Chapter 2
Section 1
Organizing
Qualitative Data
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 1 of 27
Chapter 2 – Section 1
● Learning objectives
1

Organize qualitative data in tables
2 Construct bar graphs
3
 Construct pie charts
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 2 of 27
Chapter 2 – Section 1
● Learning objectives
1

Organize qualitative data in tables
2 Construct bar graphs
3
 Construct pie charts
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 3 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 4 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 5 of 27
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
Color
Frequency
Blue
Green
Red
4
1
3
● The most commonly occurring color is blue
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 6 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 7 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 8 of 27
Chapter 2 – Section 1
● A relative frequency table for this qualitative data
is
Color
Blue
Green
Relative Frequency
.500
.125
Red
.375
● A relative frequency table can also be
constructed with percents (50%, 12.5%, and
37.5% for the above table)
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 9 of 27
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”
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 10 of 27
Chapter 2 – Section 1
● Learning objectives
1

Organize qualitative data in tables
2 Construct bar graphs
3
 Construct pie charts
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 11 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 12 of 27
Chapter 2 – Section 1
● Bar graphs for our simple data (using Excel)
 Frequency bar graph
 Relative frequency bar graph
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 13 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 14 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 15 of 27
Chapter 2 – Section 1
● A Pareto chart for our simple data (using Excel)
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 16 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 17 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 18 of 27
Chapter 2 – Section 1
● Graphs for this data (continued)
 A Pareto chart
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 19 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 20 of 27
Chapter 2 – Section 1
● An example side-by-side bar graph comparing
educational attainment in 1990 versus 2003
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 21 of 27
Chapter 2 – Section 1
● Learning objectives
1

Organize qualitative data in tables
2 Construct bar graphs
3
 Construct pie charts
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 22 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 23 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 24 of 27
Chapter 2 – Section 1
● An example of a pie chart for the 2003 data from
the side-to-side bar chart
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 25 of 27
Chapter 2 – Section 1
● Side-by-side pie charts are used sometimes, but
can be difficult to interpret (using Excel, with
substantial modifications)
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 26 of 27
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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 2 Section 1 – Slide 27 of 27