Question

the box plots represent the ages of pennies in two sets.
ages of pennies
by looking at the plots, beth says that the two means are about 5 years apart. which is true about beths statement?
she is correct because the medians are 10 years apart, which means the means are half of that, or 5 years apart.
she is correct because the maximum ages of the pennies in each set are 5 years apart.
she is not correct because the means are both equal to 12.
she may not be correct because means cannot be determined from the box plots.

Explanation:

Step1: Recall the property of box - plots and median

The median is the middle value of a data set. In a box - plot, the line inside the box represents the median.

Step2: Analyze the medians of the two box - plots

Let the median of the first box - plot (labeled as "Set 1") be \(M_1\) and the median of the second box - plot (labeled as "Set 2") be \(M_2\). By observing the box - plots, we can see that the difference between \(M_1\) and \(M_2\) is 10 years.

Answer:

She is correct because the medians are 10 years apart.