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

• The data vary by a range of 16 years.

,

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

Step-by-step 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=}(4+6)/(2)=(10)/(2)=5 \\ \text{Third Quartile=}(11+13)/(2)=(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.