~Boxplots: (also called box-and-whisker diagrams)

~Provides a graphical display of variation in each quartile

~They also provide a visual of the skewness of the distribution

(See Link on Skewness on this webpage)

~To construct, you need the 5 number summary, L, Q1, Q2, Q3, H
  (TI-83 will do this for us)

~Q1 & Q3 are called the hinges

~The lengths (visual) (see below) from L to Q1 & from Q3 to H are called whiskers

~Boxplots can be drawn horizontally or vertically

Ex:             L         Q1          M*                 Q3        H
                 |_______|_______|___________|_____|
   L=min , Q1= 1st Quartile, M*=median, Q3= 3rd Quartile, H=max

~Note: to view the box, extend the 3 middle segments downward the
same length as they are above the horizontal segment, then connect the top points of these segments & the bottom points of these segments. It will form a rectangle (BOX) in the middle.
                                                                                                                                 
~Note: Box plots are also drawn vertically, where H is the highest  pt.
                                                                                                                                  

IQR (Inter quartile range):   Q3 - Q1  (length of the box)

Outliers: Data points which are unusually far from Q1 or Q3
~Mild: more than 1.5 IQR from Q1 or Q3 (indicated by a solid dot)
~Extreme: more than 3 IQR from Q1 or Q3 (indicated by an open dot)

~Note: Boxplots also give us a way of comparing data sets graphically
~We can visualize Range, Skewness, Max, Min, IQR, Variation, & Outliers

~Ex: Get the boxplot for the following data set: 4.3, 4.9, 4.9, 5.1, 5.2, 5.2, 5.3, 5.3, 5.3, 5.4, 5.4, 5.6, 5.6, 5.7, 5.8, 5.8, 5.9, 6.1, 6.2, 6.9

~Clear lists, insert data, MUST USE FREQUENCIES OF 1 IN L2, 2ND STAT PLOT, bottom left box plot will show outliers, bottom center will not. Press Zoom 9 to automatically set the viewing window & get your box-plot. To get the 5 number summary, press trace & move the curser along the plot. You can also get these by going to the CALC menu.

~Note: There are situations in certain courses where you must set the viewing window manually. To do this click window & insert the values yourself. 

~Note: To set the window for the example given here, let Xmin = 4.3, Xmax =6.9, Xscl = .1, Ymin  =0, 1’s for the rest (doesn’t matter)

~The IQR = 5.8-5.2 = .6,  1.5 IQR = (1.5)(.6) = .9

  Q1 - .9 = 5.2-.9 = 4.3 (none lower)

  Q3 +.9 = 5.8 +.9 = 6.7 (one higher, 6.9) (Mild outlier)

  (No extreme outliers)

~To visualize more than one box-plot, use another list with the same number of data points & click on another plot under 2nd Stat Plot.