Organizing Qualitative Data Chapter 2 Section 1 Organizing Qualitative Data

Chapter 2 – Section 1 Learning objectives Organize qualitative data in tables Construct bar graphs Construct pie charts 1 2 3

Chapter 2 – Section 1 Learning objectives Organize qualitative data in tables Construct bar graphs Construct pie charts 1 2 3

Chapter 2 – Section 1 Raw qualitative data comes as a list of values … each value is one out of a set of categories These values can be organized as either a long list or in a table Interpreting the list of data can be difficult, particularly if there is a lot of data Methods are needed to aid interpretation Raw qualitative data comes as a list of values … each value is one out of a set of categories These values can be organized as either a long list or in a table

Chapter 2 – Section 1 Qualitative data values can be organized by a frequency distribution A frequency distribution lists Each of the categories The frequency for each category

blue, blue, green, red, red, blue, red, blue Chapter 2 – Section 1 A simple data set is blue, blue, green, red, red, blue, red, blue A frequency table for this qualitative data is The most commonly occurring color is blue Color Frequency Blue 4 Green 1 Red 3

Chapter 2 – Section 1 The frequencies are the counts of the observations The relative frequencies are the proportions (or percents) of the observations out of the total A relative frequency distribution lists Each of the categories The relative frequency for each category The frequencies are the counts of the observations The frequencies are the counts of the observations The relative frequencies are the proportions (or percents) of the observations out of the total

blue, blue, green, red, red, green, blue, blue Chapter 2 – Section 1 Use the same simple set of data blue, blue, green, red, red, green, blue, blue A relative frequency table is computed as follows Sum of all frequencies = 8 (there are 8 observations) Blue has a relative frequency of 4 / 8 = .500 Green has a relative frequency of 1 / 8 = .125 Red has a relative frequency of 3 / 8 = .375

Chapter 2 – Section 1 A relative frequency table for this qualitative data is A relative frequency table can also be constructed with percents (50%, 12.5%, and 37.5% for the above table) Color Relative Frequency Blue .500 Green .125 Red .375

Chapter 2 – Section 1 Tables are useful because they provide an exact count for the data However, if the data set is medium to large in size, it may be difficult to understand the data when presented in a table Additional techniques are needed to give a better idea of “the big picture”

Chapter 2 – Section 1 Learning objectives Organize qualitative data in tables Construct bar graphs Construct pie charts 1 2 3

Chapter 2 – Section 1 In general, pictures of data send a more powerful message than tables Visual methods, such as bar graphs, present a better summary than just a table A bar graph Lists the categories on the horizontal axis Draws rectangles above each category where the heights are equal to the category’s frequency or relative frequency In general, pictures of data send a more powerful message than tables Visual methods, such as bar graphs, present a better summary than just a table

Chapter 2 – Section 1 Bar graphs for our simple data (using Excel) Frequency bar graph Relative frequency bar graph

Chapter 2 – Section 1 Good practices in constructing bar graphs The horizontal scale The categories should be spaced equally apart The rectangles should have the same widths The vertical scale Should begin with 0 Should be incremented in reasonable steps Should go somewhat, but not significantly, beyond the largest frequency or relative frequency Good practices in constructing bar graphs The horizontal scale The categories should be spaced equally apart The rectangles should have the same widths

Chapter 2 – Section 1 A Pareto chart is a particular type of bar graph A Pareto differs from a bar chart only in that the categories are arranged in order The category with the highest frequency is placed first (on the extreme left) The second highest category is placed second Etc. Pareto charts are often used when there are many categories but only the top few are of interest A Pareto chart is a particular type of bar graph A Pareto differs from a bar chart only in that the categories are arranged in order The category with the highest frequency is placed first (on the extreme left) The second highest category is placed second Etc.

Chapter 2 – Section 1 A Pareto chart for our simple data (using Excel)

Chapter 2 – Section 1 An example with more data values A data set from the text Even with only 30 data values, this table cannot be interpreted easily

Chapter 2 – Section 1 Graphs for this set of data A frequency bar graph A relative frequency bar graph These graphs are more effective than the table

Chapter 2 – Section 1 Graphs for this data (continued) A Pareto chart

Chapter 2 – Section 1 Two qualitative variables can be compared by comparing their bar graphs A side-by-side bar graph draws two rectangles for each category, one for each variable The frequencies (or relative frequencies) for each category can be compared

Chapter 2 – Section 1 An example side-by-side bar graph comparing educational attainment in 1990 versus 2003

Chapter 2 – Section 1 Learning objectives Organize qualitative data in tables Construct bar graphs Construct pie charts 1 2 3

Chapter 2 – Section 1 A pie chart is a circle divided into sections, one for each category The area (angle) of each sector is proportional to the frequency of that category Pie charts are useful to show the relative proportions of each category, compared to the whole

Chapter 2 – Section 1 Good practices for constructing pie charts Different colors should be used to distinguish the categories Each category should be labeled with the category name and relative frequency Pie charts are not as effective if there are too many categories or if some relative frequencies are too small Good practices for constructing pie charts Different colors should be used to distinguish the categories Each category should be labeled with the category name and relative frequency

Chapter 2 – Section 1 An example of a pie chart for the 2003 data from the side-to-side bar chart

Chapter 2 – Section 1 Side-by-side pie charts are used sometimes, but can be difficult to interpret (using Excel, with substantial modifications)

Summary: Chapter 2 – Section 1 Qualitative data can be organized in several ways Tables are useful for listing the data, its frequencies, and its relative frequencies Charts such as bar graphs, Pareto charts, and pie charts are useful visual methods for organizing data Side-by-side bar graphs are useful for comparing two sets of qualitative data