Question

comparing data in box plots
which statement is true of the snowfall data in the box plots? check all that apply.
the median snowfall for resort a is greater than the median for resort b.
the median snowfall for resort b is greater than the median for resort a.
the interquartile range has higher values for resort a than for resort b.
the data have more variation for resort a than for resort b.
resort b has more snowfall overall than resort a does.

Explanation:

Step1: Identify median in box - plot

The median is the line inside the box. For Resort A, the median is around 275 inches. For Resort B, the median is around 325 inches. So, the median snow - fall for Resort B is greater than the median for Resort A.

Step2: Identify inter - quartile range (IQR)

The IQR is the length of the box. For Resort A, if we assume the lower quartile ($Q_1$) is around 225 and the upper quartile ($Q_3$) is around 300, $IQR_A=300 - 225 = 75$. For Resort B, if $Q_1$ is around 275 and $Q_3$ is around 375, $IQR_B=375 - 275 = 100$. So, the inter - quartile range has higher values for Resort B than for Resort A.

Step3: Analyze data variation

The range (difference between maximum and minimum values) and IQR are measures of variation. The range for Resort A is from about 175 to 400 (range $\approx400 - 175=225$), and for Resort B is from about 200 to 450 (range $\approx450 - 200 = 250$). Also, $IQR_B>IQR_A$. So, the data have more variation for Resort B than for Resort A.

Step4: Consider overall snowfall

Since the median, $Q_3$, and maximum values for Resort B are higher than those for Resort A, Resort B has more snowfall overall than Resort A does.

Answer:

• The median snowfall for Resort B is greater than the median for Resort A.
• Resort B has more snowfall overall than Resort A does.