Finding a Parking Space at the Mall Using Math – Part Two

If you have read the previous article on the subject, I imagine you were very upset by the nature of its contents. How we use math to find a parking space at the mall isn’t a typical thing you might hear people discuss at their Christmas parties. However, I think anyone with a modicum of human interest would find this the most curious topic of conversation. The reaction I usually get is, “Wow. How do you do that?” , or “Can you really use math to find a parking spot?”

As I mentioned in the first article, I wasn’t content with having math degrees and then doing nothing with them other than taking advantage of job opportunities. I wanted to know that this newfound power for which I had been studying so frantically to obtain it could actually be traced back to my personal advantage: that I would be able to be an effective problem-solver, not only of those highly technical ones but also of such mundane problems as the case at hand. Thus, I am always investigating, thinking, and looking for ways to solve everyday problems, or use mathematics to help improve or simplify a mundane task. This is exactly how I found a solution to my mall parking problem.

The solution to this question essentially arises from two complementary mathematical disciplines: probability and statistics. In general, one refers to these branches of mathematics as complementary because they are closely related and one needs to study and understand probability theory before one can attempt to tackle statistical theory. These two systems help solve this problem.

Now I’m going to give you the method (with some reasoning – fear not, because I’m not going to get into some tedious mathematical theory) on how to go about finding a parking spot. Try this out and I’m sure you’ll be amazed (just remember to message me about how awesome this is). Well, on to the method. Understand that we are talking about finding a place during peak hours when it is more difficult to get a parking lot – obviously there would be no need for a way under different circumstances. This is especially true during the Christmas season (which, in fact, is at the time of writing this article – how convenient).

Ready to try this out? Let’s go. Next time you go to the mall, choose a parking area that allows you to see at least twenty cars in front of you on either side. The reason for the number twenty will be explained later. Now take three hours (180 minutes) and divide it by the number of cars, which in this example is 180/20 or 9 minutes. Take a look at the clock and watch the time. Within nine minutes of the time you look at the clock—often sooner—one of those twenty or so dots will open. Mathematics pretty much guarantees this. Whenever I test it and especially when I show it to someone, I am always elated at the success of this method. While the others frantically circle around, she just sits there, patiently watching. You choose your region and just wait, knowing that in a few minutes, you will win the prize. How arrogant!

So what guarantees that you will get to one of those sites on time. Here is where we start to use a little bit of statistical theory. There is a well-known theorem in statistics called the central limit theorem. What this theory basically says is that in the long run, many things in life can be predicted by a normal curve. You may remember this as the bell-shaped curve, with the two tails extending outward in either direction. This is the most famous statistical curve. For those of you who are wondering, a statistical curve is a chart on which we can read information. Such a scheme allows us to make educated guesses or predictions about the population, in this case the number of cars parked at the local mall.

The charts tell us like a normal curve where we stand in elevation, let’s say, in relation to the rest of the country. If we are in the 90th percentile with respect to height, then we know that we are taller than 90% of the population. Central boundary theorem tells us that eventually all heights, all weights, and all IQs in a population will eventually smooth to follow the pattern of the normal curve. Now what does “eventually” mean? This means that we need a certain population size of things for this theory to be applicable. A number that works well is 25, but for our current situation, twenty would generally suffice. If you can get 25 or more cars in front of you, the method works best.

Once we have made some basic assumptions about parked cars, statistics can be applied and we can start making predictions about when parking spaces will be available. We cannot predict which one of the twenty cars will leave first but we can predict that one of them will leave within a certain time. This process is similar to that used by a life insurance company when it is able to predict how many people of a certain age will die in the following year, but not which of them will die. To make such predictions, the company relies on so-called mortality tables, and they are based on probability theory and statistical theory. In our particular problem, we assume that in three hours all twenty cars will be turned over and replaced by another twenty. To reach this conclusion, we used some basic assumptions about two parameters of a normal distribution, the mean and the standard deviation. For the purposes of this article, I will not go into detail regarding these parameters; The main goal is to show that this method will work very well and can be tested next time.

To summarize, choose your spot in front of at least twenty cars. Divide 180 minutes by the number of cars – in this case 20 – to get 9 minutes (note: for twenty-five cars, the interval would be 7.2 minutes, or 7 minutes 12 seconds, if you really want to be precise). Once you select your interval, you can check your watch and make sure you have a spot available in 9 minutes at most, or whatever interval you have calculated depending on how many cars you’re in; Because of the nature of the normal curve, a spot often becomes available sooner than the maximum allotted time. Try this and you will be amazed. At least you’ll score points with friends and family because of your intuitive nature.