ECON 2300 Business Statistics

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ECON 2300 Business Statistics

• Lecture 1
• 08/21/06

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Outline

• Key definitions
• Scales of measuring data
• Types of data
• Data sources
• Descriptive statistics
• Statistical Inference
• Data summary
• Qualitative data
• Quantitative data

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Key definitions

• Statistics Art and science of collecting,
  analyzing, presenting and interpreting data
• Data Facts and figures collected, analyzed and
  summarized for presentation and interpretation
• Elements Entities on which data are collected
• Variable Characteristics of interest for the
  elements

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Key definitions

• Source of data Measurements collected on each
  variable for every element
• Observation Set of measurements

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Scales of measurement

• Nominal labels or names to identify an
  attribute of the element (example stock exchange)
• Ordinal nominal rank or order of data
  meaningful (example service good, bad etc)
• Interval ordinal interval between values
  (fixed unit of measure) For example SAT scores
• Ratio interval ratio of two values meaningful
  (example height, weight etc)

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Types of data

• Qualitative and Quantitative
• Qualitative
• Labels or names
• Nominal or ordinal
• Nonnumeric or numeric
• Statistical analysis use limited
• Quantitative
• Interval or ratio
• Numeric
• Statistical analysis easily usable

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Types of data

• Cross-Sectional and Time series data
• Cross-Sectional
• Data collected at the same time or approximately
  same point of time
• Stock prices on the same day
• Time series
• Data collected over a number of time periods
• Average sales over six months

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Sources of data

• Existing Sources
• Companies/Organizations - employee records,
  production records, inventory records, sales
  records etc
• Government agencies important source for example
  department of labor, census bureau
• Statistical Studies
• Data not available from existing sources
• Collected statistical study

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Sources of data

• Example pharmaceutical firm conducting studies
  for new drug
• Statistical data of two types
• Experimental
• Variable of interest defined
• One or more variables controlled and data
  obtained to see how they influence variable of
  interest
• Example Pharmaceutical company studies
• Observational
• No attempt to control variable of interest
• Example personal interview survey

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Descriptive statistics

• Summaries of data tabular, graphical or
  numerical

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Tabular descriptive statistics
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Graphical Desc Stats
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Numerical Desc Stats

• Average market cap of 25 stocks 112.4 million
• Average Sum of all data/number of data items
  (In this example 25)

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Statistical Inference

• Population Set of all elements of interest in a
  particular study
• Sample Subset of population
• Estimating and testing hypotheses about the
  characteristics of a population using data from a
  sample
• Example data collected for height of 10
  students in class 58, 59, 6, 62,
  55, 57, 59,61, 52, 6

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Statistical Inference

• Data can be used to estimate and test hypotheses
  about the height of the whole class
• The average height of the 10 students is equal to
  5 8
• Using this value, we can possibly say that
  average height of the students in class is 58
  with a margin of -2 inches giving an interval
  of 56 and 510

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Statistical Inference
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Summarizing Qualitative data

• Tabular
• Frequency distribution
• Relative frequency distribution
• Percent frequency distribution
• Graphical
• Bar Graphs
• Pie chart

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Frequency distribution

• Tabular summary of data showing the number
  (frequency) of items in each of the several non
  overlapping classes

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Frequency Distribution
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Relative frequency Percent frequency

• Relative frequency-fraction or proportion of
  items in each class
• Relative freq of classfrequency of class/n
  (total number of items)
• Percent frequencyRelative frequency100

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Relative frequency Percent frequency
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Bar chart Pie graph

• Graphical method to represent frequency, relative
  frequency and percent frequency distributions
• X-axis labels of the classes
• Frequency, relative frequency or percent
  frequency can be used for the Y-axis.

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Summarizing Quantitative data

• Tabular
• Frequency distribution
• Relative frequency
• Percent frequency
• Cumulative frequency distribution
• Graphical
• Dot plot
• Histogram
• Ogive

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Frequency distribution

• Defining non overlapping classes to be done
  carefully (Continuous data)
• Steps
• Determine the number of nonoverlapping classes
• Determine the width of each class
• Determine the class limits
• Number of classes 5 to 20 depending on size of
  data

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Frequency distribution

• Width of classes
• Same width for all classes recommended
• Approximate class width(Largest data
  value-smallest data value)/Number of classes
• Class limits
• Each data value should belong to only one class
• Lower class limit and upper class limit
  smallest and largest possible data value assigned
  to the class

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Example
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Frequency distribution

• Number of classes- number of data items 50 -gt 5
  classes
• Width of the class
• Approximate width(33-12)/54.2
• Round it upto 5
• In practice the above two parameters trial and
  error
• Class limits 10-14, 15-19, 20-24, 25-29, 30-34

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Frequency distribution
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Relative frequency Percent frequency
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Cumulative distributions

• Shows the number of data items with values less
  than or equal to upper class limits
• Can be used to graphically represent frequency,
  relative frequency and percent frequency
  distributions.

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Cumulative distributions
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Graphical

• Dot plot
• One of the simplest graphical summary
• Each data value represented dot
• Histogram
• Graphical representation of frequency, relative
  frequency and percent frequency distributions
• Provides information about the shape or form of
  the distribution

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Dot plot
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Histogram
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Shape of distribution
Skewed left
Skewed right
Symmetric
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Ogive

• Graph of cumulative distribution
• Data values on X-axis and frequencies on Y-axis
• A point is plotted corresponding to the
  cumulative frequency of each class
• Gaps between classes eliminated by considering
  points halfway between class limits

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Summary

• Discussed key parameters and their definitions
• Data types and data sources
• Descriptive statistics and their use in making
  statistical inference (population)
• Data summary (Qualitative and Quantitative data)