Question

The double box-and-whisker plot shows the ages of the viewers of two television shows in a small town.

Compare the data sets using measures of center and variation.

Answer 1

Step 1: Data of Show $A=3540455055$

Median of Show $A=55$

Mean of Show $A=35+40+45+50+55÷2=225÷5=45$

Variation of Show

$$\begin{gathered} A={(35-45)}^2+{(40-45)}^2+{(45-45)}^2+{(50-45)}^2+{(55-45)}^2÷2 \\ ={(-10)}^2+{(-5)}^2+{\left(0\right)}^2+{\left(5\right)}^2+{\left(10\right)}^2÷5 \\ =100+25+0+25+100÷5 \\ =250÷5 \\ =50 \end{gathered}$$

Step 2: Data of Show $B=2025354055$

Median of Show $B=35$

Mean of Show $B=20+25+35+40+55÷5=35$

Variation of Show

$$\begin{gathered} B={(20-35)}^2+{(25-35)}^2+{(35-35)}^2+{(40-35)}^2+{(55-35)}^2÷5={(-15)}^2+{(-10)}^2+{\left(0\right)}^2+{\left(5\right)}^2+{\left(5\right)}^2÷5 \\ =225+100+25+25÷5 \\ =375÷5 \\ =75 \end{gathered}$$

Hence, The Show A center is likely to be greater than the measures of the center of Show B. Variation of show B is greater than Variation of show A.