In 1986, I had a hole-in-one at the Ames (IA) Country Club. As I was carrying on like a kid, my golf partner sat quietly in the golf cart. I thought maybe the ball hadn't actually gone in, but I could see the entire green and the ball wasn't on it. I asked him, “Did you see that?! It went in the cup, didn't it?!”

“Yes,” he replied, “But what were you trying to do?”

It was a good point — but it took some of the fun out of it! And, of course, this golf story ends with a round of drinks at the clubhouse — so my perfection had its price!

This story of perfection is far from my normal golf game. Like most recreational golfers, my greatest struggle with the game is consistency — 3 pars followed by a double bogey (2 shots over par).

Golf can serve as an analogy with pork production. The hole in one in pork production is the full-valued pig — the one that receives no discounts and hits most of the production performance targets.

Like the hole-in-one, the upside of variation shows the potential of swine production, and we may think, “that's what we're trying to do” — but it can be costly.

Clearly the low end of variation — the double bogies — may be eliminated fairly easily by managing the golf round or pork production a bit more carefully.

What is Variation?

To discuss variation, we need a couple of statistical definitions:

A statistical population is a collection of all possible observations in a defined space. For example, a single barn has a population of 1,200 pigs.

A sample is a subset of the population. A pen in a barn or a truckload of pigs hauled out of a barn represents a sample of the pig population in the barn.

The individual pig on the truck is the observation within the sample of the truck, drawn from the population in the barn.

I often think of the “mean” or average as a sample level statistic. It tells us very little about the individual pig. In other words, they all look the same. They look like the mean.

In contrast, I think of variation as an observation-level statistic that gives us at least a fuzzy picture of what individual pigs look like.

Variation is a measure of dispersion of a variable's observations. Statistically, variation can be measured in several different ways:

• Range is the distance from the high value to the low value of all observations.

• Mean deviation is the average difference between repeated samples of two observations.

• Standard deviation is a measure of the “deviation” around a “standard” observation — the standard usually being the mean or average of the observed values.

• Coefficient of variation, or CV, is a unitless measure of variation (quantity without physical units) relative to the mean. It is the standard deviation divided by the mean, usually reported in terms of percentages.

Standard deviation is the most commonly used measure of variation. Its value has the same unit as the variable measured.

A large standard deviation implies a large dispersion of individual observations around the mean (a large range). A small standard deviation implies a small dispersion of individual observations around the mean.

The coefficient of variation is very useful for comparing the size of variation between two different samples.

For example, one finishing barn is closed out with an average weight of 275 lb. and a standard deviation of weights of 25 lb. A second barn closes out with an average weight of 260 lb. and a standard deviation of 24 lb. Which barn has more variable pigs? The 275-lb. finishing barn has a higher standard deviation, but its coefficient of variation (CV), standard deviation divided by mean, is 9.1%, while the CV for the 260-lb. barn is 9.23%.

So the barn with lighter average weights and a lower standard deviation actually has more relative variation than the other barn.

Production Variation

If you view the pigs in a barn, or pull a truckload of pigs from a barn, you will have a snapshot of the variability in that barn.

The truckload is the most common economic snapshot because it's when pigs are weighed and priced. It shows the impact of the production variation on revenue (price sold x quantity).