Some rainy Sunday afternoon when you have nothing better to do, sit down with a pen and paper and start flipping a coin for several hours. Keep a tally of the number of heads and the number of tails that turn up. Over time, you will find that the numbers are almost equal. The chances are 50-50 that any flip of the coin will turn up either heads or tails.

When it comes to trying to predict what the chances are against being struck by lightning or in favor of winning the lottery, we all want a little better odds than 50-50. This is where research and statistical analysis come in with something more reliable than an educated guess, superstition or Old Wives' Tales.

The Science of Statistics has come up with the "Bell Curve", probably best remembered from some classes in school. Sometimes tests are graded "on the curve" as opposed to numerical grading for an arbitrary standard that may or may not apply to that particular class.

It is the same principle as calculating the batting average of a baseball player. The larger number of times at bat, the more accurate the description of the average is.

It would be a mistake to say that an average salary is $500,000 if a millionaire's and an unemployed person's incomes were the only ones taken into consideration. Both the millionaire and the unemployed person would take umbrage! A wide cross section of different salaries would need to be entered into the calculations.

A number of variations of the Bell Curve are used for different purposes with the numbers denoting different values. The pictured one is widely used to measure intelligence in IQ tests, (Intelligence Quotient.) The average or mean here is 100. The mean is shown in calculations as X.

Over the years a number of different IQ tests have been administered to thousands of people, usually students. A score of around 100 is the score the vast majority of test takers received. A score of 115, means that person's score is 34.13% higher than all rest of the people. 130 is 98% higher than the rest and there are far fewer people with that score. 145 is 99.9% higher than everybody and not many achieve that score.

Conversely, the same percentages apply below 100 only the scores are lower rather higher than the mean. Both the upper and lower ends of the curve are left open to infinity because no one can know just how high or low intelligence can be.

A child given an adult test would no doubt score zero. That does not mean the child has no intelligence, only that the child has not lived long enough to learn anything that is on the test. Or a genius could ace the test, so that would not be a good indicator of just how much he does know. An examination is only as good as the skill of the people making up the questions on the test!

This reflects a very important principle - there are no absolutes in science!  The one factor that must be taken into consideration is that human ignorance is eternal.  Further, the observation of a process, of itself, alters the process. The mere fact that the process is being studied introduces a variable that can affect the results of whatever is being tested. As often as not, this "observer bias", whether unconscious or deliberate, has a definite influence of the outcome of the study. One time a monkey was being observed through a peephole, presumably so the monkey wouldn't know he was being watched. Next thing the scientists knew was, all they could see was the eyeball of the monkey. He was observing them to see what they were up to!

Suppose a scientist wants to test something to see if it is true. He starts with a hypothesis, that is, a statement of cause and effect. Are tall people smarter than short people, or are short people smarter than tall people? Obviously, he cannot test all of the tall and short people in the world. So he has to test only a small portion of the people, called a sample, and then hope to infer that all the tall people, called the population, are smarter than the short people or vice versa.

If he can prove his hypotheses then he shows a correlation between being tall and being smart or being short and being dumb. Or maybe between short and smart or tall and dumb. Theoretically, one attribute would affect the other. No problem. Just round up a sample of both tall and short people and give all of them IQ tests and then compare the results.

This is where it gets sticky. How can he choose a sample at random that will be representative of the whole population. How tall? How short? Men or women? What ages? What level of education? Rural or urban? American or any other part of the world? How healthy? How many are willing to participate in the test? Where and when will the tests be administered? What time of day? Short blond people vs. tall blond people, short dark-haired people vs. tall dark-haired people. What about redheads of either height? Who will pay for all this testing? Who will really care? All of these questions and any more we can think of are variables that have to be factored into setting up the experiment.

Statistics recognize the fact that it is not possible to account for all the variables. A margin of error is built into the mathematical calculations to offset that problem. Whenever you see or hear of, for instance a political poll, and it says there is a margin of error of plus or minus so many points or numbers, that is what it means. Often we hear of an opinion poll in which it is stated that it is not a scientific poll. That means no hypothesis has been set up ahead of time to test the validity statistically.

Validity means, do the results accurately reflect the opinion of the wider population. For example, say a particular television program asks are you in favor of this politician's views. How many people will respond either by phone or e mail? How many are even at home? How many are tuned to that particular program at that particular time out of the hundreds of possible television channels? There are other things to do beside watch television even if the people are at home. How many have computers and are hooked up to e mail? What if a person wants to respond but there is a power short and he can't. Major frustration! Thus, the poll does not represent a random sample of all people and cannot be considered scientific or valid.

Probability has to do with the predictability that an event will occur in the future based on the correlation between cause and effect.

Demographics are groups of people in specific categories such as age, sex, religion, race, ethnic background and socio-economic status as well as combinations of those categories. Samples of the people in these demographics are used for political surveys to try to determine what the outcome of an election will be. The predictions can be quite accurate for the trend of groups but not for individuals. People have a way of changing their minds from poll to poll as circumstances and current events change.

