Question

the box plot below represents some data set. what is the interquartile range (iqr) of the data?

Explanation:

1. Recall the definition of the inter - quartile range (IQR):

• The inter - quartile range is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)).
• In a box - plot, the left - hand side of the box represents \(Q_1\) and the right - hand side of the box represents \(Q_3\).

1. Identify \(Q_1\) and \(Q_3\) from the box - plot:

• From the given box - plot, \(Q_1 = 40\) and \(Q_3=70\).

1. Calculate the IQR:

• \(IQR=Q_3 - Q_1\).
• Substitute \(Q_1 = 40\) and \(Q_3 = 70\) into the formula: \(IQR=70 - 40=30\).

Answer:

30