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:

Step1: Analyze the box - plot symmetry

A symmetric box - plot has the median in the middle of the box and the whiskers of equal length. In the given box - plot, the lengths of the whiskers and the position of the median within the box are not such that the data is symmetric. So, we can rule out the options with “the data is symmetric”.

Step2: Analyze the maximum value

The right - most point of the box - plot (the end of the right - hand whisker) is greater than 5. So, the statement “she never worked more than 5 hours” is false.

Step3: Recall the property of skewed data and quartiles

For a box - plot, the median divides the data into two halves. In a box - plot (skewed or not), the median (the line inside the box) and the quartiles (the ends of the box) are such that the inter - quartile range (IQR) is considered. The first quartile \(Q_1 = 3.5\) and the median \(Q_2=5\). In a box - plot (whether skewed or not), the number of data points between \(Q_1\) and \(Q_2\) is the same as the number of data points between \(Q_2\) and \(Q_3\). Also, the data is skewed (as we saw from the unequal whisker lengths).

Answer:

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