|The jokes on this page do not fit any of the “Other” joke categories.|
|O1||Other||The following explains why it is so difficult for psychologists to collect good data:|
To figure out how heavy a pig is, you find a good stout plank and balance it on the pole of a fence. Tie the pig onto one end of the plank, and then run around to the other side and put a rock on the opposite end. Keep trying different rocks until you get one that balances with the pig. That’s about it, all you have to do then is guest the weight of the rock!
** Thanks to Jim Robison-Cox of Montana State University for revealing the Texas method of weighing a pig. **
|O2||Other||Three roommates slept through their midterm statistics exam on Monday morning. Since they had returned together by car from the same hometown late Sunday evening, they decided on a great little falsehood. The three met with the instructor Monday afternoon and told him that an ill-timed flat tire had delayed their arrival until noon. The instructor, while somewhat skeptical agreed to give them a makeup exam on Tuesday.|
When they arrived the instructor issued them the same makeup exam and ushered each to a different classroom. The first student sat down and noticed immediately the instructions indicated that the exam would be divided into Parts I and II weighted 10% and 90% respectively. Thinking nothing of this disparity, he proceeded to answer the questions in Part I. These he found rather easy and moved confidently to Part II on the next page. Suddenly his eyes grew large and his face paled. Part II consisted of one short and pointed question….
“Which tire was it?”
** This is my own homegrown joke that was motivated by the dramatic increase in grandmother deaths on the day of an examination! **
|O3||Other||A hungry man went into a restaurant and noticed that the daily special was rabbit burgers, a real delicacy, for only 49 cents a burger. He was astounded at his good fortune to find such a bargain. When he inquired of the cook, the cook told him that in order to keep prices down he had to add some filler: in fact, only part of the burger was rabbit meat. The rest was horse meat.|
“How much of each kind of meat is in a burger?” asked the customer..
The cook replied, “There is an equal amount of horse and rabbit in the burger: One horse, one rabbit.”
** Thanks one more time to Hugh Foley for this quasi-statistical joke. **
|O4||Other||A friend was bragging to a statistician over coffee one afternoon how two-day volatility in the stock market had treated his holdings rather kindly. He chortled, “Yeah…yesterday I gained 60% but today I lost 40% for a net gain of 20%.”|
The statistician sat in horrified silence. He finally mustered the courage and said, “My good friend I’m sorry to inform you but you had a net loss of 4%!!!”
** My little tale above illustrates how pervasive innumeracy is in our society. Always remember, “Percent of What?” **
|O5||Other||“What do you get when you trade your Rolls Royce for a Chevrolet owned by Julia Childs?|
You get CHEVYCHEF’s INEQUALITY!!!
** This may be my worst one so far. Please hold the tomatoes! **
|O6||Other||Why did Yogi Bear become a statistician?|
Because he discovered that truth could be inferred on the basis of bare facts.
** Thanks go out to Alfred M. Barron for this joke that is barely funny! **
|O7||Other||A boy asked his statistician father, “Why is my body not well-proportioned just like my brother’s?”|
His father’s response, “Because, when you mother had your pregnancy, its distribution was skewed!!”
** Does Medical Science know about this? Does this mean if your pregnancy is normally distributed you will have a perfectly proportioned baby? Thanks to Okunola Olajide Ezekiel for sending this. **
|O8||Other||You know how dumb the average person is? Well, by definition, half the population is dumber than that!|
** Thanks to Barbara Kerr from Australia for sending me this. She told me that this not-terribly-nice aphorism is attributed to the fictitious Bob Dobbs of the Church of the Subgenius. **
|O9||Other||Did you hear the one about the sign outside the statistics lab?|
“DANGER: Enter at your own risk. Informavore feeding frenzy in progress.”
** Thanks to Bill Shelton for sharing this cute little joke with us. Is an informavore similar to a carnivore? **
|O10||Other||Why were so many CEOs who held doctorates in accounting fired in 2002 from their companies?|
They used “COOKBOOK” texts in the their stat courses and decided to practice their “DOCTORING” skills!!
