Question

steve determined the number of states each of his friends has visited.
number of states visited
which statement must be true according to the box plot?
the data is skewed left and shows that half of steves friends have visited 4 to 10 states.
the data is skewed left and shows that half of steves friends have visited 10 to 40 states.
the data is skewed right and shows that half of steves friends have visited 4 to 10 states.
the data is skewed right and shows that half of steves friends have visited 10 to 40 states.

Explanation:

Step1: Analyze the skewness of the box - plot

In a box - plot, if the whisker on the right side is longer than the whisker on the left side, the data is skewed right. Here, the right - hand whisker is much longer than the left - hand whisker, so the data is skewed right.

Step2: Recall the property of the box - plot

The box in a box - plot represents the inter - quartile range (IQR), which contains 50% (half) of the data. The left - hand side of the box is \(Q_1\) (first quartile) and the right - hand side is \(Q_3\) (third quartile). Looking at the box - plot, \(Q_1 = 4\) and \(Q_3=10\) does not make sense as the box is not in that range. The box is from \(Q_1 = 10\) to \(Q_3\) and the right - hand whisker extends to a larger value (40). The IQR (the box) which contains half of the data is from \(Q_1 = 10\) to \(Q_3\) and the remaining half is split between the lower whisker (from minimum to \(Q_1\)) and the upper whisker (from \(Q_3\) to maximum). But if we consider the basic property that the box (IQR) contains 50% of the data. If we assume the box is from \(Q_1 = 10\) to \(Q_3\) and the maximum is 40 (the end of the right - hand whisker), half of the data lies within the box (IQR) and the other half is split. But if we consider the incorrect assumption of \(Q_1 = 4\) and \(Q_3 = 10\) (wrong as per the box - plot length), we know that the length of the right - hand whisker (from \(Q_3\) to maximum) is large. The correct interpretation is that the box (IQR) which has half of the data. If we assume the box is from \(Q_1 = 10\) to \(Q_3\) and the maximum is 40 (the end of the right - hand whisker). The fact that the right - hand whisker is long (skewed right) and the box (IQR) (which has half of the data) is such that if we consider the position of the box. The left end of the box is \(Q_1 = 10\) and the right end of the whisker is 40. Since the data is skewed right (longer right - hand whisker), half of the data is in the box (IQR) which is from \(Q_1 = 10\) to \(Q_3\) and the other half is split. But if we consider the options, the key is the skewness (right - skewed because of the long right whisker) and the box (which represents half of the data). The box (IQR) is from \(Q_1 = 10\) to \(Q_3\) and the maximum is 40.

Answer:

The data is skewed right and shows that half of Steve's friends have visited 10 to 40 states.