Believe it or not, these variables and their inherent headaches have been worked out pretty well and fairly accurate predictions have and are being made every day by use of extremely complex mathematical calculations. It works for perhaps the majority of people but there are always individual exceptions to the predictions.

The key is that the scientists have to spell out the hypotheses in great detail, exactly what is their premise, how they intend to carry out the experiment and what conclusions they hope to find and, in the end, do find. Many of the experiments involve years of study. The most important outcome is that other scientists have to be able to use the same techniques and come up with the same deductions. No fudging with the data at any stage! Other scientists will pick up on it when they try to replicate the experiment.

Many of the remarkable advances in medicine are the result of this scientific method of experimentation and the statistical analysis that follows. Research into the causes, treatment and even cures for cancer, heart disease and the myriad of other ills, that plague mankind have been made possible in this way.

If an experiment has been scrupulously outlined in the hypothesis and carried out according to procedures, it may indicate that such-and-so is true for a majority of people or events. The highest number of subjects will fall into clusters, around the middle of the Bell Curve but then taper off toward either end. Since there are no absolutes in science, predictably there will always be a scattered few at each end of the curve. Everybody has an aunt or a grandfather that is an exception to the rule.

This gives rise to the old adage, "There are three kinds of lies: lies, damn lies and statistics!"

Another interesting use of statistics is in marketing. People's buying habits are studied carefully. The placement of products on shelves and aisles are no accident. As you push your shopping cart through the market, no matter how well you know where things are in the aisles, the brands the store is trying to promote are place in the most prominent and convenient shelves.

If there is a particular item you want, you may have to hunt for it and perhaps find it down low or up high. That is no accident either. In your search, you may spot other items you might buy that are not on your list. The whole objective is to get you to buy, buy, buy!

On the six o'clock news there are usually a few minutes devoted to health studies. The results are coached in weasel words such as "indicates", "may cause", "might be" and other disclaimers. We perk up our ears and, if a prestigious institution carried out the study, then it must be true and we tell all our family and friends. Further if any authority figure or your mother tells you something from her vast storehouse of wisdom, it has to be true, right? With all due respect, maybe so, maybe not.

There is an old parlor game called "Gossip". At a party everyone sits around in a circle. Someone writes down a few sentences on a piece of paper and once he/she has read it, whispers the message to the person sitting next to him/her. The whispering goes on around the circle. The last person says what he/she has heard. The difference between what is on the paper and what the last person said can be hilarious or frightening.

The tabloid press and some TV talk shows and talk radio seem to think they have elevated malicious gossip to an art form, for heaven's sake! The constant barrage of the same commercials over and over again illustrates the belief that if something is repeated often enough, it has to be true, right? Not necessarily but we all fall into the same trap of believing it must be true.

I am not an advocate of paranoia, but a little healthy skepticism can be a good thing.

Statisticians make extensive use of demographics. Have you noticed whenever you buy something such as a camera or appliance, there is a warranty card for you to fill out. On the back there is invariably a survey asking all kinds of personal information. Nosy. But that information is cranked into a computer and the results are used to determine which groups to target in advertising. You do not see feminine hygiene products advertised during football games nor do you see breaks for beer commercials in the course of soap operas.

We are a fear and anxiety driven society of consumers. Madison Avenue assumes that we are dirty, ugly, fat, sick, smelly, too young or too old and/or stupid. Obviously, these are bad things to be. As a result, we are insecure about everything. On top of that, we are stressed out because of all these faults. Naturally, it has just the product to fix our shortcomings - everything from what deodorant to wear so we won't smell bad and offend to what cosmetics to use to make us more attractive. We are asked do we suffer from this or that symptom? Here is the product to cure it. Do we feel unappreciated and unloved? This product will make our work more productive, we will be promoted and on top of that if we drive this particular car we will be sexier!

Once when our boys were in grade school we were preparing for school to start. The boys had seen commercials for a particular brand of sneakers that could make kids run faster and jump higher. Right there on TV was the proof! Images of boys their age were speeding along and jumping to heights that would make Superman envious! Of course the sneakers were outrageously expensive.

That time I sprang for the costly sneakers and although they looked quite handsome, our boys found to their dismay that they could not run or jump any better than before. Disillusioned, they learned not to believe everything they saw on TV.

Whether we like it our not, we are influenced and even manipulated by what we see, hear and read, often without even being aware of it. It is wise to check more than one source before drawing a conclusion. No one has a lock on the ultimate truth.

My mother taught me something once long ago that has resonated with me all these years. If you point an accusatory finger at someone else, look at your hand. The index finger points out toward the object of contempt but three of your own fingers are pointed at yourself. Perhaps if we pointed appreciative fingers at others, we would be saying nicer things about ourselves!

Before we pass critical judgment on anybody else, we should be reminded that there is not a one of us who doesn't have his/her feet firmly planted in clay from time to time. But each and every one of us has the potential to soar to heights of human kindness and achievement.