New Year and the Normal Curve

This is a strange title for my first post of 2025.

Normal Distribution is the most common or normal form of a distribution of random variables. We use this distribution to represent a large number of random variables. It serves as a foundation for statistics and probability theory. It also describes many natural phenomena, forms the basis of the Central Limit Theorem, and supports numerous statistical methods.[1]

Let me explain why this is important as we enter the new year.

The normal distribution is used to describe a variety of conditions. Don’t get hung up on the 1SD, 2SD, and 3SD labels on the axis. They represent the distance away from the mean or average value. For example, if a teacher wants to “curve” test results, she might use this curve. Perhaps the class average on a test is 50 out of 100 percent. She doesn’t want to fail half of the class, so she adjusts or “curve” the results. She selects 75% as the equivalent of 50%. A grade of “C” will be those students who receive a grade between -1SD and + 1SD. A “B” would be awarded to students whose grades are between +1SD and +2SD, and an “A” to those whose grades are equal to or greater than +3SD. On the other end of the curve, a grade between -1SD and -2SD is a “D,” and a grade less than or equal to -3SD is an “F.”

Suppose we want to chart “goodness. We might define a range between earthly angels or saints and earthly monsters or devils. Under the normal curve, we should have an equal number of saints as devils. We could also chart honesty with a range between liars and truthtellers.

This means that we know we have honest and good people in a world where dishonesty and evil prevail. This also means you can choose who you want to be and the people you want to associate with.


[1] “Normal Distribution,”https://www.geeksforgeeks.org/normal-distribution/, retrieved December 22, 2024.

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About Allen Mesch

Allen is an author, educator, and historian. He has written nine books: The Analyst; Teacher of Civil War Generals; Your Affectionate Father, Charles F. Smith; Charles A. Marvin - "One Year. Six Months, and Eleven Days", Preparing for Disunion, Ebenezer Allen - Statesman, Entrepreneur, and Spy, The Forgotten Texas Statesman, The Third Rebellion, and The Traitor. He taught classes on the American Civil War at Collin College. He has visited more than 130 Civil War sites and given presentations at Civil War Roundtables.
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