Question

2 box plots. The number line goes from 175 to 450. For resort A, the whiskers range from 175 to 375, and the box ranges from 250 to 300. A line divides the box at 375. For Resort B, the whiskers range from 200 to 400, and the box ranges from 300 to 375. A line divides the box at 325. Kevin wanted to go snowboarding for his vacation. He looked up annual snowfall of both resorts over a ten-year period to determine which resort would have the better snowfall. Compare the two box plots and use the drop-down menus to determine where Kevin should plan to go for vacation. What is the approximate median snowfall at Resort A? What is the approximate median snowfall at Resort B?.

Answer 1

Box plot 5 important descriptive measures about data that they represent.

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.

Resort B has more snowfall overall than Resort A does.

How does a boxplot show the data points?

A box plot has 5 data descriptions.

The leftmost whisker shows the minimum value in the data.

The rightmost whisker shows the maximum value in the data.

The leftmost line in the box shows the first quartile.

The middle line shows the median, also called the second quartile.

The last line of the box shows the third quartile.

How to find the interquartile range?

IQR(interquartile range)  is the difference between the third and first quartile.

Inferring the information each box plot describe, we get:

Case 1: For resort A:

Wisker's minimum value = minimum value for resort A = 175

Maximum value = 375

Box's minimum value = First quartile = 250

Box's maximum value = Third quartile = 300

First quartile = 250 < Median = Second quartile < 300 = third quartile

Thus, 250 < Median for resort A < 300

IQR = Third quartile - first quartile = 300 - 250 = 50

Range of values = Max - min = 375 - 175 = 200

Case 2: For resort B:

Wisker's minimum value = minimum value for resort B = 200

Maximum value = 400

Box's minimum value = First quartile = 300

Box's maximum value = Third quartile = 325

First quartile = 300 < Median = Second quartile < 375 = third quartile

Thus, 300 < Median for resort B < 375

IQR = Third quartile - first quartile = 325 - 300 = 25

Range of values= Max - min = 400 - 200

Thus, it is visible that:

Median for resort A < 300 < Median for resort B

or

Median for resort A < Median for resort B.

and

IQR for resort A = 50 > IQR for resort B = 25

and

Both have the same variation as both ranges are the same, which is the interval of values assumed for both resorts.

Hence, Minimum, maximum, first, and third quartile all are smaller for resort A, thus, Resort B has more snowfall overall than Resort A does.

Learn more about boxplot here:

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Answer 2

What is the approximate median snowfall at Resort A?

✔ 275 inches

What is the approximate median snowfall at Resort B?

✔ 325 inches