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}=(2+10+8+19+23)/(5) \\ \bar{X_A}=12.4 \end{gathered}`

For Set B:

`\begin{gathered} \bar{X_B}=(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