organizing qualitative data 2.1. frequency distribution qualitative data values can be organized by...
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O R G A N I Z I N G Q U A L I TAT I V E 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 listblue, green, red,
• A frequency table for this qualitative data is
• Which color occurs the most frequently?
Color Frequency
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 dataBlue, green, red
• A relative frequency table is computed as follows
Color Frequency Relative 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 2006. Draw a pie chart of the data.
Marital Status Frequency
Never married 55.3
Married 127.7
Widowed 13.9
Divorced 22.8