Question

how to calculate quartiles and draw a box plot from a sample data set containing two independent variables and one dependent variable?

Answer 1

Let’s say that we have a data set with N data points:

X – {X1, X2, X3……….. XN}

The formula for quartiles is given by:

• Lower Quartile (Q1) = (N+1) * 1 / 4
• Middle Quartile (Q2) = (N+1) * 2 / 4
• Upper Quartile (Q3 )= (N+1) * 3 / 4

What it basically means is that in a data set with N data points:

• ((N+1) * 1 / 4)^th term is the lower quartile
• ((N+1) * 2 / 4)^th term is the middle quartile
• ((N+1) * 3 / 4)^th term is the upper quartile

Let's say we have a dependent variable Y and two independent variable X1 and X2. Using the above formula, we can compute Quartiles.

The box Plot shows you how your data is spread out. Five pieces of information (the “five-number summary“) are generally included in the Plot:

• The minimum (the smallest number in the data set). The minimum is shown at the far left of the Plot, at the end of the left “whisker.”
• First quartile, Q₁, is the far left of the box (or the far right of the left whisker).
• The median is shown as a line in the center of the box.
• Third quartile, Q₃, shown at the far right of the box (at the far left of the right whisker).
• The maximum (the largest number in the data set), shown at the far right of the box.

The above figure depicts the simple example of Box Plot.

If we have two independent and one dependent variable we can make a side-by-side Box Plot of each independent variable with the dependent variable. For example :