Question

in constructing a box and whisker plot from the data set below at which value would you draw the left and right side of the box

Answer 1

A box and whisker plot is a type of statistical graph that shows the median distributions of the data set. The box represents the data median and the medias of the quartiles. The whiskers represents the lines extended from the box to the lowest and the highest data.

Take this data as an example:
3.9,  4.1,  4.2,  4.3,  4.3,  4.4,  4.4,  4.4,  4.4,  4.5,  4.5,  4.6,  4.7,  4.8,  4.9,  5.0,  5.1
First, find the middle value. That would be the median. In this case, that would be 4.4. Let's denote this as Q₂ or Quartile 2. Now, take the group of data set before and after the median. These are:

3.9,  4.1,  4.2,  4.3,  4.3,  4.4,  4.4,  4.4

and

4.5,  4.5,  4.6,  4.7,  4.8,  4.9,  5.0,  5.1

The middle of the first data set is Q₁ = 4.3, while the middle of the second set is Q₃ = (4.7+4.8)/2 = 4.75

To construct the box and whisker plot, create line for the lowest value 3,9, Q₁, Q₂, Q₃ and the highest value, 4.4. The left side of the box would be Q₁, while the right side of the box is Q₃. The line in between is the media Q₂. The whiskers are the lines connecting the lowest to Q₁, and Q₃ to the highest on the other side. The resulting box and whisker plot is shown in the attached picture.