Statistics is all about understanding the properties of a big group of numbers.
Ideally, you use the understanding to make better decisions.
Distribution and variation are for understanding: (1) how much a group of numbers is spread out … in high distribution you get a big difference between min and max values.
(2) how tightly grouped numbers are (variation).
Understanding that helps someone figure out and make decisions for a statistical study.
Things in the real world follow distributions.
If you learn well by example:
If I have two cooks and I want to test if they make burgers of the same weight I need to order a bunch of burgers and weight them. The weight of their burgers follow a DISTRIBUTION. The variance describes the width of the distribution. To test a hypothesis such as “each cook makes the same weight burger” I must know each distribution well enough to calculate a probability that each cook makes burgers that have the same distribution of weights.
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