Question

marisa recorded the number of hours she babysat each day last summer. she plotted the data in the box plot. which statement must be true according to the box plot? the data is symmetric and shows that she was equally likely to work more than 3.5 hours or less than 5 hours. the data is symmetric and shows that she never worked more than 5 hours. the data is skewed and shows that she was equally likely to work more than 3.5 hours or less than 5 hours. the data is skewed and shows that she never worked more than 5 hours.

Explanation:

• First, check for symmetry. A symmetric box - plot has the median in the middle of the box and the whiskers of equal length. Here, the box - plot is skewed (the left whisker and the part of the box to the left of the median are longer compared to the right side).
• For a box - plot, the median divides the data into two halves. The lower half of the data is below the median and the upper half is above the median. In a box - plot, the line inside the box is the median. The left end of the box is \(Q_1\) (first quartile) and the right end is \(Q_3\) (third quartile). The property of a box - plot is that 50% of the data lies between \(Q_1\) and \(Q_3\). Also, 50% of the data is less than \(Q_3\) and 50% of the data is more than \(Q_1\). If \(Q_1 = 3.5\) and \(Q_3=5\), then 50% of the data is more than \(Q_1 = 3.5\) and 50% of the data is less than \(Q_3 = 5\).

Answer:

The data is skewed and shows that she was equally likely to work more than 3.5 hours or less than 5 hours.