** I really do not want to blame the collegiate accounting programs for all the corporate woes of America. The indiscretions are probably due to simple red-green color blindness or maybe the failure to recognize the existence of a negative number. On second thought, could it just be old-fashioned greed? **
|O11||Other||It is a well-established fact that Statin Drugs ($27.8 billion sales worldwide in 2006) lower the BAD cholesterol level by 20 – 50% in most individuals upon continuous treatment. In fact, in a recent TV ad for a certain Statin Drug endorsed by Dr. Robert Jarvik (the artificial heart man), it was stated that this drug “reduces the risk of heart attack by 36%… in patients with multiple risk factors for heart disease but no heart disease.”|
“Zowie, exclaimed a friend watching the TV ad, this is comparable to penicillin. Since they called these drugs Statins because they are “Statistics Insured,” why not add this to our drinking water supply and let everybody from babies on up benefit?
**Now before you petition your city council or go out and buy stock in this drug company, let’s take a very careful look at this 36% figure which the Company itself tagged with an asterisk in the original report. Here is another prime example of innumeracy and number enhancement at its best. In smaller print the company explained that this means in a large clinical study that lasted 3 and 1/3 years, for every 100 subjects treated with the drug, 2 people had hear attacks, as compared with 3 heart attacks in a group of 100 subjects that received a placebo. In other words, for every 100 subjects who took the drug, 1 less subject was spared a heart attack (i.e. 1/3 = 33% ~ 36%). But this is a spurious percentage so we need to put hits in terms of a relatively unknown but useful statistic called the NNT. I want all my readers to etch this in their mind. The NNT is the number needed to treat for one person over the expect number to benefit! In our case, the NNT is 100…that should have a very sobering effect on the exuberant 36% reported earlier! Now to show you some other examples of this NNT: (a) NNT = 2 to cure a stomach ulcer with an antibiotic cocktail in one year of treatment (this is a great NNT); (b) NNT = 16 – 23 to prevent one hear attack with a Statin in people that have had a heart attack or other signs of heart disease (most likely group to benefit from a Statin); (c) NNT = 500+ to prevent death or serious medical condition with a Statin among patients without heart disease that have a single risk factor like high blood pressure (Probably should not be on Statin at all); (d) NNT = 1000+ for Avandia, a drug for controlling blood sugar to prevent heart disease or heart attack. (Even companies admit that this NNT is way too high for any benefits.) Of course, along with the NNT, one must also consider the side effects of the drug in making any decision about long-term usage. In the case of the State we mentioned before, it is very interesting that the Company essentially uses the NNT to downplay these side effects like muscle aches and memory problems. It states that only 1 in a 100 will experience side effects of some sort. WONDER WHY THE COMPANY CAN’T EMPHASIZE THE NNT FOR BOTH ISSUES? Much of this discussion is based on an article in the January 28, 2008 issue of BusinessWeek magazine. I urge all students of statistics and actually everyone to read this article online. This is one of the most illuminating articles on drug research that I have read and covers other key issues of drug effectiveness. By the way, the name “Statins” did not come from “Statistics Insured”…this was just part of the humor. **
|O12||Other||The statistician was asked by his friend why he always used the urinal on the far end.|
He replied: “Oh, that is a no brainer. There is half the probability of being sprayed by someone else.”
** Once again this illustrates how repressed statisticians are. They would never be could in the middle of a group for fear the person on either side would strike up a conversation. Thanks to Graeme Quinlan from Australia for passing this on. **
|O13||Other||A statistics professor dies and so the test scheduled for that day is cancelled.|
A student rings the department at 5 minute intervals to ask if the test is on. The guy answering the phone asks him, “Why the bloody hell are you ringing so often? I’ve told you 16 times the professor has passed away! What are you doing, some sort of research, are you experimenting on me? What the bloody hell is it?”
“Nah, the student replies, no research. I just like to hear you say it.”
** This is another Hal Ashburner joke from down under. It sure makes statisticians feel unwanted! **
|O14||Other||How many tents will a campground hold?|
Ten tenths since that adds up to a whole!!!
