Question

which box plot represents the data? heights of trees

Explanation:

Step1: Find the minimum and maximum values

The minimum value is \(6\) and the maximum value is \(11\).

Step2: Find the median

Arrange the data: \(6,7,8,8,9,9,10,10,10,11\). There are \(n = 10\) data points. The median is the average of the \(5^{th}\) and \(6^{th}\) values. \(\text{Median}=\frac{9 + 9}{2}=9\).

Step3: Find the lower quartile (\(Q_1\))

The lower half of the data is \(6,7,8,8,9\). The lower quartile \(Q_1\) is the \(3^{rd}\) value. So \(Q_1 = 8\).

Step4: Find the upper quartile (\(Q_3\))

The upper half of the data is \(9,10,10,10,11\). The upper quartile \(Q_3\) is the \(3^{rd}\) value of the upper half. So \(Q_3=10\).

Answer:

The box - plot with minimum at \(6\), \(Q_1 = 8\), median \(=9\), \(Q_3 = 10\) and maximum at \(11\) (the third box - plot in the given options) represents the data.