Question

question #12 which set of numbers has the mean with the least value? i {-9, -7, 0, 4} ii {-7, -4, 6, 5} iii {1, 0.1, 0.05, 0.05} iv {0, 1/2, 1 1/2, 2} a - i b - ii c - iii d - iv

Explanation:

Step1: Recall mean formula

The mean 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 for 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 for set II

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

Step4: Calculate mean for 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 for set IV

For set IV $\{0,\frac{1}{7},\frac{1}{2},2\}$, rewrite the fractions as decimals: $\frac{1}{7}\approx0.143$, $\frac{1}{2}=0.5$. Then $n = 4$, $\sum_{i=1}^{4}x_i=0 + 0.143+0.5 + 2=2.643$, and $\bar{x}_{IV}=\frac{2.643}{4}=0.66075$.

Answer:

A. $\{-9,-7,0,4\}$