Question

Find the range and mean of each data sa Use your results to compare the two data setsSet 2 10 8 19 23See. 14 16 15 17 16The range of set AS(Type an integer or a decimal.)

Answer 1

The two data sets are given as follows:

$\begin{gathered} A=\mleft\lbrace2,10,8,19,23\mright\rbrace \\ B=\mleft\lbrace14,16,15,17,16\mright\rbrace \end{gathered}$

The mean is calculated as

$\bar{X}=\frac{\text{Sum of numbers}}{Number\text{ of numbers}}$

For Set A:

$\begin{gathered} \bar{X_A}=\frac{2+10+8+19+23}{5} \\ \bar{X_A}=12.4 \end{gathered}$

For Set B:

$\begin{gathered} \bar{X_B}=\frac{14+16+15+17+16}{5} \\ \bar{X_B}=15.6 \end{gathered}$

The median is calculated as

$M=\text{Highest number - Lowest number}$

For Set A:

$\begin{gathered} \text{Highest Number = 23} \\ \text{Lowest Number = 2} \\ M_A=23-2 \\ M_A=21 \end{gathered}$

For Set B:

$\begin{gathered} \text{Highest Number = 17} \\ \text{Lowest Number = 14} \\ M_B=17-14 \\ M_B=3 \end{gathered}$

From the values Set B has a higher mean than that of Set