Question

The box plot of a data set is shown below. 

The interquartile range of the data set is _______ (in integer).

Hint:

The interquartile range (IQR) measures the spread of the middle 50% of the data, calculated as \( Q_3 - Q_1 \) using the values from the box plot.

Answer 1

Step 1: Identify the first and third quartiles from the box plot. From the box plot:
The first quartile (\( Q_1 \)) is located at 20.
The third quartile (\( Q_3 \)) is located at 35.
Step 2: Calculate the interquartile range (IQR). The interquartile range (IQR) is the difference between the third quartile (\( Q_3 \)) and the first quartile (\( Q_1 \)): \[ {IQR} = Q_3 - Q_1 = 35 - 20 = 15 \] Thus, the interquartile range of the data set is \( \boxed{15} \).