Understanding & Comparing Distributions Chapter 5

Objectives Design and understand the box & whisker plot. Compare different groups (histograms/box plots). Understand Outliers. Apply the think/tell/show strategy.

Boxplots & 5-number Summaries Making a boxplot (vertical) Boxplots are effective ways for comparing groups and displaying outliers. Outlier: Any point more than 1.5 IQR away from either end of the box is labeled an outlier. Far Outlier: Any point more than 3 IQR from either end of the box.

Comparing Groups with Histograms You need to consider the shape, center, and spread.

Comparing Groups with Boxplots Compare the Shapes Compare the Medians Compare the IQRs Use the IQR to talk about Variance Check for Outliers

Outliers What should you do with them? Do not ignore them. Once identified, Investigate!! If they an error then correct. Never leave an outlier in place and proceed as nothing is unusual. Never drop an outlier with out commenting. If you exclude an outlier you must justify why?

Timeplots Displays data that change over time. Smooth curves are sometimes added to show long term patterns.

Re-Expressing Data: Improve Symmetry When the data is skewed, it can be hard to summarize. One approach is to re-express or transform. This makes the distribution more symmetric. This is done by taking either the log or square root of the data values. Then re-express.