Posts tagged ‘statistics’
When law professor Richard D. Friedman appeared in front of the Supreme Court, he stated that an issue was “entirely orthogonal” to the discussion. Chief Justice John G. Roberts Jr. stopped him, saying, “I’m sorry. Entirely what?”
“Orthogonal,” Friedman replied, and then explained that it meant unrelated or irrelevant.
Justice Antonin Scalia was so taken by the word that he let out an ooh and suggested that the word be used in the opinion.
In math class, orthogonal means “at a right angle,” but in common English, it means that two things are unrelated. Many mathematical terms have taken a similar path; moreover, there are many terms that had extracurricular meanings long before we ever used them in a math classroom. Average is used to mean “typical.” Odd is used to mean “strange” or “abnormal.” And base is used to mean “foundation.” To name a few.
The stats teacher said that I was average, but he was just being mean.
You know what’s odd to me? Numbers that aren’t divisible by 2.
An exponent’s favorite song is, “All About the Base.”
Even words for quantities can have multiple meanings. Plato used number to mean any quantity more than 2. And forty used to refer to any large quantity, which is why Ali Baba had forty thieves, and why the Bible says that it rained for forty days and forty nights. Nowadays, we use thousands or millions or billions or gazillions to refer to a large, unknown quantity. (That’s just grammatical inflation, I suspect. In a future millennium, we’ll talk of sextillion tourists waiting in line at Disneyland or of googol icicles hanging from the gutters.)
Zevenbergen (2001) provided a list of 36 such terms that have both math and non-math meanings, including:
The alternate meanings can lead to a significant amount of confusion. Ask a mathematician, “What’s your point?” and she may respond, “(2, 4).” Likewise, if you ask a student to determine the volume of a soup can, he may answer, “Uh… quiet?”
It can all be quite perplexing. But don’t be overwhelmed. Sarah Cooper has some suggestions for working mathy terms into business meetings and everyday speech. Like this…
For more suggestions, check out her blog post How to Use Math Words to Sound Smart.
If you really want to sound smart, though, be sure to heed the advice of columnist Dave Barry:
Don’t say: “I think Peruvians are underpaid.”
Say instead: “The average Peruvian’s salary in 1981 dollars adjusted for the revised tax base is $1452.81 per annum, which is $836.07 below the mean gross poverty level.”
NOTE: Always make up exact figures. If an opponent asks you where you got your information, make that up, too.
This reminds me of several stats jokes:
- More than 83% of all statistics are made up on the spot.
- As many as one in four eggs contains salmonella, so you should only make three-egg omelettes, just to be safe.
- Even some failing students are in the top 90% of their class.
- An unprecedented 69.846743% of all statistics reflect an unjustified level of precision.
You can see the original version of “How to Win an Argument” at Dave Barry’s website, or you can check out a more readable version from the Cognitive Science Dept at Rensselaer.
Zevenbergen, R. (2001). Mathematical literacy in the middle years. Literacy Learning: the Middle Years, 9(2), 21-28.
How many copies of Math Jokes 4 Mathy Folks do you think sold last week?
|Make Your Prediction Here (Google Form)|
Why would you want to make a prediction? Well, lots of reasons…
- Like the author (and readers) of this blog, you’re a math geek.
- You swoon at the sight of data.
- You’ve never met a puzzle you didn’t like.
- You want to show the world how awesome you are.
- You’d like to win a signed copy of Math Jokes 4 Mathy Folks, some cool MJ4MF stickers, and a surprise gift, all shipped to you in exclusive MJ4MF packaging!
- All of the above.
If you’re reading this blog, then you surely love being alive in the Age of Big Data. I love it, too, and I devour any data that I can get my hands on.
