Question

given the 3 sets of data below, rank the mean in order from lowest to highest. set 1 = { -4, -2, 0, 2, 4} set 2 = {-15, -12, 0, 10, 15} set 3 = { 30, 30, 30, 30, 30} set 2, set 1, set 3 set 3, set 2, set 1 set 2, set 3, set 1 set 1, set 2, set 3

Explanation:

Step1: Calculate mean of Set 1

The formula for the mean $\bar{x}$ of a set of numbers $x_1, x_2, \dots, x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. For Set 1: $\{-4, - 2,0,2,4\}$, $n = 5$. $\sum_{i=1}^{5}x_i=-4+( - 2)+0 + 2+4=0$. So mean $\bar{x}_1=\frac{0}{5}=0$.

Step2: Calculate mean of Set 2

For Set 2: $\{-15, - 12,0,10,15\}$, $n = 5$. $\sum_{i = 1}^{5}x_i=-15+( - 12)+0+10 + 15=-2$. So mean $\bar{x}_2=\frac{-2}{5}=-0.4$.

Step3: Calculate mean of Set 3

For Set 3: $\{30,30,30,30,30\}$, $n = 5$. $\sum_{i = 1}^{5}x_i=30\times5 = 150$. So mean $\bar{x}_3=\frac{150}{5}=30$.

Step4: Rank the means

Comparing the means: $\bar{x}_2=-0.4$, $\bar{x}_1 = 0$, $\bar{x}_3=30$. So the order from lowest to highest is Set 2, Set 1, Set 3.

Answer:

A. Set 2, Set 1, Set 3