Question

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Explanation:

Identify the five-number summary values

Using the Box-and-Whisker Plot knowledge point

• The problem states that about \(75\%\) of students studied no more than \(6.5\) hours per day. In a box-and-whisker plot, the third quartile \(Q_3\) represents the \(75\text{th}\) percentile. Thus, \(Q_3 = 6.5\).
• Part (b) states that about \(50\%\) of students studied more than \(4.5\) hours per day. The median \(Q_2\) divides the data into two halves (\(50\%\) above and \(50\%\) below). Thus, the median \(Q_2 = 4.5\).

Determine the value of the first quartile

Using the Five-Number Summary knowledge point

• A standard box-and-whisker plot is divided into four quarters, each containing approximately \(25\%\) of the data:
• Minimum to \(Q_1\): \(25\%\)
• \(Q_1\) to \(Q_2\) (median): \(25\%\)
• \(Q_2\) to \(Q_3\): \(25\%\)
• \(Q_3\) to Maximum: \(25\%\)
• Looking at the values given in parts (a) and (b), the key boundaries are \(Q_3 = 6.5\) and \(Q_2 = 4.5\).
• Part (c) asks for the likelihood that a randomly selected student studied less than \(2\) hours per day.
• In this dataset's box-and-whisker plot, the first quartile \(Q_1\) is located at \(2\) hours.

Calculate the likelihood for part (c)

Using the Percentiles and Quantiles knowledge point

• The value \(2\) corresponds to the first quartile \(Q_1\).
• By definition, the first quartile \(Q_1\) represents the \(25\text{th}\) percentile of the dataset.
• Therefore, approximately \(25\%\) of the data values lie below \(Q_1 = 2\).
• The likelihood of selecting a student who studied less than \(2\) hours per day is about \(25\%\).

Answer:

• 25% (Correct answer)
• 30%
• 75%
• 40%
• 10%
• 50%
• 60%