The 2 sigma comes from two standard deviation, sigma, the symbol for standard deviation.

2 sigma 来自两个均方差，sigma 是均方差的符。

Readers have to wait until page 65 before reaching the first serious concept, standard deviation, which feels too late.

读者得等上65页才能接触到第一个严肃的统计学概念——标准差，让人感觉度太慢。

1, 2, 3 standard deviations below the mean.

低于平均值 1、2、3 个标准差。

The critical variable was the standard deviation of the means divided by the mean of the standard deviations.

关键变量是均值的标准差除以标准差的均值。

It has a standard deviation of 0.7 liters or 0.7 liters.

它的标准偏差为 0.7 升或 0.7 升。

And we'll talk-- and we'll move into the standard deviation.

我们讨论——我们标准差。

So the standard deviation-- maybe I'll draw it this way.

所以标准偏差——也许我会这样画。

So this result right here is 3 standard deviations away from the mean.

所以这里的结果与平均值相差 3 个标准差。

Raymond, you were the one who scored one standard deviation higher than Debra.

雷蒙德，你的成绩应该比黛布拉高一个等级。

So based on the data given for this population, and using the standard deviation formula, what do you think this variable is?

以这个人口数据为基础再用标准差公式，你觉得变量是多少？

If I did 1 standard deviation, 2 standard deviations, 3 standard deviations-- that's in the positive direction.

如果我做了 1 个标准差、2 个标准差、3 个标准差——那就是正方向。

And then one standard deviation is going to be 0.7 liters away.

然后一个标准偏差是 0.7 升。

That right there is the standard deviation to the right, that's the standard deviation to the left.

右边是右边的标准差，左边是标准差。

So we go down another standard deviation in that direction and another standard deviation above the mean.

所以我们在那个方向上再下降一个标准差，在平均值之上再下降一个标准差。

Now if we're talking about two standard deviations around the mean-- so if we go down another standard deviation.

现在，如果我们谈论均值附近的两个标准差——那么如果我们再下降一个标准差。

So above three standard deviations below the mean, and below three standard deviations above the mean.

所以高于均值三个标准差，低于均值三个标准差。

That we are less than 2.02 standard deviations above the mean.

我们比平均值高出不到 2.02 个标准差。

So they gave us the mean and the standard deviation.

所以他们给了我们平均值和标准差。

And we know that the standard deviation is equal to-- I'll write the 0 in front, 0.7 liters.

我们知道标准偏差等于——我会在前面写上 0，即 0.7 升。

The standard deviation-- actually maybe put it a better way.

标准差——实际上也许可以用更好的方式表达。