Section 1.4: Types of Data and
Some Simple Graphical Displays
Definitions
• Variable – Is any characteristic whose
value may change
• Data – Result from making observations
either on a single variable or
simultaneously on two or more variables
• Univariate Data Set – Consists of
observations on a single variable made on
individuals in a sample or population
Univariate Data Sets
• Two Types of Univariate Data Sets:
– Categorical Data Set – Individual
observations are categorical responses
(nonnumerical)
– Numerical Data Set – Individual observations
are numerical (quantitative) in nature
Airline Safety Violations
• The Federal Aviation Administration (FAA)
monitors airlines and can take administrative
actions for safety violations. Information about
the tines assessed by the FAA appeared in the
article “Just How Safe Is That Jet?” Violations
that could lead to a fine were categorized as
Security (S), Maintenance (M), Flight Operations
(F), Hazardous Materials (h), or Other (O). Data
for the variable type of violation for 20
administrative actions are given in the following
list.
Airline Safety Violations List
S S M H M O S M S S
F S O M S M S M S M
What type of data set is this list?
Because type of violation is nonnumerical,
this is a categorical data set.
More than one variable
If an observation consists of two or more
responses or values:
Two: Bivariate data set
More than two: Multivariate data set
Revisiting Airline Safety Violations
Example of Bivariate Data Set
The same article gave
data on both the
number of violations
and the average fine
per violation for 10
major airlines. The
resulting data are
given in the following
table:
Airline
# of
Violations
Average
Fine
Alaska
258
5038.76
America
West
257
3112.84
American
1745
2693.41
Continental
973
5755.39
Delta
1280
3828.13
Northwest
1097
2643.57
Southwest
535
3925.23
TWA
642
2803.74
United
1110
2612.61
US Airways
891
3479.24
Numerical Data
• Two types of Numerical Data
– Discrete – If the possible values are isolated
points on the number line
– Continuous – if the set of possible values
forms an entire interval on the number line
Definitions
• Frequency Distribution for Categorical Data – A
table that displays the possible categories along
with the associated frequencies or relative
frequencies
• Frequency – For a particular category is the
number of times the category appears in the
data set
• Relative Frequency – For a particular category is
the fraction or proportion of the time that the
category appears in the data set.
Definitions continued
Relative Frequency is calculated as:
frequency
relative frequency =
number of observations in the data set
When the table includes relative frequencies
it is sometimes referred to as a relative
frequency distribution.
Preferred Leisure Activities
Below is a report on physical activity patterns in
urban woman. The following coding is used: W =
walking, T = weight training, C = cycling, G =
gardening, A = aerobics
W T A W G T W W C W
T W A T T W G W W C
A W A W W W T W W T
The corresponding frequency distribution is given.
Frequency Distribution for
Preferred Activity
Bar Charts
• A graph of the frequency distribution of
categorical data.
How to construct
1. Draw a horizontal line, and write the category
names or labels below the line at regularly
spaced intervals.
2. Draw a vertical line and label the scale using
either frequency or relative frequency.
3. Place a rectangular bar above each category
label. The height is determined by the frequency
and weight should be the same.
Why students drop out
An article examined the
reasons that college
seniors leave before
graduating. 42
seniors that dropped
out were interviewed.
Here is the data from
the interview.
Reason for leaving
Frequency
Academic Problems
7
Poor teaching
3
Needed a break
2
Economic Reasons
11
Family Responsibilities
4
To Attend another
school
9
Personal Problems
3
Other
3
Bar Chart for why students drop out
Dotplots
• A picture of numerical data in which each
observation is represented by a dot on or above
a horizontal measurement scale.
How to construct
1. Draw a horizontal line and mark it with an
appropriate measurement scale
2. Locate each value in the data set along the
measurement scale, and represent it by a dot. If
there are two or more observations with the
same value, stack the dots vertically.
Graduation Rates for NCAA Division I
Schools in California and Texas
The data is of freshmen who earned a
bachelor's degree by 6 years.
California: 64 41 44 31 37 73 72 68 35 37
81 90 82 74 79 67 66 66 70 63
Texas:
67 21 32 88 35 71 39 35 71 63
12 46 35 39 28 65 25 24 22
Dotplot of Graduation Rates for
California and Texas
Activity: Head Sizes