This unique population distribution creates a lot of fascinatingly bizarre situations across the continent.

这种独特的人口分布在整个大陆上形成了许多令人着迷的怪异情况。

So let's look at the population distributions here.

那么让我们看看这里的人口分布。

Once again, it'll be a narrower distribution than the population distribution.

再一次，它将是一个比人口分布更窄的分布。

The population distribution for y divided by m.

y 的人口分布除以 m。

Because scoring is now based on a statistical population distribution among age peers, rather than simply dividing the mental age by the chronological age and multiplying by 100.

因为现在分数计算是以同龄群体在统计学意义上的人口分布为基础的，而不是简单地用智力年龄除以生理年龄再乘以 100。

Then you're taking m samples from this population distribution up here, taking its mean.

然后你从这里的这个人口分布中抽取 m 个样本，取其平均值。

Our population distribution has-- or maybe I should write 30% have internet access.

我们的人口分布——或者我应该写 30% 的人可以上网。

Now what are these, in terms of the original population distribution?

现在，就原始人口分布而言，这些是什么？

In fact, our standard deviation became smaller than our original population distribution, or our original probability density function.

事实上，我们的标准偏差变得小于我们原来的人口分布，或者我们原来的概率密度函数。

You sum them all up, you would get 60% saying yes, and that's exactly what our population distribution told us.

你把它们加起来，你会得到 60% 的人说是，这正是我们的人口分布告诉我们的。

This is right here is the same thing as the variance of our population distribution.

这与我们的人口分布方差是一回事。

This is the actual population distribution, not the sampling distribution of the sample mean.

这是实际的总体分布，而不是样本均值的抽样分布。

So there's some population distribution here.

所以这里有一些人口分布。

So this is what the population distribution looks like based on our assumption, based on this assumption right over here.

这就是基于我们假设的人口分布，基于这里的假设。

We know that this thing is the same thing as the variance of the population distribution divided by n.

我们知道这个东西和人口分布的方差除以n是一回事。

Mexico ended up discovering exactly how to transform their mostly negative geography into a positive and will be interesting to see how that influences the pace of Mexico's population distribution over the coming decades.

墨西哥最终发现了如何将其不利的地理位置转化为有利的地理位置，这将对墨西哥未来几十年的人口分布速度产生怎样的影响，让我们拭目以待。

So what z is, z is a random variable where you're taking n samples from this distribution up here, this population distribution, taking its mean.

那么 z 是什么，z 是一个随机变量， 你从这里的这个分布中抽取 n 个样本， 这个人口分布， 取它的均值。

And we know that the mean of each of the sampling distributions is actually the same as the mean of the population distributions.

我们知道每个抽样分布的均值实际上与总体分布的均值相同。

You take the square root of this, you get the standard deviation of the difference of the sample means is equal to the square root of the population distribution of x.

你取这个的平方根，你得到样本均值之差的标准差等于 x 的总体分布的平方根。

And when you don't know anything about the population distribution, the thing that we've been doing from the get-go is estimating that character with our sample standard deviation.

当你对人口分布一无所知时，我们从一开始就做的事情就是用我们的样本标准差来估计这个特征。