Question

what percentage of the data values falls between the values of 27 and 45 in the data set shown? 25% 75% 50% 100%

Explanation:

Step1: Recall the properties of a box - and - whisker plot

In a box - and - whisker plot, the box represents the inter - quartile range (IQR). The left end of the box is the first quartile ($Q_1$) and the right end is the third quartile ($Q_3$). The whiskers represent the range of the data. The value of $Q_1$ is the value below which 25% of the data lies, and $Q_3$ is the value below which 75% of the data lies.

Step2: Analyze the given box - and - whisker plot

The left end of the box (lower quartile, $Q_1$) is at 33 and the right end of the box (upper quartile, $Q_3$) is at 45. The lower whisker is at 27. But when calculating the percentage of data between 27 and 45, we note that 27 is the minimum value (assuming the whisker starts at the minimum). The formula for the percentage of data between two values in a box - and - whisker plot:
The percentage of data between the minimum and $Q_3$:
The percentage of data between the minimum (27) and $Q_3$ (45) is 75% because $Q_3$ represents the 75th percentile.

Answer:

75%