Question

marisa recorded the number of hours she babysat each day last summer. she plotted the data in the box plot.
number of hours of babysitting each day
box plot image with number line from 0 to 10
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 Box Plot Symmetry

A box plot's symmetry is determined by the position of the median (middle line in the box) and the lengths of the whiskers. Here, the box is centered around the middle, and whiskers are balanced, so data is symmetric.

Step2: Evaluate Each Option

• Option 1: Symmetric data means the median (around 4 - 4.5) implies equal likelihood around the center. 3.5 and 5 are symmetric around the center, so this makes sense.
• Option 2: The whisker goes to 7, so she worked more than 5 hours. False.
• Option 3: Data is symmetric (not skewed). False.
• Option 4: Data is symmetric (not skewed) and whisker to 7. False.

Answer:

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