Question

the box plot below represents some data set. what percentage of the data values are between 110 and 170?

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR). The left side of the box is the first quartile ($Q_1$) and the right side is the third quartile ($Q_3$). The median is the line inside the box. The IQR contains 50% of the data. Also, the whiskers and the box together contain approximately 99.7% of the data in a normal - like distribution.

Step2: Identify quartile positions

Assume that 110 is close to $Q_1$ and 170 is close to $Q_3$.

Step3: Determine percentage

Since the data between $Q_1$ and $Q_3$ is the inter - quartile range, 50% of the data values are between $Q_1$ and $Q_3$. So, if 110 is $Q_1$ and 170 is $Q_3$, 50% of the data values are between 110 and 170.

Answer:

50%