Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?I

题目

Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?

I. r - 2, s - 2, t - 2

II. 0, r - s, t - s

III. r - 4, s + 5, t - 1

选项

I only

II only

I and II only

I and III only

I, II, and III

解析

如果给集合中的每一项都加上或减去一个常数，**标准差不会改变**。 - 集合\(\{r-2, s-2, t-2\}\)是给\(\{r, s, t\}\)的每一项减去2得到的； - 集合\(\{0, r-s, t-s\}\)是给\(\{r, s, t\}\)的每一项减去\(s\)得到的； - 集合\(\{r-4, s+5, t-1\}\)与\(\{r, s, t\}\)完全无关（不是统一加减常数）。因此答案是仅I和II。答案：C

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