Amazon feeds my desire by providing two valuable pieces of data about Math Jokes 4 Mathy Folks. First, they provide the sales rank for the book, which is updated hourly. Second, they provide weekly sales data. The downside to this latter stat is the delay in its release — they provide data for Monday-Sunday, but it isn’t released until the following Friday. The upside is that big dorks like me use the time from Monday through Thursday to make predictions.
The chart below shows the average sales rank and weekly sales for Nov 24 through Dec 14. (The “average sales rank” is the average of the sales ranks for the seven days each week. Although it’s updated hourly, I don’t have the time to check it that frequently, so I rely on Author Central, which reports the sales rank at the end of each day.) It also shows the average sales rank (but not sales) for last week, Dec 15‑21.
|Week||Amazon Sales Rank
The question: How many copies of MJ4MF were sold last week?
Oh, sure… I could just wait until Friday to find out — but what fun would that be?
Instead, I constructed several mathematical models, and then I tweaked them to predict how many books were sold. The tweaks were based on some things I’ve learned over the past couple of years:
- Holiday sales are most vigorous in the first two weeks of December. They slow down a bit in the third week. Consequently, a sales rank of 1,655 on Dec 1 does not equal a sales rank of 1,655 on Dec 21.
- The long-term trend is not linear. In fact, this graph from Foner Books shows that it’s logarithmic.
Which brings us to the contest. Go to the Google form and enter your prediction and email address. (The email is only so I can contact you if you win.) Closest guess to the actual number of sales will win the grand prize. In the event of a tie, a winner will be randomly selected (or if I’m feeling generous, maybe there will be multiple winners… it’s hard to predict my disposition on any given day).
So, what are you waiting for? Open Excel or SPSS or your stat software of choice, muddle through a few regressions, and submit your entry!
Winners will be announced on Saturday, December 27, 2014. The exact time will depend on what time I roll out of bed, what activities my wife and kids propose for the day, and my particular disposition on Saturday. On second thought… safest if you check back on Sunday.
Well, no, actually it’s not my birthday. And it’s not my friend Jacqui’s birthday, either, but she did just celebrate a milestone with us that she wanted to share. Via email, she announced,
I’ve been alive for two billion seconds, a milestone I passed this morning.
This reminded me of a problem from Steve Leinwand’s book, Accessible Mathematics, in which he tells kids his age as a unitless number, then asks them to identify what units he must be using. Along those lines, here are some questions for you.
- How old (in years) is my friend Jacqui?
- What is her date of birth?
- If I tell you that my age is 22,333,444, what units must I be using? Assuming I’m not telling a fib, of course. And what is my age in years and my date of birth?
This reminds me of two math jokes about birthdays.
Statistics show that those who celebrate the most birthdays live longest.
A algebraist remembers that his wife’s birthday is on the (n – 1)st of the month. Unfortunately, he only remembers this when he is reminded on the nth.
Matt Parker is a funny dude — and a bit warped.
He created a show called Your Days are Numbered which, as the name implies, is about the statistics of death. The tagline reads, “You’ve got a 0.000043% chance of dying during this show.”
He claims that his favorite number is 3,435, because 33 + 44 + 33 + 55 = 3,435.
And he took two diametrically opposed careers — math teaching and stand‑up comedy — and morphed them into one.
What do you get when you cross a mathematician and a stand-up comic?
But Matt Parker is not only funny and warped. He’s also wicked smart. Check this out…
Being a math guy and wanna-be funny guy, I interviewed Matt with the hope that maybe I could learn a little.
Popular belief holds that both Brits and mathematicians are notoriously unfunny. How do you explain your phenomenon?
I am one of many counterexamples.
Your show Your Days Are Numbered: the Maths of Death deals with the probability of dying in various ways. What’s your favorite statistic about death?
You are more likely to die from falling out of bed than falling off a ladder or cliff.
You’re clearly not dead, but have you ever had a near-death experience?
I once nearly died trying to find the integer crossing point of two lines of latitude and longitude in the Australian desert. But I made it to the ‘confluence’ and back.