** Sorry, I lost the attribution on this one. However, you may wonder what this has to do with statistics. A possible incorrect answer to this question would be “one tenth(tent)” since in a one-way analysis of covariance with one covariate, the pooled within groups regression coefficient is not obtained by adding the separate regression coefficients within each group but rather by dividing the pooled numerators of each of the within group coefficients by the pooled denominators of each of the within group coefficients. In our example, using regression-type pooling, 1/10 + 1/10 +1/10 + …for ten terms = 10/100 or 1/10 but that is absurd! Now isn’t that special! I am sure you followed me. Is it any wonder that students have trouble with statistics when they are presented with esoteric “word salad” like the above? Please don’t take my ramblings seriously. I am only having FUN!!! **
|O15||Other||What do you call a tea party with more than 30 people?|
A Z party!!!
** This is a great one from Stacey Ecott. I always thought a Z party was a roomful of slumbering statisticians listening to a keynote address at a convention. **
|O16||Other||What is a triple-blinded, completely randomized case-control clinical drug trial?|
One in which the patients do not know which drug treatment they are receiving, the nurses do not know which drug treatment they are administering, and the physicians conducting the study do not know what they are doing!!!
** I have always wondered why physician’s recommendation from medical research studies changes almost every six months. Thanks to Kenn Finstuen from Texas for another dandy. This should immediately be recognized by Stanley and Campbell in their work that classifies types of experimental designs. **
|O17||Other||IRS statistics show that the average American now works 3 and 1/2 hours every day for the government, which comes out to 1 and 1/2 more hours than civil servants do!!|
** This is really a shocker. I always knew civil employees were underpaid but there now appears to be a fringe benefit. I am sorry I don’t have an attribution on this neat comparison. **
|O18||Other||Three of the Most Embarrassing Outcomes for a Statistician and Their Workarounds:|
(1) Result: The intercorrelations between a fairly large set of variables has exactly 5% of the coefficients that are significant at the .05 level. Solution: Try to remain upbeat. Lighten up and use the .10 level of significance and stress to the readers that these results represent an early exploratory study!
(2) Result: In a 3x3x4x4x5 Factorial ANOVA the Five-Way Interaction turns up significant at the .01 level. Solution: Curse under your breath that you used a five-factor design. Then instruct your graduate assistant to conduct FIVE Four-Way ANOVAs, one for each of the five levels of the 5th independent variable, to take two aspirin, and call back in the morning!
(3) Result: The F-test for a One-Way ANOVA with five treatment groups is significant at the .05 level but NONE of the pairwise comparisons between the five means is significant. Solution: Cry hard and then work your tail off to find some obscure, meaningless complex comparison that is significant such as the average of the first three treatment means is significantly different from the average of the last two treatment means!
** The above are my own dreaded results. I am sure the readers have their own convoluted and shocking statistical anomalies. Please e-mail me your most feared and or realized statistical outcome and I will put it in the Gallery. **
|O19||Other||A reader of this Gallery sent me a very amusing story…|
He took advantage of one of those online offers…a free credit report. He was delighted to learn that his credit rating was better than 100% of those who had received such a report…which obviously included himself. “Whoopee!!!, he exclaimed, my credit rating was better than MY OWN!!! It just doesn’t get any better than that.”
** Harley (I need your last name), thanks for this cute anecdote. This does hit on a point that I have been frequently asked about. Can a person’s score in any distribution fall at the 100th percentile or more precisely can his score have a percentile rank of 100? If you subscribe to classical test theory, the answer is technically NO. Supposed that person A had a top score of 23 on a 25 item test with the remaining 49 other students scoring below 23, Then assuming the scores are continuous, person A’s true score would be between the real limits of 22.5 and 23.5. The only way that person A’s score would have a percentile rank of 100 would be if his true score was between 22.5 and 23. Since it is just as likely that his true score is between 23 and 23.5, we generally compromise and assume 1/2 of his score is between 22.5 and 23 and the other half is between 23 and 23.5 (a wacky assumption but more plausible if you had several scores of 23). Thus the percentile rank of a person A would be (49 + (1/2 x 1))/50 = 49.5/50 = 99. Most modern authors subscribe to the above line of thinking but as we all know, statistics is heavily laden with many assumptions. **
|O20||Other||Checking some questionnaires that had just been filled in, a census clerk was amazed to note that one of them contained figures 121 and 125 in the spaces for “Age of Mother, if Living” and “Age of Father, if Living.”|
“Surely your parents can’t be as old as this?” asked the incredulous clerk.
