Question

find the median of the data set using the box plot.
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Explanation:

Step1: Recall the definition of median in a box - plot

In a box - plot, the median is represented by the line inside the box.

Step2: Locate the line inside the box on the number line

The line inside the box is at \(7\) (assuming each tick mark is \(2\) units. The box starts at \(4\) and the line is at the mid - point of the first half of the box. If we consider the left - hand side of the box (the first part of the split box) which spans from \(4\) to \(8\), the mid - point between \(4\) and \(8\) is \(\frac{4 + 8}{2}=6\) if we assume equal - length sub - boxes. But if we consider the scale: each tick is \(2\) units. The left end of the box is at \(4\), and if we count the position of the median line (the vertical line inside the box), since the box is split into two parts (visually), and the number line has ticks at \(0,2,4,6,8,\cdots\). The median line is at \(6\).

Answer:

\(6\)