某公司 10 位员工的月工资（单位：元）为 x_ 1 ,…——2014 高考数学第 9 题答案解析

## 【答案】 $D$

## 【解析】

试题分析：由题得：$x_{1}+x_{2}+\cdots+x_{10}=10 \times \bar{x}=10 \bar{x} ;\left(x_{1}-\bar{x}\right)^{2}+\left(x_{2}-\bar{x}\right)^{2}+\cdots+\left(x_{10}-\bar{x}\right)^{2}=10 \times s^{2}=10 s^{2}$若从下月起每位员工的月工资增加 100 元，则这 10 位员工下月工资的均值和方差分别为：
均值 $\bar{y}=\frac{\left(x_{1}+100\right)+\left(x_{2}+100\right)+\cdots+\left(x_{10}+100\right)}{10}$

$$ =\frac{\left(x_{1}+100\right)+\left(x_{2}+100\right)+\cdots+\left(x_{10}+100\right)}{10}=\frac{\left(x_{1}+x_{2}+\cdots+x_{10}\right)+10 \times 100}{10}=\frac{10 \bar{x}+10 \times 100}{10}=\bar{x}+100 $$

方差 $=\frac{\left[\left(x_{1}+100\right)-(\bar{x}+100)\right]^{2}+\left[\left(x_{2}+100\right)-(\bar{x}+100)\right]^{2}+\cdots+\left[\left(x_{10}+100\right)-(\bar{x}+100)\right]^{2}}{10}$

$$ =\frac{\left(x_{1}-\bar{x}\right)^{2}+\left(x_{2}-\bar{x}\right)^{2}+\cdots+\left(x_{10}-\bar{x}\right)^{2}}{10}=\frac{10 s^{2}}{10}=s^{2} $$

故选 $D$
考点：均值和方差．