Question

The ages of the cousins in the Miller family are 2. 18, 6, 13, 8, 6, 11, and 4 years. Use the range and interquartile range to describe how the data vary.The data vary by a range of ____years. The middle half of the data values vary by ____years

Answer 1

Answer:

• The data vary by a range of 16 years.

,

• The middle half of the data values vary by 7 years.

Explanation:

The ages of the cousins in the Miller family are 2, 18, 6, 13, 8, 6, 11, and 4 years.

Arranging the ages in ascending order gives:

$2,4,6,6,8,11,13,18$

First, determine the range.

$\begin{gathered} \text{Range}=\text{Highest Value-Lowest Value} \\ =18-2 \\ =16 \end{gathered}$

Next, determine the interquartile range:

$\begin{gathered} \text{Interquartile Range=Third Quartile-First Quartile} \\ \text{First Quartile=}\frac{4+6}{2}=\frac{10}{2}=5 \\ \text{Third Quartile=}\frac{11+13}{2}=\frac{24}{2}=12 \\ \implies\text{IQR}=12-5=7 \end{gathered}$

Therefore, we conclude that:

The data vary by a range of 16 years. The middle half of the data values vary by 7 years.