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## Box Plots

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**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. Rosenkrantz**Information Needed**• Data Array • Minimum values • Maximum values • 25th percentile = q1 • 50th percentile = q2 = median • 75th percentile = q3 (c) Dr. Phillip R. Rosenkrantz**Box Plot (a.k.a. Box-Whisker Plot)**(c) Dr. Phillip R. Rosenkrantz**Box Construction: q1 – q3**(c) Dr. Phillip R. Rosenkrantz**Non-parametric View of the Data**Min Max (c) Dr. Phillip R. Rosenkrantz**Interquartile Range (H) = q3 – q1**(c) Dr. Phillip R. Rosenkrantz**“Fences” are calculated based on the interquartile**range. (They are not included in the plot). (c) Dr. Phillip R. Rosenkrantz**“Whisker Construction”**(c) Dr. Phillip R. Rosenkrantz**Outliers are beyond the “fences”**(c) Dr. Phillip R. Rosenkrantz**Final Box Plot (does not include fences)**(c) Dr. Phillip R. Rosenkrantz**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. Rosenkrantz**Example of side-by-side Box Plots**(c) Dr. Phillip R. Rosenkrantz