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Why do we use standard deviation? Why do we use averages?

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Define standard deviation. Define mathematical averages. Why is the standard deviation less than the mathematical average? Why do we use standard deviation? Why do we use a mathematical average?

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Define standard deviation

The standard deviation is the spread of the data around the mean. Here is a visual using a normal distribution (symmetrical shape of data):

See attached for diagram

Standard Deviation vs Mathematical Averages
Define standard deviation. Define mathematical averages. Why is the standard deviation less than the mathematical average? Why do we use standard deviation? Why do we use a mathematical average?
Define standard deviation

The standard deviation is the spread of the data around the mean. Here is a visual using a normal distribution (symmetrical shape of data):

See attached for diagram

In the distribution to the left, the standard deviation is larger with data falling farther away from the mean than in the data distribution to the right.

Define mathematical averages

The math average is just all the data points added up and divide by the number of data points. This average is the mean (center of the distributions above).

Why is the standard deviation less than the mathematical average?

The standard deviation is how far away from the mean most of the data points occur. Some will be close and some will be far. The degree of dispersion is the standard ...

Solution Summary

Your tutorial is 361 words plus a diagram to give you a visual. This is a theoretical discussion (no computations or equations) suitable for a novice as it is in everyday language.

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