Question

the box - and - whisker plot below represents some data set. what percentage of the data values are less than or equal to 82?

Explanation:

Step1: Recall the properties of box - and - whisker plots

In a box - and - whisker plot, the box is divided into two parts by the median. The left part of the box represents the lower half of the data, and the right part represents the upper half. Each part of the box (the lower half and the upper half) accounts for 50% of the data. Also, the whiskers and the box together cover all the data.
The value 82 is close to the third - quartile (Q3) value. The first quartile (Q1) divides the data such that 25% of the data is below Q1, the median (Q2) divides the data such that 50% of the data is below Q2, and the third quartile (Q3) divides the data such that 75% of the data is below Q3.

Since 82 is in the upper half of the box (the part of the box from the median to Q3), and considering the structure of the box - and - whisker plot where each quartile represents 25% of the data. The median (Q2) is at 78 (approximate mid - point of the box). The value 82 is in the third quartile range.

The first quartile (Q1) to the third quartile (Q3) contains 50% of the data. The part of the data from the minimum to Q1 is 25%, and from Q1 to Q2 is another 25%. Since 82 is in the Q3 region, and we know that the first three quartiles (from the minimum to Q3) cover 75% of the data.

Answer:

75%