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