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Standard Deviation & Bell-Shaped Curve

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What does the standard deviation unit really represent? Is the distinction among various parts of the bell-shaped curve arbitrary or is there certain logical and rational principle involved that creates such distinctive demarcations shown in a chart like this?

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This solution explains what the standard deviation unit really represents. By discussion and example, it also explains the concept of the bell-shaped curve and if the distinction among various parts are arbitrary or if there are certain logical and rational principle involved that creates such distinctive demarcations shown in a chart like this.

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Please see response below, which is also attached.

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Interesting question! Please see the response below. I provided an example to illustrate the theory and link to graphs representing the bell-shaped curve as well for further research and understanding.

Let's take a closer look. I added an example for illustrative purposes only.

1. What does the standard deviation unit really represent? Is the distinction among various parts of the bell-shaped curve arbitrary or is there certain logical and rational principle involved that creates such distinctive demarcations shown in a chart like this?

The standard deviation is a mathematical unit used to describe or represent the "spread" or dispersion of a set of data. Each item or unit in the data set has a deviation from the mean (the ordinary average) of the data. The standard deviation is computed by taking the squares of these individual deviations, averaging these squares, and then taking the square root. For instance, if the data set conforms to a known distribution, such as the normal ("bell curve") distribution, then one can compute the ...

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