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

2 sigma 来自两均方差，sigma 均方差的符号。

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

读者得上65页才能接触到第严肃的统计学概念——标准差，让人感觉进度太慢。

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

以这人口数据为基础再用标准差公式，你觉得变量多少？

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级。

Do you know how to calculate the standard deviation ?

你知道如何计算标准差吗？

The calculated standard deviation of the data in Table 2 is 12.14 .

表2中数据的计算标准差为12.14。

What if we got two standard deviations more conscientious?

如果我们得到两更认真的标准差呢？

Table 4 compares the percentages based on using the standard deviation and the variances.

表 4 比较了基于标准差和方差的百分比。

Let's say 2.79 is the standard deviation.

假设2.79标准偏差。

So, you know M for mean,   as for standard deviation but both in Greek.

所以，你知道 M 代表平均值，M 代表标准差，但两者都希腊语。

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

关键变量均值的标准差除以标准差的均值。

And the standard deviation is 0.5.

标准偏差为 0.5。

So it's going to have a smaller standard deviation.

所以它的标准偏差会更小。

Which basically just rescales the units so that the standard  deviation of our expression will equal one.

这基本上只重新调整单位，使我们的表达式的标准差于 1。

And if you take its square root for the standard deviation, which is what we do right here, it's 0.49.

如果你用它的平方根来表示标准偏差，这就我们在这里所做的， 它 0. 49。

DUCKWORTH: So, we've not only gotten smarter, we've become two standard deviations smarter than we were 100 years ago.

DUCKWORTH：所以，我们不仅变得更聪明了，而且比 100 年前更聪明了两标准差。

The standard deviation is 9.07. This is the value you will get if you use the STDEV function in Excel.

标准差为 9.07。 这在 Excel 中使用 STDEV 函数时将获得的值。

The arrow on the figure depicts the distance from the average (100) to 1 standard deviation above the average (100.75).

图中的箭头描绘了从平均值 (100) 到高于平均值 (100.75) 1 标准差的距离。

The total variation is based on the standard deviation.

总变异基于标准差。

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标准差——那么如果我们再下降标准差。