机经里的一道题，求各位大神

fzygrrace · 发表于 2011-8-16 23:07:12

During an experiment, some water was removed from each of 6 water tanks.If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

为什么是A?

堕落雨季 · 发表于 2011-10-7 22:01:50

S2=0.7S1

马乙 · 发表于 2012-6-9 20:28:30

是0.49S1哦

sl200820 · 发表于 2013-2-25 13:16:16

方差性质，每一项同时增加或减少一样的数，方差不变，同时增加一样的倍数，方差也增加同样的倍数！

绝不放弃 · 发表于 2017-5-12 11:35:51

sl200820 发表于 2013-2-25 13:16
方差性质，每一项同时增加或减少一样的数，方差不变，同时增加一样的倍数，方差也增加同样的倍数！ ...

但是题目没说每个tank的volum是一样的啊。如果是不一样的，30%乘以不同的volume得到的是不一样的水量啊。每一项同时减少不同的水量方差还会一样吗

机经里的一道题，求各位大神

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