1. Describing Data
Charts and Graphs

2. Lecture Objectives You should be able to: Define Basic Terms
Recognize Types of Data and Data Scales
Draw appropriate graphs based on type of data and type of analysis desired.
Interpret the graphs

3. Basic Terms Data, Information, and Knowledge Populations and Samples
Variables and Observations
Types of Data:
Categorical and Numerical
Cross Sectional and Time Ordered

4. Data, Information, and Knowledge
Data are building blocks of information. These are observations on entities (observation units). Variables are used to measure observations.
Information is processed data (organized, summarized, analyzed and filtered) that are made meaningful and relevant to the situation/phenomenon being understood.
Knowledge is the ability to apply/use information to decision situations. Meaning associated with information is knowledge …. Actionable Information!
Processing
Analysis
Reports
Application
Meaning
Relevance

5. Populations and Samples
Population: Collection of all possible entities of interest
Described by Parameters
Sample: Subset of collection
Described by Statistics
Statistical Inference
Art and science of using samples to make conclusions about populations.
Statistical Inference is the process by which a characteristics/aspects of a population are understood (known).
Conclusions about the population are drawn (inferred) based in the knowledge gained from the sample.
A sample should be a good representation of the population.

6. Variables and Observations
Entity
Height
(inches)
Weight
(pounds)
Age
(years)
Sex
(Category)
Person 1
Person 2
Person 3 * 67 61 72
170
120
220 33 38 62
Male
Female
O B S E R V A T I O N S
Variables are characteristics (aspects) of entities that are different for different entities. Observations on an entity are values of these characteristics that have been measured.
So, a dataset is a collection of observations on a group (sample) of entities. Each row is an observation on a particular entity. Each column is an aspect or characteristic of individual entities (measured as variables).
Measurement

7. Types of Data: Categorical and Numerical
We can do arithmetic on numerical data (age and salary). These data are actual measurements.
Categorical data is qualitative. Sometimes qualitative data is coded. For example, opinion can be coded 1-5 and arithmetic (calculations) can be performed. Such data is ordinal (has implied order). State is a categorical variable and cannot be used for calculations. Such data are nominal.
Categorical
Numerical

8. Data Scales Data are generally classified into four types:
Nominal – Categorical data
Ordinal – shows ranks, intervals may vary
Interval – intervals are constant, arbitrary 0
Ratio – Numeric data with a ‘real’ 0 value.
Ordinal, Interval and Ratio scales are all Numeric data.

9. Types of Data: Time Series and Cross-sectional
Population
Month
(Millions)
1900 56
1910 58
1920 60
1930 65
1940 76
1950 84
1960 95
1970
120
1970
Population
GDP
Gender
Country
(Millions)
$ Billion
Ratio
USA
160
575
0.998
China
800
155
1.105
India
600
Nigeria
100
Japan
120
Canada 30
Variable(s) at one point in time
across multiple entities (countries in this case)
Variable(s) over time

10. Numeric Data (Interval or Ratio): Frequency Tables
A Frequency Table showing a classification of the AGE of attendees at an event.
Relative
Class
Frequency
Percent
10 to 20 3
0.15 15
20 to 30 6
0.30 30
30 to 40 5
0.25 25
40 to 50 4
0.20 20
50 to 60 2
0.10 10
1.00
100
Class is a range for the values of a variable.
Frequency is the number of observations associated with a class.
Relative Frequency is the proportion of observations (frequency) associated with a class.

11. Frequency Histograms
A graphical display of distribution of frequencies

12. Developing Frequency Tables and Histograms
Sort Raw Data in Ascending Order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35,
37, 38, 41, 43, 44, 46, 53, 58
Find Range: = 46
Select Number of Classes: 5 (usually between 5 and 15)
Compute Class Interval (width): 10 (range/classes = 46/5 then round up)
Determine Class Boundaries (limits): 10, 20, 30, 40, 50
Compute Class Midpoints: 15, 25, 35, 45, 55
Count Observations & Assign to Classes

13. Categorical Data: Bar Charts
Obs
Age
Gender
State
Salary 1 25 M FL 2 28 F SC 36 3 31 GA 44 4 35 38 5 56 6 68 7 42 79 8 51 64 9 55 88 10 61 71 11 62 92 12 65 54
State
Freq FL 3 SC 5 GA 4

14. Categorical Data: Pie Charts
State
Freq FL 3 SC 5 GA 4

15. Numeric Data by CategoryF M FL
66.00
25.00 GA
70.00
74.67 SC
53.67
67.50

16. Bivariate Numerical Data Scatter Plot

17. Two variables, different units
Year CO
Nox
1990
154,188
25,527
1991
147,128
25,180
1992
140,895
25,261
1993
135,902
25,356
1994
133,558
25,350
1995
126,778
24,955
1996
128,859
24,786
1997
117,911
24,706
1998
115,380
24,347
1999
114,541
22,843
2000
114,465
22,599
2001
106,263
21,546
2002
109,235
21,277
2003
107,062
20,476
2004
104,892
19,564
2005
102,721
18,947
2006
100,552
18,226
Source:

18. Chapter Summary Categorization: Bar, Pie charts
Distribution: Stem and Leaf, Histogram, Box Plot
Relationships: Scatter Plots, Line Charts
Multivariate: Spider Plots, Maps, Bubble Charts