Let's Make a (Car) Deal!
“Let’s Make a Deal” was the name of a TV game show that began in 1963 and lasted for over two decades. It was best known for what came to be called the “Monty Hall” problem that captured the counter-intuitive nature of probability.
What interests me here is showing how to calculate in your head the approximate monthly payment you will have to make on a car, given its price and the interest rate applied in financing it. (The assumption is that you are not paying full price at the time of buying. Most of us don’t have that much cash, true for maybe 99% of the population!)
Percentages Level the Playing Field
In a recent article in the NY Times on how mistakes made by doctors lead to harm for patients, this sentence conveyed the statistics: “Of the 651 hospital patients studied, 309 had errors on their medication lists, and over half those errors had the potential to cause harm”
By itself, the sentence seems to convey the gravity of the situation. Yet the average reader is unable to gain a foothold with the numbers. What if more (or less) patients were studied, what would the number of mistakes be then? And how would you compare different studies over time to gauge whether the situation was improving or not?
Raising the Significance Bar
To prove a hypothesis in statistics, we often use what is called the p-value method. Without resorting to technical jargon, it identifies whether something has happened by chance or by design. If it has happened by chance, we say that the Null Hypothesis (something that happens by chance) is true (technically, we say that we fail to reject the Null, same as in courts where the verdict is either “guilty or not guilty” and not “guilty or innocent.”) If, on the other hand, the event cannot be explained on the basis of chance, we conclude that it happened by design. That marks the event as being ‘statistically significant.’
Feynman and Elementary Algebra
When you compare Feynman’s treatment of the subject with that in regular textbooks, you will realize why so many students fear algebra, are bored by it and why some of them drop out when they come in contact with algebra for the first time in their lives. The Feynmans of the world are rare but that shouldn’t keep us lesser mortals – particularly math teachers - from taking cues from Feynman about how to make the subject come alive through connections, associations and serendipity. May 11, 2018, marks the centennial birth anniversary of the iconic Nobel-laureate physicist Richard Feynman. Born on May 11, 1918, in Far Rockaway, NY, and regarded as a child prodigy, Feynman taught ‘freshman physics’ at California Institute of Technology from 1961 to 1963. The course was published as the three-volume The Feynman Lectures on Physicsin 1964. It brought him world-wide fame not only as a physicist’s physicist but also as a peerless teacher. (The Lectures are available for free at feynmanlectures.caltech.edu)
How many years are there in a billion seconds?
In other words, 1,000,000,000 seconds = how many years? You divide the seconds by 60 to get the equivalent number of minutes, then divide the result by 60 to get the hours, divide again by 24 to get the days, and finally divide the days by 365 (we don’t the precision of leap years in this estimate) to get the required number of years.
1 billion seconds is approximately equal to 31.69 years.
Statistics Draws Meaning From Data
Statistics surround us, whether graphing data, calculating probability, finding a relationship between variables, or testing a claim. In the age of the Internet, it is important to learn to think critically about data and information.
Here are 6 points to consider when trying to master basics of statistics:
Experience the Power of Normal
In everyday usage, ‘normal’ means usual. Today, Wednesday, May 9, 2018, here in San Jose, California, it is a sunny day, 72 degrees Fahrenheit, with a light wind blowing, that entices me outdoors. It’s what I expect this day to be in San Jose at this time of the year, a typical day.
In statistics, on the other hand, ‘normal’ refers to a special type of distribution (also known as bell-shaped or Gaussian distribution) that describes how variables we are familiar with from everyday life such as height, weight, temperature, and salary vary by proportion or probability. The shape of the bell (symmetric or almost symmetric) suggests that most of the values are concentrated near the center while few values are at the edges, that is, near the two tails, relatively far from the center.
Playing with Percentages
Suppose that your portfolio dropped in value by 30% last year but gained in value by 30% this year. Has your original portfolio value gained, lost or remained the same? If gained or lost, by what percent? If the loss and gain are reversed, that is, if your portfolio gained in value by 30% last year but lost in value by 30% this year, would the result be the same or different?
The Power of Being Imprecise
Ray Dalio started his investment company Bridgewater Associates at 26 and built it into one of the wealthiest private companies in the following 42 years. Time identified him as one of the 100 most influential people in the world, while Forbes ranked him among the 100 wealthiest. CIO magazine called him "the Steve Jobs of investing." His latest book, Principles, describes in detail how he learned his business acumen from his mistakes and from his unwavering belief in accountability, transparency, humility, truth, long-term view and fact-driven decision making.
You want to buy a high-end camera listed at $500 that is being sold at a 10% discount . The sales tax is 9.75%. Which will be a better price for you as a consumer: Applying the discount first and then the sales tax, or applying the sales tax first and then the discount?
Everyday, we run into quantitative challenges that defeat or intimidate us. Yet most of these problems require nothing more than basic arithmetic. Young and adult Americans alike often make basic math and statistical mistakes or choose bad numerical or financial options that cost them dearly, cut into a company's profit and decreases productivity.
Hasan Z Rahim
Hasan Z. Rahim is a professor of mathematics and statistics at San Jose City College,
located in the heart of Silicon Valley, California.