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Chapter 9
Describing Variations in Data
Copyright Kaplan University 2009
A variable is…
 A single characteristic that can vary and
can be measured
 Medical Variables:





Biological Differences
Presence, Absence & Stage of Disease
Conditions of Measurement
Techniques of Measurement
Measurement Error
How to Interpret Data
The Decision Factor
 Decide if data is “quantitative” or
“qualitative”
 Identify any variable which may affect data
usage
Types of Variables
 Nominal:
 “the name game”, classifying in a nonnumerical way. Ex: Male/Female; Yes/No;
A,B,AB,O (BLOOD TYPES)
 Each classification can be given a numerical
data code or point for ease of statistical
inference. Example: Male = 1; Female = 2.
Gender
Frequency
1
Percent
.8
Valid Percent
.8
Cumulative
Percent
.8
1.00
44
36.4
36.4
37.2
2.00
74
61.2
61.2
98.3
3.00
2
1.7
1.7
100.0
121
100.0
100.0
Valid
Total
1.00 = Male
2.00 = Female
3.00 = Unknown
Types continued…
 Dichotomous or Binary Variable:
 Variables that reflect two extreme opposites
 Example: Living/Dead
 Dichotomous and nominal variables are also
called “discrete variables” because the
categories are different from one another
Variables, continued
 Ordinal Variables:
 Ranked variables that follow an order.
 Example: Surveys that ask participants to rank
answers/opinions as “very satisfied”; “satisfied”
and “not satisfied”
 Continuous (Dimensional) Variables:
 Measurements which may reflect a
continuous line of data.
 Example: Height, Weight, Blood Pressure, other
readings that can change regularly
Ratio Variables:
- A continuous scale in which “0” has a meaning
 Fahrenheit/Celsius
Scale
Both pictures are taken from google images.com
 Centrigrade Scale
Methods of Documenting
Observations
 Frequency Table
 Consists of a x and y
axis and is used to
show two
characteristics that
relate to one another
 X Axis = Scores
 Y Axis = Frequency of
each score
Score
Below 75
Frequency
4
76 - 80
14
81 - 85
2
86 - 90
8
91 - 95
5
96 - 100
1
Taken from google images
Combining Data
 The grouping of
similar values
together in order to
simplify examination
of the data
 Of the two sets of birth
weights of babies at
Cabbage Patch
Hospital which is
easier to decipher?





1-3 pounds = 10
4-6 pounds = 45
7-9 pounds = 25
10-12 pounds = 12
13+ pounds = 8
2,11,13,14,16,12,10,7,6,8,2,
6,1,12,11,10,9,4,7,2,9,1,8
7,2,6,1,8,7,6,5,6,3,5,2,4,1
2,13
Frequency Distribution
 Recording observations of one variable by
using X Axis for variable and Y Axis for the
frequency of occurrence
 Look at Table 9-2 and 9-3 (pp. 142, 143)
 Which has more interpretive meaning to you?
 Why?
Gaussian Distribution
 Also Known as
“normal distribution”
 Real data seldom
follows this slope
 The larger the data,
the more Gaussian or
“bell shaped” it would
look
Images taken from google
images.com
Types of Visual Representation
Histogram of Smokers
Age at Last Birthday
60
40
20
0
Smoke >=2 PackDay Now
smoke>=1 and <2
PackDay Now
Smoke<1PackDay Now
>=1 PackDay and Quit <3
Years
>1 PackDay and Quit >=3
Year
<=1 PackDay and Quit
<=3 Year
<=1 PackDayand Quit
>=3 years
Never Smoked
Smoking Habits
 Histogram: A bar graph of vertical bars. The area of the
bars represent proportions of all observations that fall
within range of the bar
 Frequency Polygon: This is a histogram minus the bars
which are replaced by dots which are then connected
Images taken from google images.com
Measurements
 Mode: Most commonly seen value in a group of
measurements
 Example:
 6 9 6 8 10 6 4 4 8 11 6 10
 The mode is 6
 Median: Middle observation of a data group is
derived by putting numbers in order and finding
the center number. If there are an even amount
of data points, take the middle two and take an
average.
Median continued…
 Example:
 1 4 9 20 23 27 31 48 56 58
 23 + 27/2 = 25
 Mean: The average of a group of data
points (add all numbers then divide by the number of numbers)
Example: Using the numbers above the
mean is 27.7
Your Turn (time limit: 5 minutes)
 Compute the Mode, Median and Mean of
the following monthly glucose readings for
Fred:
 Jan = 120
July = 98
 Feb = 100
Aug = 127
 Mar = 110
Sept = 134
 April = 128
Oct = 141
 May = 138
Nov = 128
 June = 121
Dec = 146
Answer
Mode = 128
Median = 127.5
Mean = 124.5
Questions…
Homework Time
 This chapter covered a great deal, so…
 Please re-read the remainder of the chapter
beginning with page 149 – “Problems in
analyzing a Frequency Distribution.
 This information is a review/continuance of what
we have covered tonight
 Please drop me an e-mail after you have re-read this area
and indicate if you have any further questions or if you are in
complete understanding of the information.
Any Further Questions