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  • Here is a visual representation of a Normal distribution.

  • You have surely seen a normal distribution before as it is the most common one.

  • The statistical term for it is Gaussian distribution, but many people call it the Bell Curve as

  • it is shaped like a bell.

  • It is symmetrical and its mean, median and mode are equal.

  • If you remember the lesson about skewness, you would recognize it has no skew!

  • It is perfectly centered around its mean.

  • Alright.

  • So, it is denoted in this way.

  • N stands for normal, the tilde sign denotes it is a distribution and in brackets we have

  • the mean and the variance of the distribution.

  • On the plane, you can notice that the highest point is located at the mean, because it coincides

  • with the mode.

  • The spread of the graph is determined by the standard deviation.

  • Now, let’s try to understand the normal distribution a little bit better.

  • Let’s look at this approximately normally distributed histogram.

  • There is a concentration of the observations around the mean, which makes sense as it is

  • equal to the mode.

  • Moreover, it is symmetrical on both sides of the mean.

  • We used 80 observations to create this histogram.

  • Its mean is 743 and its standard deviation is 140.

  • Okay, great!

  • But what if the mean is smaller or bigger?

  • Let’s first zoom out a bit by adding the origin of the graph.

  • The origin is the zero point.

  • Adding it to any graph gives perspective.

  • Keeping the standard deviation fixed, or in statistical jargon, controlling for the standard

  • deviation, a lower mean would result in the same shape of the distribution, but on the

  • left side of the plane.

  • In the same way, a bigger mean would move the graph to the right.

  • In our example, this resulted in two new distributionsone with a mean of 470 and a standard

  • deviation of 140 and one with a mean of 960 and a standard deviation of 140.

  • Alright, let’s do the opposite.

  • Controlling for the mean, we can change the standard deviation and see what happens.

  • This time the graph is not moving but is rather reshaping.

  • A lower standard deviation results in a lower dispersion, so more data in the middle and

  • thinner tails.

  • On the other hand, a higher standard deviation will cause the graph to flatten out with less

  • points in the middle and more to the end, or in statistics jargonfatter tails.

  • Great!

  • In our next lesson, we will use this knowledge to talk about standardization.

  • Stay tuned!

Here is a visual representation of a Normal distribution.

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B1 中級

正規分布 (The Normal Distribution)

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    林宜悉 に公開 2021 年 01 月 14 日
動画の中の単語