“Well no,” was the answer, “But they would be IF LIVING!”
** Is this telling us that census data is biased on age of parents? Thanks Michele McIndoe for sending me this neat little joke. **
|O21||Other||The secretary of defense gave the president his daily briefing. He concluded by saying: “Yesterday, 3 Brazilian soldiers were killed.”|
“Oh No!” the president exclaimed, “That’s terrible!”
His staff was stunned at this display of emotion, nervously watching as the president sat, his head in his hands.
Finally, the president looked up and asked, “Just how many is a brazillion?”
** Here is another example of the ubiquitous innumeracy that is gripping this country. Thanks to my good friend Merle (Pear Diver) Howard, an emeritus Professor of Speech Pathology at Illinois State University, for forwarding this little story to me. I wonder if the White House could us a good speech pathologist as a consultant these days? **
|O22||Other||A freshman college student had the misfortune of having several auto accidents while living at home with his parents. One day his statistics professor told his class that 83% of all auto accidents happen within 20 miles of your home. The very next day the student moved 22 miles from home and never had another accident during his entire college career!!!|
** This young man found a neat way to beat the odds. I just wonder what would have happened had his parents decided to move in with him? Thanks go out to Jon Holmen, a student at Illinois State University, for passing along this story. **
|O23||Other||A cannibal goes shopping for dinner. His wife wants to prepare brains that day. At the butcher’s shop he is told that there are three prices: First, there is statistician’s brain at 1 dollar per pound. Secondly, they have lawyer’s brain at 2 dollars a pound. And finally, he can buy politician’s brain at 4 dollars a pound.|
The cannibal is bewildered at this price range and asks the butcher, “Why on earth should a pound of politician brain cost that much more than statistician brain? Do you really think that the quality is so much better?”
The butcher replies, “No, but if you count how many politicians it takes to get a pound…”
** I wonder if the cannibal should agree to a plea bargain and buy the lawyer brain? This ghoulish joke was forwarded to me by a reader of the Gallery who wished to remain anonymous because this was not his creation. Many thanks to the sender anyway. **
|O24||Other||What is the name of the only known motel chain that caters to professional draftsmen?|
** The wonderful statisticians who pioneered the field of multivariate analysis in the 1930’s and 40’s need much more recognition than what they have received and Harold Hotelling was among these (And think about his–they did it without computers!!!). This statistics, of course, is the bivariate counterpart of the univariate t-test. Story has it that William S. Gosset was granted a lifetime pass to any motel in Dr. Hotelling’s chain. **
|O25||Other||TEACHER ARRESTED IN NEW YORK|
NEW YORK, NY – A public school teacher was arrested today at John F. Kennedy International Airport as he attempted to board a flight while in possession of a ruler, a protractor, a box of plastic pocket protectors, and a graphing calculator.
In a morning press conference, the Attorney General said he believes the man is a member of a spin off group, St. Atistic, of the notorious Al-Gebra movement. He did not identify the man, who has been charged by the FBI with carrying weapons of math instruction. He also revealed that the situation was extremely tense and touch-and-go for a short time since the plastic protectors were discovered half-melted.
“Al-Gebra and particularly St. Atistic are problems for us,” the Attorney said. “They recruit mean deviants who are then well trained in the use of multiple modes to search out an absolute value. They use secret code names like ‘x’ and ‘y’ and refer to themselves as ‘unknowns’, but we have determined they belong to a common denominator of the axis of medieval with coordinates in every country. As the Greek philanderer Isosceles used to say, ‘There are three sides to every triangle.'”
When asked to comment on the arrest, the President said, “if God had wanted us to have better weapons of math instruction, He would have given us more fingers and toes.” White House aides told reporters they could not recall a more intelligent or profound statement by the President.