As far as I know, you’re the first mathematician ever to do a national comedy tour. Tell us how this came to be. What was the trajectory?
I was working as a stand-up comic in regular comedy clubs as well as being a maths teacher. Slowly, the two careers started to merge. In stand-up comedy, you cannot help but talk about what you are interested in, so I would talk about maths. I wouldn’t do maths jokes — they are notoriously unfunny — but I would use maths and being a maths teacher as the basis for my jokes.
Eventually I got a following for talking about maths and so my material could gradually get more and more nerdy. My maths tour show Matt Parker: Number Ninja contains a lot of maths, but it’s still a comedy show in its own right. You don’t need to be a mathematician to enjoy it — just like I enjoy political comedians without having a big interest in politics — but there is an extra layer of jokes for the extra-nerdy.
[Ed. note: The opinions expressed by Matt Parker about math jokes being “notoriously unfunny” do not necessarily reflect the views and opinions of the MJ4MF blog.]
Why do you call yourself “the number ninja”?
A mathematician is not someone who does lots of boring sums, like what most people remember from school maths. A mathematician is someone who plays with numbers and maths and tries to solve puzzles. The phrase “Number Ninja” helps to get this sense of playfulness across.
What’s the funniest thing you’ve ever said during a lecture?
I was once showing a spreadsheet which was an RGB digital photo of myself, turned into a series of conditionally formatted cells. I couldn’t help but say, “I’ve really exceled myself.”
Who’s the funniest mathematician or professor you know? What’s the funniest thing that he or she ever said?
A surprising number of stand-up comedians were once mathematicians. The fantastic Dave Gorman is always worth looking up. [Ed. note: You might like Dave Gorman’s bit about perfect numbers.]
Where is it harder to be funny — on stage, or at the front of a classroom?
The stage is far easier because you’re expected to be funny. The classroom is a place to communicate maths. There is a lot you can learn from performing comedy when you are in the classroom, but jokes are the very last thing. The real transferable skills from comedy to teaching are things like structuring a lesson and knowing how to pace a talk.
What’s your favorite blog post that you’ve written for The Guardian?
I am rather proud of Mobile Phone Masts Linked to Mysterious Spikes in Births.
Matt Parker will be performing in the Festival of the Spoken Nerd in London through July 12.
So, I understand what Baltimore Ravens coach John Harbaugh meant when he said:
I never thought you could feel 100% elation and 100% devastation at the same time. But I learned tonight you can.
But it sure sounds to me like he has twice as much capacity for emotion as the rest of us. It reminds me of Yogi Berra’s famous quote:
Baseball is 90% mental, and the other half is physical.
Or the anonymous quote about our favorite subject:
Mathematics is 50% formulas, 50% proofs, and 50% imagination.
Dare to guess what percent of Americans wouldn’t be able to identify the math errors in those statements?
Here’s a good old-fashioned math joke involving percents:
What’s a proof?
One-half percent of alcohol.
And a slightly longer one:
“Statistics is wonderful!” said a statistician.
“How so?” asked his friend.
“Well, according to statistics, there are 42 million alligator eggs laid every year. Of those, only about 50% hatch. Of those that hatch, 75% are eaten by predators in the first 36 days. And of the rest, only 5% get to be one year old for one reason or another.”
“What’s so wonderful about that?”
“If it weren’t for statistics, we’d be up to our asses in alligators!”
The most popular post of the year was At 41, I’m Pretty Happy (1,640 views). It’s good to know that my old age is a topic of interest.
And when 1,796 people went searching for “ant” on October 6, they were directed to an image on Mathy Animals. (Phishers?)
No matter you’re reason for visiting, thanks for stopping by in 2012.
(Should you care, feel free to take a peek at the MJ4MF year-end report from WordPress.)
I know a fair bit about the probability of winning the lottery.
State-run lotteries are a tax on the mathematically challenged.
