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• Welcome back!

• In this lecture we are going to introduce one of the most commonly found continuous

• distributionsthe normal distribution.

• For starters, we define a Normal Distribution using a capital letter N followed by the mean

• and variance of the distribution.

• We read the following notation asVariable “X” follows a Normal Distribution with

• meanmuand variancesigmasquared”.

• When dealing with actual data we would usually know the numerical values of mu and sigma

• squared.

• The normal distribution frequently appears in nature, as well as in life, in various

• shapes of forms.

• For example, the size of a full-grown male lion follows a normal distribution.

• Many records suggest that the average lion weight between 150 and 250 kilograms, or 330

• to 550 pounds.

• Of course, there exist specimen which fall outside of this range.

• Lions weighing less than 150, or more than 250 kilograms tend to be the exception rather

• than the rule.

• Such individuals serve as outliers in our set and the more data we gather, the lower

• part of the data they represent.

• Now that you know what types of events follow a Normal distribution, let us examine some

• of its distinct characteristics.

• For starters, the graph of a Normal Distribution is bell-shaped.

• Therefore, the majority of the data is centred around the mean.

• Thus, values further away from the mean are less likely to occur.

• Furthermore, we can see that the graph is symmetric with regards to the mean.

• That suggests values equally far away in opposing directions, would still be equally likely.

• Let’s go back to the lion example from earlier.

• If the mean is 400, symmetry suggests a lion is equally likely to weigh 350 pounds and

• 450 pounds since both are 50 pounds away from that the mean.

• Alright!

• Instead of going through the complex algebraic simplifications in this lecture, we are simply

• going to talk about the expected value and the variance.

• The expected value for a Normal distribution equals its mean - “mu”, whereas its variance

• sigmasquared is usually given when we define the distribution.

• However, if it isn’t, we can deduce it from the expected value.

• To do so we must apply the formula we showed earlier: “The variance of a variable is

• equal to the expected value of the squared variable, minus the squared expected value

• of the variable”.

• Good job!

• Another peculiarity of the Normal Distribution is the “68, 95, 99.7” law.

• This law suggests that for any normally distributed event, 68% of all outcomes fall within 1 standard

• deviation away from the mean, 95% fall within two standard deviations and 99.7 - within

• 3.

• The last part really emphasises the fact that outliers are extremely rare in Normal distributions.

• It also suggests how much we know about a dataset only if we have the information that

• it is normally distributed!

• Fantastic work, everyone!

Welcome back!

B1 中級

# 正規分布を理解する [統計学チュートリアル] (Understanding the Normal Distribution [Statistics Tutorial])

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林宜悉 に公開 2021 年 01 月 14 日