ORGANIZING QUALITATIVE DATA 2.1

FREQUENCY DISTRIBUTION Qualitative data values can be organized by a frequency distribution A frequency distribution lists Each of the categories The frequency for each category

FAVORITE COLOR Pick your favorite color of the list blue, green, red, A frequency table for this qualitative data is Which color occurs the most frequently? ColorFrequency Blue Green Red

RELATIVE FREQUENCY ● 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 sum of the relative Frequencies MUST BE EQUAL TO 1 !!!!

RELATIVE FREQUENCY Use the same simple set of data Blue, green, red A relative frequency table is computed as follows ColorFrequencyRelative Frequency Blue Green Red

TABLES 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

BAR GRAPHS ● 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

BAR GRAPH EXAMPLE Bar graphs from our simple data Frequency bar graph Relative frequency bar graph

BAR GRAPHS ● 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

CONFUSING DATA An example with more data values A data set from the text Even with only 30 data values, this table cannot be interpreted easily

Graphs for this set of data A frequency bar graph A relative frequency bar graph These graphs are more effective than the table

SIDE-BY-SIDE BAR GRAPH 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

SIDE-BY-SIDE BAR GRAPH

PIE CHARTS Circle divided into sectors Each sector represents a category Each sector is proportional to the frequency of the category.

PIE CHARTS The following data represent the marital status (in millions) of U.S. residents 18 years of age or older in Draw a pie chart of the data. Marital StatusFrequency Never married55.3 Married127.7 Widowed13.9 Divorced22.8