(c) Dr. Phillip R. Rosenkrantz1 Box Plots Very useful graphical descriptive statistic Gives a clear picture of the data without using parametric statistics (such as the mean and standard deviation) Can tell if the data is skewed Outliers are obvious Easy to compare data by time period, location, or other variables of interest

(c) Dr. Phillip R. Rosenkrantz2 Information Needed Data Array –Minimum values –Maximum values 25 th percentile = q1 50 th percentile = q2 = median 75 th percentile = q3

(c) Dr. Phillip R. Rosenkrantz3 Box Plot (a.k.a. Box-Whisker Plot)

(c) Dr. Phillip R. Rosenkrantz4 Box Construction: q1 – q3

(c) Dr. Phillip R. Rosenkrantz5 Non-parametric View of the Data MinMax

(c) Dr. Phillip R. Rosenkrantz6 Interquartile Range (H) = q3 – q1

(c) Dr. Phillip R. Rosenkrantz7 “Fences” are calculated based on the interquartile range. (They are not included in the plot).

(c) Dr. Phillip R. Rosenkrantz8 “Whisker Construction”

(c) Dr. Phillip R. Rosenkrantz9 Outliers are beyond the “fences”

(c) Dr. Phillip R. Rosenkrantz10 Final Box Plot (does not include fences)

(c) Dr. Phillip R. Rosenkrantz11 Variations All outliers look the same (no extreme outliers) Whiskers go to maximum and minimum values (no recognition of outliers) Mean shown as a “plus” sign Quartiles designated as q1, q2 & q3 Values shown on the plot Boxes can be shown horizontally or vertically, depending on aesthetics

(c) Dr. Phillip R. Rosenkrantz12 Example of side-by-side Box Plots