3.8 是 5 个正数 a, b, c, d 和 e 的平均数。
它们的平方和为 360。现在将每个数都乘以 2。
求新的标准差。 答：...

1. Find the original standard deviation from the mean and sum of squares.

For the original 5 numbers,
$\bar{x}=3.8,\quad n=5,\quad \sum x^2=360.$
$\text{standard deviation}=\sqrt{\frac{360}{5}-(3.8)^2}$
$=\sqrt{72-14.44}$
$=\sqrt{57.56}$

2. Apply the effect of multiplying all data values by 2.

When each number is multiplied by $2$, the standard deviation is also multiplied by $2$.
$\text{new standard deviation}=2\sqrt{57.56}$
$=16.96\ldots$