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What are the implications of statistical variation?

Variation in the Universe

What are the implications of statistical variation? Why are we interested in understanding and measuring variation?

Besides using variation in the world of quality, there are also social implications. For example, what does statistical variation suggest about how we ought to judge and treat ourselves and others? Cite an example of these implications from your own experience.

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Statistical variation gives us an idea of the spread of the data points above and below the mean or median. We are interested in understanding the variation because the spread of data tell us whether the points are mostly alike or widely different. For example, what if I gave a test and the mean was 80%. If the standard deviation was 4 points, then all the scores were within 68%-92% (about 3 standard deviations gets 99% of the points) and I might be pleased with this result. If the mean was 80% but the standard deviation was 16, then the range was much wider between the high and low scores, meaning that for every high score, there were failing scores. I might be less impressed with that result, even though the mean ...

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Your tutorial is 536 words and includes a visual diagram, two practice examples and clear explanations of the concepts in everyday language suitable for a novice.