** Thanks to my good friends Sherry and Shailer Thomas for sending me this clever story by way of another looping e-mail. Shailer Thomas is an Emeritus Professor of Sociology at Illinois State University and understandably has a keen eye for deviant group behavior. **
|O26||Other||A team of researchers from a large eastern university in the U.S. has recently published a monumental finding. The team discovered what the leading cause of divorce is.|
It is marriage!!! You see, everyone who has been divorced has been married first.
** Well, I wonder what journal was responsible for propagating in print this causal relationship. I was told the same journal had advocated a temporary moratorium on marriage as an attempt to cut the divorce rate. Thanks to Jonathan Schinhofen for suggesting this bit of sheer tomfoolery. **
|O27||Other||I really can’t see the attraction|
Of trying to fit interaction.
The last time I tried
I woke up on my side
With an arm and a leg both in traction.
Of trying to fit interaction.
** Thanks go out to Debby Apthorpe again from Australia for one of her famous statistical limericks. It appears that interaction is quite similar to some of the positions in the game Twister. **
|O28||Other||50% of marriages end in divorce. Thus if you don’t file for divorce, your wife will.|
** This a cute little variation of all the 50-50 jokes. But wait a minute! This says the probability of any marriage ending in divorce is one. Sorry I don’t have an attribution on this one. **
|O29||Other||My scatterplot’s not monotonic|
I’m sad and a trifle ironic.
The dreaded kurtosis
Is causing psychosis;
Please bring me a strong gin and tonic
** Another limerick from the collection of Debby Apthorpe in Australia. **
|O30||Other||A statistician was reliving a weird and vivid dream for an accountant friend one day.|
He explained, “In this strange dream, 20 or 30 accountants were sitting stark naked together in a large room at separate computers . But the eerie and contradictive part of this scene was that the accountants were all on the same auction website on their screens, each attempting to sell a spanking new package of a single pair of ‘Jockey Shorts’ that each was waving in his hand.”
The statistician in a puzzled tone continued, “I just could not understand why the accountants just didn’t slip on their pair of shorts instead of selling them on the Internet. This is the most vexing part of the dream!”
The accountant, with a sly little grin, immediately piped up, “Oh that has a simple interpretation. This is a perfect example of NAKED SHORT SELLING!”
** To understand my little joke you must at least dabble in the stock market. I have nothing but disgust and distrust toward the entire market and financial system in the United States after the total collapse of investments during the Spring and Summer of 2008. The permitting of “Short Selling” has contributed greatly to the debacle we are still witnessing at this writing. I ASK YOU, WHERE ELSE ARE YOU ALLOWED TO SELL THINGS YOU DON’T OWN? Enough said! **
|O31||Other||One legacy of the Iraq War will be the unstated but implied “so-called” Rumsfeld Test. This was suggested serendipitously from a Department of Defense new briefing on Feb. 12, 2002. The Secretary stated, “Reports that say that something hasn’t happened are always interesting to me because as we know, there are known knowns; these are things we known we know. We also known there are known unknowns; that is to say we know there are some things we don’t know. But there are also unknown unknowns – the ones we don’t know we don’t know.” (This sounds like gibberish but Rummey is on to something here.)|
Now Mr. Secretary, to validate your intelligence work, we suggest that you look at a fourth category of perceiving something unknown that is really known (Yes, we said that), and this gives us the basis for a neat 2×2 chi-square test. This would be the famed nonparametric test of independence whose table of observed (O) and expected (E) counts of Intelligence Items appears for each cell in the above diagram.
