Times n times the mean of the xy values, the arithmetic mean.

乘以 n 乘以 xy 值的平均值，即算术平均值。

And remember, expected value, in a lot of contexts, you could view it as just the arithmetic mean.

请记住，期望值，在很多情况下，您可以将其视为算术平均值。

They are the mean-- actually, there are types of means, but we'll stick with the arithmetic mean.

它们是平均值——实际上，有多种类型的平均值，但我们将坚持使用算术平均值。

The arithmetic mean was skewed by what they'd call an outlier.

算术平均数被​​他们所谓的异常值所扭曲。

So the mean, or the arithmetic mean, is probably what you're most familiar with when people talk about average.

所以当人们谈论平均值时，平均值或算术平均值可能是您最熟悉的。

But the idea is almost as straightforward as the arithmetic mean.

但这个想法几乎和算术平均数一样简单。

So the arithmetic mean of both of these populations are the same number.

所以这两个总体的算术平均值是相同的数字。

So instead of taking the mean-- let's say how I wanted to calculate the average by taking the arithmetic mean.

因此，与其取平均值，不如说我想如何通过取算术平均值来计算平均值。

And then you take the arithmetic mean of those two numbers.

然后你取这两个数字的算术平均值。

Well, here, sure their mean, their arithmetic mean, is 2.5, but they're further away from 2.5.

好吧，在这里，确定他们的平均值，他们的算术平均值，是 2.5，但他们离 2.5 更远。

Why don't we just use arithmetic mean all the time?

为什么我们不一直使用算术平均数呢？

So what's the arithmetic mean here?

那么这里的算术平均值是多少？

But if we're being a little bit more particular, this is the arithmetic mean of this set of numbers.

但如果我们更具体一点，这就是这组数字的算术平均值。

If you think about the squared distance from some central tendency, and the best central measure we can have of y is the arithmetic mean.

如果你考虑与某种集中趋势的平方距离，我们可以得到的 y 的最佳集中度量是算术平均值。

In every day speak when people talk about an average-- I think you've already computed averages in your life-- they're usually talking about the arithmetic mean.

在每天的谈话中，当人们谈论平均数时——我想你在生活中已经计算过平均数——他们通常在谈论算术平均数。

So normally when someone says, let's take the average of these numbers and they expect you to do something, they want you to figure out the arithmetic mean.

所以通常当有人说，让我们取这些数字的平均值并且他们希望你做某事时， 他们希望你计算出算术平均值。

So if I take the average of 3 and 3-- I should be particular with my language-- if I take the arithmetic mean of 3 and 3, I get 3.

所以如果我取 3 和 3 的平均值——我应该特别注意我的语言——如果我取 3 和 3 的算术平均值，我得到 3。

Instead of taking the arithmetic mean of this entire group of 150 million people, I might just be happy taking the mean of this sample, and that'll be called the sample mean.

与其取整个 1. 5 亿人群体的算术平均值，不如取这个样本的平均值， 这将被称为样本平均值。

Hopefully now, we can kind of connect what we thought about in terms of just arithmetic mean and central tendency and population versus sample, and then connect that to the notion of a random variable.

希望现在，我们可以将我们在算术平均数和集中趋势以及总体与样本方面的想法联系起来， 然后将其与随机变量的概念联系起来。