一道机经

smart

有四个数（其实有一些描述，但是简单说就是这样），问standard deviation
A, range=0
B, 其中一个数是**（一个具体的数）
思路：range=0，说明四个数相等，因此平均数M就等于这四个数，
standard deviation=[（X1-M）^2+(X2-M)^2+(X3-M)^2+(X4-M)^2]^(1/2), 其实就是每个数减掉平均数之后的平方和再开方，因为四个数与平均数相等，所以平方和为0，所以standard deviation=0, 根据条件2算不出SD, 所以答案选A
[确认]：A
[思路]：如JJ作者思路，
standard deviation^2=[ (X1-M)^2+(X2-M)^2+(X3-M)^2+(X4-M)^2] /4


I don't agree with the solution...
range=0  means all of the 4 number is  equal?
range= the largest number - the smallest number... am I right?
if I am right, the answer of this question should be E, not A

your understanding about range :range= the largest number - "the smallest number"is right, but do you think about two other numbers  when the largest number is equal to the smallest one. If two other numbers were different, the subtraction of these two numbers would not be zero and therefore the range of the sequence would not be 0, thus contradicting the question. So the answer should be A.