Now theoretically, if our intelligence system is operating with high efficiency, for any large set of intelligence items, the perceived observed proportion of known knowns should significantly exceed the perceived observed proportion of unknown knowns and correspondingly the perceived observed proportion of unknown unknowns should significantly exceed the perceived observed proportion of known unknowns. This is the desired direction of the dependence (Look at main diagonal of table). Remember under the assumption of independence of perceived and true items, the expected E for any cell is the row sum of O’s that cell is in times the column sum of O’s that cell is in divided by the overall sum of all the O’s. This is repeated to get the expected E for each cell. We then substitute into the formula x2 = Σ [O – E)2/E] to get the test statistic Frequency Chi-Sqaure with df = 1. Finally, this value from the data table is referred to either the 95th or 99th percentile from the Table of the Chi-Square Distribution. For Rummey’s sake we hope and pray that this obtained value is larger than the critical percentile. If it is… WHOOPEE!! RUMSFELD’s INTELLIGENCE TEAM HAS BEEN VALIDATED!! But wait just one moment. We have ONE thing to check yet. Bad Dependence can also occur! If the perceived observed proportion of unknown knowns should significantly exceed the perceived observed proportion of known knowns and correspondingly the perceived observed proportion of known unknowns should significantly exceed the perceived observed proportions of unknown unknowns (Look at secondary diagonal of table), significant masculinizing of the true nature of the items has occurred. THIS WOULD MEAN UTTER FAILURE OF THE INTELLIGENCE TEAM!! SO THE RUMSFELD TEST IS FRAUGHT WITH DANGER FOR INEXPERIENCED STATISTICIANS. WE MUST ONLY APPLAUD RUMSFELD’S SUCCESS WHEN KNOWN KNOWNS AND UNKNOWN UNKNOWNS PILE UP SIGNIFICANTLY IN THE TABLE. THIS IS INTUITIVELY OBVIOUS BUT MUST ALWAYS BE VERIFIED AFTER A SIGNIFICANT TEST.
**Thanks to John A. Hansen of Indiana University for suggesting the new Rumsfeld Test. Quite frankly, I originally decided it was too esoteric to mess with as are many of Rummeys long and dry explanations. Finally, with some trepidation, I decided to finish what Rumsfeld had started at the news conference and write it in a fashion that would mimic his style of taking something simple and making it convolutedly complex. Did I succeed? It was sure load so fun and I even, quite honestly, had trouble keeping my mind focused enough to proof read the material. But in all seriousness…NO, and I repeat NO statistical concepts should ever be explained in the gobble-de-gook word obfuscation that this writing produced. We certainly can’t blame students for rebelling against instructors who intentionally or unintentionally spew out garbage such as this in the classroom? Knowing and understanding the material thoroughly and being able to clearly and concisely explain it to someone else are two entirely separate but critical components of the teaching enterprise. **
|O32||Other||Husband returns home from a doctor’s visit with a sad face.|
Wife: “What did the doctor say?”
Husband: “I have Dyscalculia. It’s a math disorder.”
Wife: “How bad is it?”
Husband: “The Doctor said not to worry. 100 out of every 15 people have it.”
** This has to be one of the worst examples of innumeracy I have heard. Regarding comedians shying away from statistics jokes, this joke was attributed to David Letterman. If this occurred, this has to be a rarity where a stand-up comedian told a statistical joke. Thanks much to Larry DiFiore, Ph.D, Malloy College of Rockville Centre, NY for sending this counter-example. **
|O33||Other||Don’t kid yourself. The deep recession of 2008-09 is really a depression. Then to witness business guests clapping at the close of the NY Stock Exchange at the podium every single day is like statisticians clapping for nonsignificant results on hypothesis tests!|
** Maybe this is the core problem. Financial people have lost their way and have been unable to distinguish good performance from bad performance. From loan approvals to CEO compensation, they have lost all sense of what laudable behavior means. **
|O34||Other||There was a bright student named Bobby|
Who collected stat jokes as a hobby
But when his friends deemed them lame
He was stricken with shame
And mailed them in bulk to Abu Dhabi.
** Yes, this one is all mine. I know this is not the greatest stat limerick to ever hit print but at least it is a starter. I have been yearning to write one of these for a long time. Our expert, Debby Apthorpe in Australia, will have to pass judgement on it. Debby, are you out there? **
|035||Other||See Santa at the North Pole by his sleigh|
He regrets using statistics each and every day
If naughty is the null adoption
And nice is its only option
He must greatly inflate alpha or stay.
