Probability & statistics - part 4

Box plot

• Boxplot is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation (sample minimum), lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation (sample maximum). A box plot may also indicate which observations, if any, might be considered outliers.

Steps of drawing a box plot:

1. Calculate the median and the quartiles (the lower quartile is the 25th percentile and the upper quartile is the 75th percentile).
2. Plot a symbol at the median (or draw a line) and draw a box (hence the name--box plot) between the lower and upper quartiles; this box represents the middle 50% of the data--the "body" of the data.

3.       Calculate the interquartile range (the difference between the upper and lower quartile) and call it IQ.

4.       Calculate the following points:

5.       L = lower quartile - 1.5*IQ
U = upper quartile + 1.5*IQ

6.       The line from the lower quartile is drawn from the lower quartile to the smallest point that is greater than L. Likewise, the line from the upper quartile is drawn to the largest point smaller than U.

7.       Points less than L or greater than U are drawn as small circles.

• Thus the box plot identifies the middle 50% of the data, the median, and the extreme points. The following figure illustrates the box plot for weight data.

Laahiru.C.fernando.