Question

5
the box plot shows the wattages of a group of appliances in a kitchen. which statement is most true?
a) approximately 25% of the appliances are 600 - 850 watts. superbowl sunday
b) approximately 50% of the appliances are less than 600 watts or greater than 850 watts. groundhog day
c) approximately 75% of the appliances are greater than 700 watts. cinco de mayo
d) approximately 50% of the appliances are less than 850 watts. black friday
© gina wilson (all things algebra®, llc), 2023

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), which contains 50% of the data. The lower whisker represents the bottom 25% of the data and the upper whisker represents the top 25% of the data.

Step2: Analyze each option

• Option A:

The range \(600 - 850\) is the IQR. The IQR contains 50% of the data, not 25%. So, this option is incorrect.

• Option B:

The data less than \(600\) (lower 25%) and greater than \(850\) (upper 25%) together make up \(25\%+25\% = 50\%\) of the data.

• Option C:

The median (the line inside the box) is \(700\). Approximately 50% of the data is greater than \(700\) (since the median divides the data into two equal parts), not 75%. So, this option is incorrect.

• Option D:

Since \(850\) is the upper quartile (\(Q3\)), approximately 75% of the data is less than \(850\) (25% in the lower whisker + 50% in the box), not 50%. So, this option is incorrect.

Answer:

B. Approximately 50% of the appliances are less than 600 watts or greater than 850 watts.