Question

question #10 which set of numbers has the mean with the greatest value? i {-9, -7, 0, 4} ii {-7, -4, 0, 5} iii {1, 0.1, 0.05, 0.05} iv {0, 1/2, 1 1/2, 2}

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ of a set of numbers $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.

Step2: Calculate mean of set I

For set I $\{-9,-7,0,4\}$, $n = 4$, $\sum_{i=1}^{4}x_i=-9+( - 7)+0 + 4=-12$, and $\bar{x}_I=\frac{-12}{4}=-3$.

Step3: Calculate mean of set II

For set II $\{-7,-4,0,5\}$, $n = 4$, $\sum_{i = 1}^{4}x_i=-7+( - 4)+0 + 5=-6$, and $\bar{x}_{II}=\frac{-6}{4}=-1.5$.

Step4: Calculate mean of set III

For set III $\{1,0.1,0.05,0.05\}$, $n = 4$, $\sum_{i=1}^{4}x_i=1 + 0.1+0.05 + 0.05=1.2$, and $\bar{x}_{III}=\frac{1.2}{4}=0.3$.

Step5: Calculate mean of set IV

For set IV $\{0,\frac{1}{2},\frac{1}{2},2\}$, rewrite $\frac{1}{2}=0.5$. Then $n = 4$, $\sum_{i=1}^{4}x_i=0 + 0.5+0.5 + 2=3$, and $\bar{x}_{IV}=\frac{3}{4}=0.75$.

Step6: Compare means

Since $0.75>0.3>-1.5>-3$, set IV has the greatest mean.

Answer:

D. IV