Given the odds of winning, then you might wonder why I occasionally buy scratch-off lottery tickets. Lord knows, my wife often wonders aloud about it. Believe it or not, there are three reasons that I buy these tickets:
- First, I’m from a rural town in the-middle-of-nowhere Pennsylvania. The rural poor are infamous consumers of lottery tickets. Consequently, I believe that buying lottery tickets is part of my genetic code.
- Second, it’s a guilty pleasure that is easier to indulge than buying PowerBall or Daily Number tickets. When you buy one of those, there is a human interaction, and I imagine that the clerk selling me the ticket is thinking, “Loser! Don’t you know how low your odds of winning are?” For the scratch-off tickets, you insert your money in a vending machine, and the tickets are dispensed. Sure, you may get a disapproving eye from a passer-by, but at least there’s no formal exchange with another human.
- Third, and most importantly, I know a bit about probability, but I also know a little about the intersection of math and psychology. As it relates to the lottery, the idea is fairly simple — make every third or fourth ticket a winner, and people who buy scratch-off tickets will win often enough that they’ll keep coming back for more. Truth is, the winning tickets usually have a prize equal to the price of the ticket or twice the price of the ticket. For instance, if the tickets cost $5, then the winning tickets usually have a pay-out of $5 or $10. When four tickets are sold for $5 each, the state collects $20 and only pays out $5 or $10. Good work if you can get it, eh?
This last point is actually the one that hooks me in. If I buy four tickets at a time, I can almost guarantee that one of them will be a winner. Consequently, I’ll only be giving $10 or $15 to the state instead of $20. (What a bargain, right? I walked into the store with $20, and I get to leave with $5 or $10. Who could pass that up?) But on the off chance that there are two winners in this group of four, or if one of the tickets is a big winner with a prize of more than double the price, well, then, this could work out all right for me.
Yes, I am fully aware that my argument is irrational and that I am slightly delusional. Recognizing my irrationality and delusion, I don’t buy scratch-off tickets very often; but, I do buy them occasionally.
So, why am I telling you all this? Because this morning, I bought four scratch-off tickets at the local supermarket.
First Ticket: It had a “5 Times” logo next to $10. That means I won $50.
“Wow!” I thought. “I’m already ahead $30.” And then, of course, I realized how unlikely it was that the other three would be winners.
Second Ticket: I matched not one, not two, but three of my numbers to the winning numbers for $5 each. That means $15 in winnings on the second ticket.
“Holy schnikeys!” I said out loud, though probably too soft for anyone else to hear. (I hope.)
Third Ticket: I matched two numbers for $5 each. That means another $10.
Fourth Ticket: Nada.
But, whatever. I was up $55, so who cares about that stupid fourth ticket?
I collected my winnings, and I walked across the street to Panera and ordered a chai tea latte and a bagel. I handed my MyPanera card to the clerk — indicentally, I hate the recent trend of naming something as MySomething, because then it’s really awkward when I want to refer to the MySomething that belongs to me by calling it my MySomething; but, I digress — and he told me that I had earned a free bagel. “You can have this one for free, if you want,” he said. Well, hell yeah!
A few hours later, I went to lunch with a new professional acquaintance. Even though I had asked her if she wanted to meet for lunch, she picked up the tab!
Can you believe it? Fifty-five dollars in lottery winnings, a free bagel, and a free lunch. Financially speaking, this could have been the luckiest day of my life. (Well, except for the day when I learned that an essay I’d written had won a honeymoon in Oaxaca for my wife and me. But that’s a story for another day.)
Yep, the chances of one good thing happening in a day are low. But the chances of three good things happening in a day? Infinitessimal! Guess I’m just blessed.
My former boss, Jim Rubillo, knows a thing or two about probability and statistics, too. Somehow, his favorite line seems appropriate for this post.
If you don’t believe in the power of random sampling, then the next time your doctor requests a blood sample, tell her to take it all!