Unit 2: Exploring Data with Graphs and Numerical Summaries Lesson 2-2a – Graphs for Categorical Data Probability & Stats Essential Question: How do we best summarize and graphically represent categorical variables?

Learning Objectives 1. Distribution 2. Graphs for categorical data: bar graphs and pie charts 2

Learning Objective 1: Distribution We use the word ‘distribution’ to describe all the possible values a variable takes as well as the occurrence of those values (both frequency and relative frequency). A graph or frequency table is a tool used to describe a distribution, containing and/or displaying the variables of interest. 3

Learning Objective 2a: Bar Graphs Bar graphs are used for summarizing a categorical variable Bar Graphs display a vertical bar for each category The height of each bar represents either counts (“frequencies”) or percentages (“relative frequencies”) for that category Usually easier to compare categories with a bar graph than with a pie chart 4

Learning Objective 2a: Bar Graphs  This is a standard vertical bar graph with the categorical variable of… 5 How can we determine if a bar graph is relative or relative frequency? If total of bars = 100, it is relative generally ?

Learning Objective 2a: Bar Graphs  Side-by-side (grouped) bar graphs allow you to compare the same variables next to one another. 6

Learning Objective 2a: Bar Graphs  Stacked (composite) bar graphs can show similar data as a side-by-side, but are helpful in that they show the full total reached by both variables. 7

Learning Objective 2a: Bar Graphs  A horizontal bar graph may be preferred for certain sets of data. 8  Is this frequency or relative frequency? What’s going on?

Learning Objective 2a: Bar Graph Example 9 Bar Graphs are called Pareto Charts when the categories are ordered by their frequency, from the tallest bar to the shortest bar

Learning Objective 2: Class Exercise There are 7 students in a club who are either freshman, sophomores, juniors, or seniors. The number of students in this club who are juniors is _____. 10

Learning Objective 2: Class Exercise Now try the practice example on the notes. 11

Learning Objective 2b: Pie Charts Pie charts: Used for summarizing a categorical variable Drawn as a circle where each category is represented as a “slice of the pie” The size of each pie slice is proportional to the percentage of observations falling in that category Can we make a pie chart with just straight frequencies? 12

Learning Objective 2: Pie Chart Example 13

Constructing a Pie Chart 1)Create a Frequency table of your data 2)Find the proportion for each Category 3)Find the angle of each “slice” angle = proportion * 360 ⁰ Gather informal class data for example problem and pie chart construction. 14

Learning Objective 2: Pie Chart Example 15  The very first pie chart, created in 1801.

Learning Objective 2: Pie Chart Example 16  Pie charts don’t necessarily have to display values, they can just be used to describe general truths of data like this pie chart.

Learning Objective 2: Pie Chart Example 17  Don’t use pie charts for more than 5-6 categorical variables.

Learning Objective 2: Pie Chart Example 18  Use pie charts responsibly.

Learning Objective 2: Pie Chart Example 19  Or purposely use them irresponsibly.

Learning Objective 2: Pie Chart Example 20  Marshall from “How I Met Your Mother” will close this lesson appropriately.

21