Monday, December 29, 2008

Do you always believe other people's claim?

We often have to make decisions based on what other people state or claim. However, how do you know if their statement or claim is a solid and valid argument? For example, we all enjoy going out for dinner with family and friends. When you pick up and look at the restaurant's menu, you notice there is a significant automatic charge for service that will be included in your bill. You question this charge with the owner of the restaurant, who tells you the charge is due to the trend in which large parties often pay less in tips than small parties. Would you take as a fact what the owner claimed?

Mathematics is a useful tool to prove or disprove someone's claim. The excerpts clipped to this post came from an interesting article from Plus Magazine web site (i.e. Issue 49), which explains how Statistics is used to make sense of all the information we receive from different sources. I encourage you to read the article and become aware how mathematics can help you make informed decisions.
clipped from plus.maths.org
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We live in a world full of information and it's a statistician's job to
make sense of it. This article explores ways of analysing data and shows how
they can be applied to anything from investigating diners' tipping behaviour to
understanding climate change and genetics.

Have you recently sat down in a lovely restaurant, picked up the menu, and read
"12.5% discretionary service charge will be added to your bill"? In the UK this
is now a common occurrence. In the USA the extra service charge is often made
dependent on the size of your party: if you're more than six people, the charge
will be added automatically. So what is the connection between party size and
service charge?
One reason for this fairly recent change in procedures is that restaurant owners
and workers collect data on their diners, and it has been discovered that larger
dining parties tend to tip less.
The model says that the tip rate decreases by a little under 1% for each
additional diner in the party.
 blog it

Saturday, December 13, 2008

Almost Fooled on Black Friday!




People take the opportunity to do most of their Christmas shopping the day after Thanksgiving Day, which the media and retailers call "Black Friday, since almost everything on sale have considerable discounts. People arrive way before the stores are open, waiting in line for hours to be the first ones buying the best or most popular items at bargain prices and before it sold out. My wife was one of those early shoppers, leaving at 4 a.m. to the mall.

During Black Friday, people should be very careful not being tricked when purchasing items they may think are at bargain prices. The shopping hype or frenzy of such day could easily distract people for using their critical thinking skills or skepticism when something looks too good to be true. This is exactly what happened with my wife when she tried to buy a nice golf shirt as my Christmas gift. The regular price of the golf shirt was $32 but with a 25% discount, which my wife thought to be good deal even though she did not know the exact amount she was going to pay for the golf shirt.

Like many people, my wife had always questioned the reasons for learning mathematics other than the basics, even though she did fairly well in math courses during her schooling years and college. She was one of those students who did not see any practical reasons for learning advance math topics, such as Algebra, Geometry, Statistics, etc. since she was not going to be a scientist, engineer, or any career that involves mathematics. My wife was one of those students who believed that Algebra made simple problems too complicated. In summary, she was not fully aware of the usefulness of learning mathematics for her daily life activities.

However, it was the experience she gained in the mathematics courses that helped her develop the ability to make sense of numbers. And it was this ability that helped her decide not buying my Christmas gift when the cashier notified it was $30 for the purchase. Probably, many people would have paid the $30 for the golf shirt due to their excitment of being part of big event such as Black Friday, in which the belief is that all purchases are the best bargains. Fortunately, my wife did not get caught in the hype of Black Friday and she questioned the purchasing amount for the golf shirt. The cashier explained the purchase amount was a good bargain even after the discount and sales tax were applied to the purchase.

For a few seconds, my wife hesitated to follow her common sense or number sense since after all, she wanted to give me a gift. However, she told the cashier to cancel the purchase since she was convinced the purchase amount was too high for an item that was a 25% off and a sales tax of 7%. In the way back home, my wife was regretting her decision for not buying my gift. When she got home, she immediately asked me if her decision was correct or not since she did not remember how to calculate the discount of 25% and the sales tax of 7%. I showed her the computations: 25% of $32 is $8, so the sale price should have been $24. The sales tax of $24 is $1.68 (7% of 24), so the purchase amount should have been $25.68. My wife felt relief about her decision! My wife's common sense about numbers was something she developed from taking math courses. A great benefit indeed for learning mathematics!

Wednesday, December 3, 2008

Aha! Cops need math too!




In the episode "Falling" of season 19 of Law & Order, detective Lupo said "Who needs math?, I told my teachers. I'm gonna be a cop." Detective Lupo was studying financial reports to find out a possible motive to solve a murder case. He was having difficulties understanding the mathematics involved in the financial reports and he was regreting the fact that he did not pay careful attention in math classes during his schooling years.


Why I find interesting this scene of Law & Order? Well, this scene demonstrates the typical attitude many students show when learning mathematics. Many students quickly become desinterested learning mathematics if they cannot find an immediate practical use or real-life application for what they are learning. Unfortunately, not every math concept or skill has a practical or real-life application. In many instances, there will be math concepts and skills that are only necessary to grasp more complex or advance math concepts.


There are also those students who often assume there are certain careers (e.g. law enforcement) that do not require mathematical knowledge to perform and excel. However, students who can develop their mathematical skills will also be developing their ability to be critical thinkers and problem solvers. To my knowledge, there are always problems or issues to solve in every career or job, and employers are always looking for those who can solve these problems and issues. Let's not forget that life is also full of challenges that we need to overcome, and those with the critical thinking and problem solving skills are usually the ones who struggle the least overcoming the challenges. They work smarter not harder!


We should avoid minimizing the critical role that mathematics play in our lives solely based on if we can apply it in real-life or not. It is not always possible to forsee the ramifications and uses of the math knowledge we acquire. Today, it may seem useless to learn about a particular math concept or skill, but tomorrow, that same concept or skill could be the difference for becoming successful or not in whatever endeavors we pursue. Therefore, we should view learning mathematics as an important exercise to become better critical thinkers and problem solvers. Otherwise, we will probably regret (the same way as detective Lupo did in the Law & Order episode) for our poor decisions to minimize the role mathematics play in our lives.