The Box Plot

·        describe behavior of

o       middle data distribution

o       tails (ends) data distribution

·        can be used to identify outliers

Steps to construct Box Plot

·        Compute m, Q₁, Q₃ and  IQR

Rules for finding  Q₁ and Q₃

• Sort the data in increasing order

• Q₁ is the value of x with position 0.25*(n+1)

• Q₃ is the value of x with position 0.75*(n+1)

• If 0.25*(n+1) and 0.75*(n+1) are not integer, use interpolation.

• IQR =  Q₃ - Q₁(Inter Quartile Range).

·        Draw a horizontal line representing the scale of measurement.

·        Form a box just above the horizontal line with the right and left ends at Q₁ and Q₃

·        Draw a vertical line through the box at the location of the median.

·        Detect outliers (Mark them with *):  observations that are beyond:

o       Lower fence: Q₁ -1.5(IQR)

o       Upper fence: Q₃ + 1.5(IQR)

·        Draw two tails (called whiskers) from Q₁ to min. and Q₃ to max.

Example: