Displaying and describing categorical data Chapter 3 Part 1 Displaying and describing categorical data

When analyzing data, always remember to make a picture! Things may be revealed that aren’t otherwise obvious Patterns will likely show up

3 Types of Displays for Categorical Data in one variable: Frequency Tables Bar Graphs Pie Chart

We can organize counts of data values into a frequency table Frequency Tables We can organize counts of data values into a frequency table This table displays the number of passengers on the Titanic, categorized by class.

Relative Frequency Tables A relative frequency table is similar to a frequency table, but the frequency is given by the percent of the total, rather than by a count.

Frequency and relative frequency tables Both types of tables show how cases are distributed across the categories.

Example: An article in the Winter 2003 issue of Chance magazine reported on the Houston Independent School District’s magnet schools programs. Of the 1755 qualified applicants, 931 were accepted, 298 were wait-listed, and 526 were turned away for lack of space. Create a frequency table and a relative frequency table of the decisions made, and write a sentence describing it.

Bar Charts A bar chart displays the distribution of a categorical variable, showing the counts for each category for easy comparison. The columns should always have the same width.

Relative Frequency Bar Chart A relative frequency bar chart displays the relative proportion of counts for each category. The proportion of counts is the same as the percentage of the total.

Side by Side Comparison: Notice the heights and distribution appear the same.

Example: In the same article that reported on the Houston Independent School District’s magnet schools programs, it was stated that 517 applicants were black or Hispanic, 292 were Asian, and 946 were white. Create a bar chart and a relative frequency bar chart of the decisions made, and write a sentence describing it.

Pie Charts

Pie Charts When you are interested in parts of the whole, a pie chart might be your display of choice. Pie charts show the whole group of cases as a circle. They slice the circle into pieces whose size is proportional to the fraction of the whole in each category.

The internet has radically changed the way we consume and purchase music, but it isn't the first game changer. In 30 years, the music industry has moved from vinyl singles, to cassettes, to CDs, to downloads, to music subscriptions. In this gif, created by Digital Music News, you can watch those revenues change.

Be Careful! Do you notice anything wrong here? If you add up the categories, they total 108.2%. The categories should always add to equal 100%, no more, no less.

Segmented Bar Graph These are preferred over pie charts. Each bar represents 100% split into categories, just like a pie chart.

Chapter 3 Exercises: pg. 38 #8, 11-17 Today’s Assignment: Chapter 3 Exercises: pg. 38 #8, 11-17