Question

the organizers of the red maple college fun run gathered data about the runners ages. this box plot shows the results. runners ages what percent of the runners were between 20 and 45 years old? % submit

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), from the first quartile ($Q_1$) to the third quartile ($Q_3$), which contains 50% of the data. The median ($Q_2$) divides the box into two halves. The whiskers extend to the minimum and maximum values within 1.5 times the IQR.

Step2: Identify quartile values

Assume the box - plot has $Q_1 = 20$, $Q_2=30$, $Q_3 = 40$. The lower whisker starts at 15 and the upper whisker ends at 65. The value 45 is at the end of the box (i.e., $Q_3$).

Step3: Calculate the percentage

The value 20 is $Q_1$ and 45 includes all the data from $Q_1$ and the entire middle 50% (from $Q_1$ to $Q_3$) plus some additional data. Since $Q_1$ represents the 25th percentile and $Q_3$ represents the 75th percentile, and 45 is at or near $Q_3$, the percentage of data between 20 and 45 is 75%.

Answer:

75