and we sell those packages.

There's no probability in sorting eggs - they don't come out of the chickens and drop into boxes by random chance - every egg is graded, sized and sorted. The speculations of the amateur mathematicians were completely  incorrect because they knew nothing about the egg business.