** Maybe this prompts us to cut some slack to the researchers who elevate their alphas to .10 a posteriori to calculating the statistic. Just kidding of course. This is only my second limerick so bear with me. The Christmas song “Santa Clause Is Coming To Town” inspired me to express Santa’s concern here. **
|O36||Other||What famous person was credited with telling the very first statistics joke and what was it?|
Sigmund Freud the Father of Psychoanalysis. A hot-headed patient of his when lying on the couch got cold feet and failed to reveal the origin of his pent up rage. Freud admonished him and ordered that before they continue he should place his head in a bucket of ice and his feet in a stove and that would on the average make him feel fine!
** That is strange. I could swear that I have always heard this the opposite way with the head going in the oven and the feet in the bucket of ice. But that would only exacerbate the poor client’s problem. I would never want to be accused of making a Freudian Slip here. **
|O37||Other||** I want to remind all our readers that this joke represented the bicentennial joke recorded in the Gallery. Who in their wildest dreams would of thunk it? I have heard bloggers exclaim many times that recognizing any humor in statistics is the biggest joke of all (Maybe this should be considered the 201st?). But we did it and will continue to create, with your help, many many more funnyisms and transform the statistical enterprise into a light-headed discipline. **|
Two graduate students were spending their spring break in a large city in southern Florida. One night they decided to visit a casino for a little relaxation and fun. However, being college educated, they knew the games always favored the “House” so they set limits on their play and analyzed which games were inclined to have more favorable odds toward the player. As they walked into the casino amidst darting lights and piercing sounds, the students spotted a strange game near the entrance that they had never seen before. A metal drum rotated on a spindle attached to a table with 100 identical balls inside the drum with dollar amounts stamped on each ball. The frequency and probability distribution were as follows:
Instructions stated that for a charge of $12, the player was entitled to rotate the drum a number of times to mix the balls thoroughly and then reach through a latched door on the side of the drum to pick a single ball, sight unseen. The attendant running the game would then pay the player the dollar amount stamped on the ball. Finally, the drawn ball was returned to the drum and the entire process was repeated per interest in the game.
The students decided that if the game were deemed close to being fair, each would play the game 15 times for a total of 30 trials and any winnings would be split evenly. The first student looked worriedly at this buddy and remarked, “I never have subscribed to the notion of an expected value in gambling games. The concept is entirely too subjective and unreliable. In our case the value that is expected is a $160 total loss over all 30 trials. My reasoning is that we will draw primarily $1’s and $5’s (the modes) and a couple $10’s and this would get us up to about $100 of winnings overall. But this is $260 short of the $360 expenditure we would put out over 30 trials! On the other hand, the “House” has a value that is expected that is even higher than this first estimate. The “House” reasons that since $2 is the median value of the balls, 40% of the draws are below this. Thus, $12 – $2 = $10 and 30 x $10 = $300 is the expected total winnings for the “House.” “Either way, the expected values do not favor us.”
The second student nods his head and retorts, “Good friend, I agree with you that the expected value is just not well-defined. However, I would tend to pick the mean of $13.18 to help evaluate our chances of winning. Since this value is barely larger than the cost to play of $12 and the odds are 99:` against our winning on any trial, the game tips decisively toward the “House.”
THERE WAS A PAUSE. THE STUDENTS LOOKED AT EACH OTHER, SHRUGGED THEIR SHOULDERS, AND WALKED AWAY!
** Holy Cow! The statistical misinformation and falsehoods are running rampant in this story. It is certainly apparent that these students were not introduced to basic statistics at the undergraduate level. The expected value is indeed the mean of a relative frequency distribution. However, the expression is commonly used in math stat to impart a touch of mystery (only kidding) and in applied statistics when a gambling experiment is associated with the frequency or probability distribution and repeated an infinity of times. In our example, a student pays $12 per draw, receives the value on the ball, the “House” replaced the ball, and the experiment is repeated many many times. The most fascinating interpretation of expected value here is that it represents the fair price to pay per trial ($13.18) or the price that in the long haul, both the player and the “House” break even. The first student was just flat out off base in his logic. However, the second student correctly identified the mean as critical but totally bungled the conclusion. Surprisingly, the game favored the students since the charge of $12 was less than the expected value of $13.18. With an infinity of trials (30 may be too few), the “Big smacker” of $1000 should be drawn just enough times to give the students modest winnings (About $35.40!) All right hotshot statistics students out there–Where did this value come from?” **