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 What makes a normal distribution normal? -2

Good question ...
What is 98.60 degrees normal?
What makes people sane?

As a rule, references to a statistical distribution or simply “distribution” mean “frequency distribution”. That is, what is the number of times or the frequency with which each value occurs in the distribution.

As it turned out, a large percentage of all frequency distributions correspond to the same set of criteria. Such contributions are called “normal.” A more popular term is the “bell curve”.

NOTE: “Bell” is not a technical term. However, since the term "stuck", for convenience, it is used in this series.

These normal types of distributions have many applications in market research and other statistical applications. Many statistical theories applicable to market research suggest normal distributions.

Examples of normal distributions in humans include: height; the weight; test results, especially for standardized tests such as IQ; and various abilities, practices, tastes and preferences. Everyone assumes that a large number of people are "measured." One of the notable exceptions is the earnings, which will be discussed in the next article with irregular rates.

Normal distributions are also common in nature and in business. For example, lamp packs contain information on the number of hours for which the lamp should be designed, watts (energy used) and lumens (light output).

Each of these numbers is the arithmetic average of the frequency distribution generated when testing a large number of light bulbs. Each of these distributions is bell-shaped or normal.

So what are the criteria for normalizing distribution?

1) Distribution is unimodal (only one most common value).
2) The arithmetic mean, mode and median have the same value. This value is a value that represents the highest point in the distribution;
3) The distribution is bilaterally symmetrical.
WHAT?!
Bilateral symmetric means that the left half is a mirror image of the right half (unless you are left, then the right half is a mirror image of the left half).
4) One standard deviation - here indicated as 1OOE - measured each way from the arithmetic mean (what is called plus or minus one standard deviation or ± 1OOE) is just over 68 percent of all values ​​in distribution. ± 1.96 OOE represent an average of 95 percent of the values. You can go to easily accessible tables to find out how many standard deviations from the average are related to what percentage of all values ​​in the distribution. This percentage is often called the “area under the curve.” For example, ± 1OOE covers just over 68 percent of the area under the curve. The curve is a graphical representation of the frequency distribution.
and
5) There are other criteria, but the main ones (at least for the moment).

Normal distributions come in different sizes and shapes, but they all meet the above criteria. Some normal distributions look as if they are relatively short and common; other normal distributions look relatively tall and thin. The largest percentage of all normal distributions is between these more extreme forms and are true bell curves.

In market research, you can ask consumers how they will evaluate the services they received. A properly designed survey will give options such as “excellent” “good” “honest” “poor” “very bad”. The future article will address the problems of such surveys. The point here is that the choice should be symmetrical in terms of balancing the elections around the middle of distribution. Results should ensure a normal distribution. If the results are not “normally distributed,” you should be suspicious of the results. Contrary to what many think, not everything is good or excellent.




 What makes a normal distribution normal? -2


 What makes a normal distribution normal? -2

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