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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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# 正規分布 (The Normal Distribution)

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林宜悉 に公開 2021 年 01 月 14 日