## Posts tagged ‘statistics’

### The Year in Review – MJ4MF 2012

The thank-you note that I posted earlier today was premature. This afternoon, the good folks at WordPress delivered annual statistics for the MJ4MF blog.

How revealing.

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?)

For what it’s worth, I think my best posts this year were 12 Math Knock-Knock Jokes and Math Tom Swifties. But what do I know?

No matter you’re reason for visiting, thanks for stopping by in 2012.

Thanks, also, to those who encouraged folks to stop by, like Valerie Strauss of The Answer Sheet (*Washington Post*), Casey Frushour at Casey’s Head, and Mike at Spiked Math.

And big props to Xander Henderson, Outlier Babe, Jims Maher, and Keith Raskin for providing commentary.

(Should you care, feel free to take a peek at the MJ4MF year-end report from WordPress.)

### P(Winning Lottery) > 0… but Just a Little

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!

### At 41, I’m Pretty Happy

Wonder when you’ll be happiest? You could look for statistical research to find the answer, but remember that 83.74% of all statistics are made up.

As it turns out, a large number of statistics that aren’t made up don’t really provide much help, either.

The Pew Research Center says that men are happiest over age 65 and that we are least happy in our 20’s. Friends Reunited says that people are happiest at age 33. A Gallup poll from 2009 said that men are least happy in their 50’s and late 80’s, but a different Gallup poll from 2008 claimed that people are happiest at 85. This last result agrees with a report from the National Academy of Sciences, which states that people are most depressed at age 44, as shown by the U-bend happiness curve below:

Well, shoot. With all this conflicting information, how will I know when to be happy? Until I get this all sorted out, I’ll just have to keep doing the activities that make people happiest. (Are you really surprised by the first item on that list?)

Jean Jacques Rousseau once defined happiness as follows:

Happiness: a good bank account, a good cook, and a good digestion.

But I would define it thus:

Happiness: a sharp pencil and some paper, a good problem, and a quiet place with some time to think.

It has been said that happiness adds and multiplies, as we divide it with others. But let’s not forget how subtraction can bring happiness, too…

Some people bring happiness

whereverthey go. But you? You bring happinesswheneveryou go.

[**Update, 4/13/12:** When I checked into a Comfort Inn hotel last night, I was given a bag with fresh cookies. On the outside it said:

Happiness is a warm chocolate chip cookie.

That might be the best definition yet!]

### Conversation with a Statistician

Yesterday, I ran into a friend who’s a statistician. When I asked, “How’s your husband?” she responded, “Compared to whom?”

We chatted for a while, and she updated me on some recent research. Among the recent discoveries that she shared…

- Birthdays and cigarettes both improve health. Recent research has shown that people who celebrate the most birthdays live longest, and smokers are less likely to die of age-related illnesses.
- A team of researchers has discovered that marriage is the leading cause of divorce. There is a signficant correlation between those who get married and those who get divorced. It is also well known that 50% of marriages end in divorce… which means that if you don’t file for divorce, your wife will.
- It was recently discovered that 83.638867% of statistics have an unjustified level of precision, and 78.46% of all statistics are made up on the spot.

She also relayed this recent incident at the Census Bureau.

Checking some questionnaires, a census clerk was amazed to note that one of them listed 121 in the space for “Age of Mother, if Living” and 125 in the space for “Age of Father, if Living.”

Incredulously, the clerk said to the survey taker, “Both of your parents are alive and over 120 years old?”

“Well, no,” replied the survey taker, “but they would be —

if living!”

### Mean and Standard Deviation

As a follow-up to yesterday’s post, here’s a poem titled *Mean and SD* by Norman Chansky, professor emeritus at Temple University. Ostensibly, the poem first appeared in the Journal of Irreproducible Results, though I was unable to find an exact citation.

The mean is a measure of location,

The center of a population.

If at random a score you drew,

The mean’s the most likely score you’d view.You can compute the mean in your slumber:

Sum the scores, and divide by the number.

At the mean, sample scores converge;

From the mean, these scores diverge.

Near the mean, the scores are many.

In the tails, there are hardly any.But to measure a distribution’s variation,

From the mean, find each score’s deviation.

Each difference ofDscore, now you square.

Sum allDscores, all scores’ share.

Now this sum, divide byN.

That’sV, the variance, then.The square root of

Vis calledSD,

The gauge of a trait’s variability.

We’ve found two moments of a distribution,

Developed from each score’s contribution.Picturing a universe, try to see:

Its center, the mean; its orbit,SD.

### Statistically Speaking…

My favorite quote from Lewis Carroll happens to be one of my favorite quotes:

If you want to inspire confidence, give plenty of statistics. It does not matter that they should be accurate, or even intelligible, as long as there is enough of them.

Here are a few statistical facts worth noting:

One of every four mathy folks suffers from mental illness. Now, think of three calculating friends. If they’re okay, then it’s you.

Fifty percent of Americans have an understanding of statistics that is below average.

69.8724% of all statistics reflect an unjustified level of precision, and 83.85% of all statistics are made up on the spot.

There are two kinds of statistics — the kind you look up, and the kind you make up.

There are three kinds of statisticians — normal, deviant, and skew.

### More Math One-Liners

As we were dressing to play in the snow, I asked my son Eli if I could wear his hat. His response was an emphatic, “No!” When I asked why, his one-liner response made me chuckle:

Because your chin is too far from your head.

Here are some other one-liners that I’ve always enjoyed.

Pure mathematicians are like lighthouses in the middle of a swamp — brilliant, but completely useless.

If God wanted us to use the metric system, why did Jesus have 12 apostles?

I’m not worried about losing my job to a computer. They’ve yet to invent a machine that does absolutely nothing.

For every complex mathematical problem, there is a simple and elegant solution that is completely wrong.

For every complex mathematical problem, there is a solution. The difficulty lies in finding it.

A mathematics lecture is a process for transferring the notes of the teacher to the notes of the student without passing through the minds of either.

In a graph, the thickness of the curve is inversely proportional to the reliability of the data.

Statistics are like a bikini — what they reveal is suggestive, but what they conceal is vital.