Prep DS - 34 标准方差题

yongwangzhiqian

34.  

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.

选A,能请大家说一下思路吗？看着这么长的题心就慌。谢谢了。 

选A,能请大家说一下思路吗？看着这么长的题心就慌。谢谢了。 

GreenHorse

题目长的问题关键要看清楚关键字和隐含条件。

这道题目说的其实就是标准差与平均数的关系。方差是（样本减去平均值）平方的和，最后在除以样本个数n。标准差是方差开根号，是一样的道理。

条件1，由于每桶水是按比例下降30%，所以样本值下降30%，平均值下降30%，

（70%x1-70%a)^2+(70%x2-70%a)^2……可以把70%提出来。这样就可以把标准差算出来了。

条件2，光知道平均值没有用的，因为每桶水抽得量不知道，不能算标准差。

yongwangzhiqian

谢谢你精彩的解释，totally understood!

zhousaints

同意楼上说法。必须清楚each tank的增减情况才能影响到方差.