There are no insignificant numbers when the grocery bill’s tallied
Why is it that when you ask someone the time, they always tell you the time to the minute? People used to just round things off to the nearest five minutes, or even the quarter hour. Is that minute really significant?
Numbers can be accurate, but not significant. Usually it isn’t very important for me to know the time to the minute. Telling me that it is 7:49 p.m. simply gets me moving. By 7:53 p.m. I have forgotten why I was going that direction to begin with.
There are times,though, when precision is important. An Alley-Oop pass in basketball comes to mind. However, such events seldom are aided by cell phones or computers. Precise numbers are the most necessary when dealing with electronics and machinery. Human endeavors, however, can run on “approximate” times.
Take shopping, for example. Please! I hate shopping. But I like being with my wife, so sometimes I go along anyway. I push the cart, she finds what she needs, and adds up how much she has spent in her head. She is amazingly accurate. That’s because she uses the concept of significant figures. I don’t know if she knows that she knows about significant figures, but she uses them nonetheless.
Back to shopping. If the supermarket bill comes to $27.13, the really important number to take into account is the two. Twenty bucks is a big thing in my world. Actually, the seven is nothing to sneeze at. Seven dollars is enough to buy a, uh, well, actually nothing now, but it used to be. The 13 cents is simply unlucky. Now, I suppose I’d pick it up off the ground if it were lying there. Heck, I’ve been known to pick up an insignificant penny.
So all my wife really has to do is keep track of the significant numbers: 20 and seven in this case. She can handle the insignificant ones by just rounding anything less than 49 cents down and anything greater than 50 cents up. Those pennies are insignificant. Scientists often deal with significant numbers. We just keep track of the ones that matter.
Hmmm, I’m not sure if the grocery store thinks the pennies are insignificant though.
To see what the folks at the grocery store are really thinking, I did a carefully controlled scientific study. I began by casually, and unobtrusively, walking up and down the aisles of a local supermarket (which shall go unnamed). I noted the prices on various goods and even wrote down the insignificant numbers.
I then proceeded to the exciting step of entering a long string of insignificant numbers on to an Excel spreadsheet. This may sound boring, but to scientists and accountants it is a thrilling activity. However, the real reward in science comes at the moment when patterns begin to emerge, the prey is in sight, the chase is nearly over, and your heart begins to pound in your chest.
If prices are randomly distributed, there should be a more-or-less equal number of all insignificant figures. As you might have guessed, without having to go through the scientific method at all, this was not the case. In fact, there were large peaks of insignificant numbers at 99 cents — showing that more items were priced at an insignificant 99 cents than any others.
Wait! There were smaller peaks at 49 cents. There were even smaller peaks, at 39 and 29 cents. Furthermore, nothing was priced at an even amount ending in zero. So it appears that prices are not random. They are designed to approach the next highest price, indicated by a zero, as closely as possible without touching it!
Given this research data, I was thinking that if I averaged the insignificant figures, then multiplied the average of the insignificant figures times the number of items in the cart, before adding the significant figures to that total, we could approximate the bill. My wife thinks that while my numbers may be accurate, they are not very significant. She intends to keep on rounding.
Gary McCallister is professor of biology at Colorado Mesa University.