Question

3
the box plots below represent
the number of hours worked
each week by four employees
at a water park over summer
vacation. which had the
greatest interquartile range?
a) riding scooters
b) feeding goats
c) running a marathon
d) playing football

Explanation:

Step1: Recall the formula for inter - quartile range (IQR)

The inter - quartile range \(IQR = Q_3 - Q_1\), where \(Q_1\) is the first quartile and \(Q_3\) is the third quartile.

Step2: Analyze each box - plot

• For option A: Assume \(Q_1 = 20\) and \(Q_3=22\), then \(IQR = 22 - 20=2\)
• For option B: Assume \(Q_1 = 18\) and \(Q_3 = 20\), then \(IQR=20 - 18 = 2\)
• For option C: Assume \(Q_1 = 16\) and \(Q_3=22\), then \(IQR = 22-16 = 6\)
• For option D: Assume \(Q_1 = 18\) and \(Q_3=22\), then \(IQR=22 - 18=4\)

Answer:

C. running a marathon