GRE数学题，麻烦大神们帮我看一下SetXconsistsof100numbers.Theaverage(arithmeticmean)ofsetXis10,andthestandarddeviationis4.6.Whichofthefollowingtwonumbers,whenaddedtosetX,willdecreasetheset’sstandardd

Question

GRE数学题，麻烦大神们帮我看一下
Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?
-100 and -100
-10 and -10
0 and 0
0 and 20
10 and 10

Answer 1

必须是10和10啊，方差是[(X1-平均)^2+(X1-平均)^2......+(X100-平均)^2]/100如果增加X101＝10和X102=10，分母上面的和不变，因为(X101-平均)^2＋(X102-平均)^2=0＋0=0，而分母变成了102，所以除得的数值就会变小。如...