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According to Wikipedia the way those involved in probability analysis and statistical analysis, like scientists and actuaries, for example, explain the mean and standard deviations from the mean is as follows:

“At least 75% of the values in any population are at most two standard deviations away from the mean (see Chebyshev’s inequality). The actual percentage depends on the distribution, for example approximately 95% if the population has a normal distribution.

A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean.

The term standard deviation was introduced to statistics by Karl Pearson On the dissection of asymmetrical frequency curves, 1894.

The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean. For example, in the population {4, 8}, the mean is 6 and the standard deviation is 2. This may be written: {4, 8} ˜ 6±2. In this case 100% of the values in the population are within one standard deviation of the mean.

Standard deviation is the most common measure of statistical dispersion, measuring how spread out the values in a data set are. If the data points are all close to the mean, then the standard deviation is close to zero. If many data points are far from the mean, then the standard deviation is far from zero. If all the data values are equal, then the standard deviation is zero.”

Unoh. This may not be as easy of a concept to understand as we had anticipated.

Most folks have seen a chart presentation of the bell shaped curve. This is a presentation chart used by scientist, economists, and even marketers, to show the distribution of data points in a population of collected data. Since about 95% of the population of data points will be centered in a normal distribution the curve will have a high point in the center and on each side of the center will be long tails that gradually approach zero.

You know what a bell looks like, right?

Why is all of this important as we explore self improvement, life,  and the human experience?

Well, most of the time most of us operate within two standard deviations of the mean of normal behavior. Normal being defined as behavior that is widely expected and approved of by the population of the societies that we live in. So our normal “data points” of behavior may be to get married by the time we are 35, to work for a boss or big corporation or the government, to retire at age 65, to obey the law, and so forth. If our activities are being plotted they will be near the high point or center of the bell shaped curve. 

The interesting thing, however, is that at times not only individuals but entire populations can have their concept of what is normal shifted to several deviations from the old mean. This places their collective behavior far to the left or right of what is or used to be the center.

For example, someone who has been a good citizen all of his life but who in a moment of rage kills his wife has just made the long leap from being centered with most or all of his behavior to being way out on the long tail of the distribution curve. Fortunately, there aren’t too many killers running around within our society even though at times it would seem so from the TV news stories.

Nazi Germany is a prime example (I won’t use the term good) of this distribution shift taking place among a large population. A large part of a well educated society who had a long legacy of accomplishment and had a history of having established an advanced culture evolved within a few years into a society that permitted severe and gross human rights violations even though only a small percentage of the population directly took part in committing atrocities.

How is this possible? And since it is possible how can we act to prevent acts that under a civilized society are considered unthinkable to become the norm? How can we protect ourselves and
our loved ones from becoming such unthinking spokes in the wheel that we allow ourselves in our behavior to become extreme deviations from the mean?

If most of an entire population moves in behavior to what was previously an extreme data point is the new horrible behavior now normal? If it is normal does that make it OK and right?

As you can see there are a lot of issues to think about as we examine extreme deviations from the mean as the model applies to human behavior. The possibility of entire population shifts in large enough numbers to create a new mean that was formally an extreme deviation is highly interesting as well as scary to contemplate if the shift is towards violence and a anything goes mentality.

But dear reader and fellow blogger we shall be brave and push forward into closely examining as many extreme deviations as we can find. Who should take responsibility for such extreme shifts in behavior?

I expect that exercise will keep us busy for a very long time. Deviations From the Mean, Part Three will be coming soon.                 

 
 

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