1. Chapter 2 Describing Data: Graphs and Tables
Basic Concepts
Frequency Tables and Histograms
Bar and Pie Charts
Scatter Plots
Time Series Plots
Some information adapted from:
Levine, Brenson and Stephan’s
Statistics for Managers
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2. Basic Concepts in Data Analysis
Data, Information, and Knowledge
Populations and Samples
Variables and Observations
Types of Data: Categorical and Numerical
Types of Data: Cross Sectional and Time Ordered
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3. 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
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4. Populations and Samples
Statistical Inference
Sample: Subset of collection of all possible entities (observation units)
Data on sample is what is available.
KNOWN
Statistics are used to describe samples. These can vary across samples.
Population: Collection of all possible entities (observation units)
Data on the whole population is usually not available.
UNKNOWN
Parameters are used to describe populations. These are constants for a population.
Statistical Inference is the art and science of drawing inferences/ conclusions about a population of interest.
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.
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5. 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
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6. 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
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7. Types of Data: Cross-sectional and Time Ordered
Questions
What was the absenteeism at Plant 1 in Jan. 1998?
Was the annual absenteeism the same for all plants?
Was absenteeism stable at plant 1 during 1998?
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8. Percentage Class Frequency Frequency Tables
A Frequency Table showing a classification of the AGE of attendees at an event.
Class Frequency
10 but under
20 but under
30 but under
40 but under
50 but under
Total
Relative
Frequency
Percentage
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.
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9. A graphical display of distribution of frequencies
Frequency Histograms
A graphical display of distribution of frequencies
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10. 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
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11. Displaying Categorical Data
Bar and Pie Charts
Displaying Categorical Data
CD 14%
Investment Category Amount Percentage
(in thousands $)
Stocks
Bonds CD
Savings
Total
Savings 15%
Stocks 42%
Bonds 29%
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12. Side by Side Chart
Displaying Categorical Bivariate Data: Contingency Tables and Side-by-Side Charts
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13. Scatter Plot for bivariate numerical data
Shows relationship between two variables.
Can one be used to predict the other?
Time-Series and Regression Analysis are used to predict one variable’s value based on the other. Correlation analyses is used to measure the strength of linear relationship among two variables.
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14. Chapter Summary
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