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

2 sigma 来自两个均方差，sigma 均方差符号。

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?

以这个人口数础再用标准差公式，觉得变量多少？

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

雷蒙德，成绩应该比黛布拉高一个等级。

Do you know how to calculate the standard deviation ?

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中数计算标准差12.14。

What if we got two standard deviations more conscientious?

如果我们得到两个更认真标准差呢？

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

表 4 比较了于标准差和方差百分比。

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，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.

关键变量均值标准差除以标准差均值。

And the standard deviation is 0.5.

标准偏差 0.5。

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

所以它标准偏差会更小。

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

这本上只重新调整单位，使我们表达式标准差等于 1。

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

如果用它平方根来表示标准偏差，这就我们在这里所做， 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 年前更聪明了两个标准差。

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

标准差 9.07。 这在 Excel 中使用 STDEV 函数时将获得值。

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

图中箭头描绘了从平均值 (100) 到高于平均值 (100.75) 1 个标准差距离。

The total variation is based on the standard deviation.

总变异于标准差。

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两个标准差——那么如果我们再下降一个标准差。