1. ANATOMY OF A BOXPLOT: Traditional Boxplot
Boxplots present the five-number-summary statistics, as well as provide a visual presentation of the data’s distribution. In a Traditional Boxplot the whiskers are drawn all the way to the minimum and maximum values. See also: Modified Boxplot.
Building a Traditional Boxplot:
1) Draw the horizontal axis.
2) Label the axis (pounds, cm., sec., etc.) and insert the scale being used (e.g. 440 – 700 ).
3) Determine the values of the five-number-summary.
4) Place a dot above the scale line for each of the five points.
5) Draw vertical lines through the points representing Q1 and Q3. Connect these lines, forming a rectangle.
6) Draw a vertical line through the Median and connect it to the box.
7) Draw lines (whiskers) out from Q1 to the Minimum value and from Q3 out to the Maximum value. A short vertical line at the minimum and maximum is optional (not shown).
8) Add a title describing the chart’s contents and any other information about the data that might be useful.
Title
A Boxplot is divided into four sections by the three quartile values Q1 , Q2 (Median), and Q3. While all sections contain the same number of data values, the “size” of these four sections may vary in “length.” This appearance is due to the density of values within each section (i.e. whether the values are close together, creating a “shorter” appearing quartile or farther apart, creating a “longer” appearing quartile).
Related Items:
A Boxplot may be presented either vertically or horizontally (as done here).
The Inter-Quartile Range (IQR) encompasses the middle 50% of the data and is obtained via the formula: IQR = Q3 - Q1.
x-axis scale.
The Lower Whisker extends to the Minimum value in the data set = 440 lbs.
The Median (Q2) = 558 lbs..
The Upper Whisker extends to the Maximum value in the data set = 707 lbs.
Q1, the first quartile = lbs..
Q3, the third quartile = lbs..
The Data: Flour Used (lbs.)
440, 481, 482, 483, 483, 514, 514, 554, 554, 554,
562, 612, 623, 631, 638, 664, 671, 677, 690, 707
Historical Note: Who invented this useful tool for quick data analysis? John Tukey, Statistician