A flagpole is n feet tall. On this pole we display flags of the following types: red flags that are 1 foot tall, blue flags that are 2 feet tall, and green flags that are 2 feet tall. The sum of the heights of the flags is exactly n feet. Prove that there are 2 3 2 n C 1 3 .1/n ways to display the flags.

STAT 206: Chapter 2 (Organizing and Visualizing Variables) Methods to Organize and Visualize Variables For Categorical Variables: Summary Table; contingency table (2.1) Bar chart, pie chart, Pareto chart, side-by-side bar chart (2.2) For Numerical Variables (Array), Ordered Array, frequency distribution, relative frequency distribution, percentage distribution, cumulative percentage distribution (2.3) Stem-and-Leaf display, histogram, polygon, cumulative percentage polygon (2.4) Other methods later… 2.1 Organizing Categorical Variables Must identify variable type to determine the appropriate organization and visualization tools èRecall Variable Types Categorical (Category) Nominal – Name of a Category Ordinal – Has a natural ordering Numerical / Quantitative (Quantity) Discrete – distinct cutoffs between values Continuous – on a continuum Definitions: Summary Table: shows values of the data categories for one variable and the frequencies (counts) or proportions/ percentages for each category Contingency Table: shows values of the data categories for more than one variable and the frequencies or proportions/percentages for each of the joint responses Each response counted/tallied into one and only one category/cell Example (Problem 2.2, p. 40): The following data represent the responses to two questions asked in a survey of 40 college students majoring in