1. Lesson 2 - 1 Organizing Qualitative Data

2. Objectives • Organize qualitative data in tables • Construct bar graphs • Construct pie charts

3. Vocabulary • Frequency Distribution – lists each category of data and the number of occurrences for each category of data • Relative Frequency Distribution – is the proportion (or percentage) of observations within a category • Bar Graph – a graph showing frequency or relative frequency on the y-axis and categories on the x-axis • Pareto chart – bar graph whose bars are drawn in decreasing order of frequency or relative frequency • Side-by-Side bar graphs – use relative frequency since sample or population sizes may be different • Pie Charts – circle divided into sectors; each sector represents a category of data; area is proportional to the frequency of the category; all data must be represented

4. Different Views

5. Frequency Distributions & Histograms • There are no hard and fast rules for constructing frequency distributions and histograms for continuous data since there are no natural categories. The way out of this dilemma is to define our own categories. One drawback is that individuals working with the same set of data, may construct distributions with different appearances. The reason for this variation lies in the choice of the number of classes to use and the choice of the width of the classes. Using too few classes gives an inaccurate picture by smoothing out too many details. Too many classes present too much detail and the overall view can be lost (forest and trees analogy). • Another problem is the adverse effect on histograms of outliers in the data. When outliers are present some artistic modification is required. Although somewhat arbitrary, the following rule is presented to allow for some uniformity in constructing frequency distributions and histograms. • The number of classes k to be constructed can be roughly approximated by k = number of observations To determine the width of a class use w = (max – min) / k and always round up to the same decimal units as the original data.

6. Example 1 Construct a frequency distribution and a histogram. Below are the net weight (in ounces) of 30 cans of peas from the Grumpy Blue Midget Company. 16.2 15.8 15.8 15.8 16.3 15.6 15.7 16.0 16.2 16.1 16.8 16.0 16.4 15.2 15.9 15.9 15.9 16.8 15.4 15.7 15.9 16.0 16.3 16.0 16.4 16.6 15.6 15.6 16.9 16.3

7. Example 1 Graph

8. Summary and Homework • Summary • Charts help to display data more visually with fewer words • Homework: • pg 67 – 73; 6-8, 11, 13, 15, 22, 30