# Count This: A Primer for the Study of Statistics

## A brief explanation of 3D barcodes – what they are and how they are used.

In recent years manufacturing companies have been trying to implement a barcoding system similar to the barcodes for purchases and the retail industry. The only problem is that in manufacturing there are high temperatures, extremely solvents being used, as well as a wealth of chemicals and processes that inhibit the use of a label with bars on it. The manufacturers need to identify individual parts and not just the entire batch as it has been done for years. They wished to improve their inventory and tracking system – and have done so through the use of 3D barcodes.

3D barcodes use the same basic principle as linear and 2D barcodes. An image of some sort is applied to a product and then read by a device to log, categorize, inventory, or track an individual product. As previously stated, the manufacturers need a more permanent solution than a label or sticker. The 3D barcode is engraved or applied to the product itself as a part of the manufacturing process. The bars are not read by variances in reflected light as with linear barcodes but by determining the height of each line. The time it takes the laser to bounce back and be recorded determines the height as a function of distance and time and the character represented by the code can be interpreted.

The 3D barcodes are embossed on the product and the scanner recognizes new characters in the string by the lower regions of the code. This works in much the same way as the white lines or spaces in linear barcodes. The gap allows the system to record a new height of a line, and thus a new number or alpha character. The 3D barcodes also make it nearly impossible to alter or obstruct the barcode’s information and results in fewer inventory mistakes and in turn lowers operating costs of a manufacturing process. The code can be part of the manufacturing process or applied after with a press.

A barcode reader for 3D barcodes captures the reflected image after passing a laser over it; the same laser technology used in home digital or office scanners for documents and images. Once the data has been recorded it is digitized and a digital processing unit is employed to interpret the image. Since the system works on height variances the addition of color or paint has no effect on the end result, especially since manufacturers are extremely precise with the application of paint in regards to the thickness of the coat which could, but does not, affect the height of the 3D barcode.

To the lay outsider, statistics can seem as complex and confusing as doing magic. But the truth is that statistics surround us every day. In fact, statistics is just a field of study that focuses on summarizing data, drawing conclusions, and predicting the future based on what’s already known. Statistics can be challenging, but it’s also one of the versatile and useful fields for all kinds of real world applications. Statistics are used in everything from science and sports to architecture and investing. During World War II, month-to-month estimates of German tank production provided by Allied statisticians were much more accurate – and much, much lower – than the same estimates provided by intelligence professionals. So, in a way, statisticians can even be spies (though it doesn’t come up all that often!) Few other fields have quite as many applications as statistics, allowing statisticians to combine their professional interests with most any personal one.

Statisticians use mathematics to model and understand problems. To do this, they need to employ probability. Probability is simply a numerical measure of the likelihood of a given outcome in any situation. Probability is expressed as a number between 0 and 1. A probability of 0 means the given outcome will never occur; 1 means that it is certain to occur. This elegant concept is the basis of an amazing array of statistical theories dealing with how probability should be interpreted, and what kind of inferences and conclusions can be reached based on a mathematical model. It also gives rise to a whole variety of different subfields and considerations – something for everyone. For example, descriptive statistics are used to summarize data clearly. Inferential statistics are used to support some statement about the population that the statistics represent. Inferential statistics might be used to generalize, based on a sample group, what customers will think about a new brand of soda (or even about its packaging, commercials, and so on.)

Everybody uses statistics. Statistics are there to help set up household budgets and make day-to-day purchasing decisions. Statistics are there whenever anyone plays a friendly game of cards, helping everyone make informed decisions about whether to stay or fold. (In fact, some of the best poker players have revealed they use probability calculations in every hand.) Weather forecasts are built around complex weather forecasts based on statistical models, and stores use statistics based on those forecasts to decide which products to ship to stores and when – no kidding! Statisticians may seem mysterious, but they have a wide variety of rewarding job options. Medical research relies on thorough and effective statistical analysis, as do the government surveys that determine so much about public services and the market research that leads to new products. Anyone with a knack for numbers and an interest in solving puzzles that make a real difference in the “real world” should consider a career as a statistician. For the right kind of person, it can be a lot of fun – and it doesn’t hurt that statisticians tend to be very well paid!

What Is Statistics?: An overview from the University of Melbourne Statistical Consulting Centre that also includes some of the fun and interesting problems that statisticians have encountered.

Careers in Statistics: Great information on career options from the American Statistical Association.

Careers Involving Probability and Statistics: A listing of potential career fields in statistics with a collection of high-quality links to learn more. Provided by the University of Texas at Austin.

An Introduction to Probability: Basic information on one of the important tools that makes statistics possible.

Descriptive Statistics: Understanding and working with descriptive statistics, broken down by operation.

Inferential Statistics: Basic intro with definitions and practice exercises.

Ask Dr. Math Archives: College Statistics: An archive of dozens of questions related to college-level statistics explained by “Dr. Math.”

Statistics: An open and free full course in Statistics with all materials, provided by Carnegie Mellon University as part of the Opening Learning Initiative. Great for self-paced learning and a painless introduction to statistics!

The World-Wide Web Virtual Library: Statistics: A huge index of universities offering degrees in statistics, web-based educational resources on statistics, statistical associations and research groups, and much more.

Cast Your Vote!: An interesting interactive exhibit on the use of statistics in political polling.