Business Statistics

1
Business Statistics

• Introduction to Statistics

2
Overview

• What is statistics?
• Description (Data analysis) ---gt Stage I
• Inference (Applying results) ---gt Stage 2
• Data types
• Numeric
• Categorical
• Introduction to descriptive analysis
• Informal (tables charts)
• Summary measures

3
Schematic View
4
Sampling
Population
Sample
Statistic
Parameter
5
Very Important

• Type of analysis depends upon data
• Numeric
• Categorical

6
Descriptive Analysis

• Three general forms
• Informal
• Tables
• Charts
• Formal Numeric (i.e., statistics)
• Forms basis for performing inferential analyses

7
Numeric Data Charts Tables

• Ordered array
• Stem-leaf display
• Frequency distribution
• Absolute frequencies
• Relative frequencies ()
• Cumulative frequencies
• Cumulative relative frequencies
• Histogram (frequencies)
• Ogive (cumulative frequencies)

8
Stem-Leaf Display

• Best to start from ordered array
• Procedure
• Consider any number XXXXX.XXX
• Determine between which digits to split
• Digits on left become the stem
• Digit on the right becomes the leaf
• Split all values in the data the same way
• Split should be such that number of stems is
  between 4 and 10 (roughly)

9
Stem-Leaf Example

• GNI Data (revised stem-leaf)
• Test Scores
• Stem Leaf
• 9 1 7
• 10 0 0 2 2 3 3 4 6 8 8 9
• 1 1 5 7 8 8
• 12 2 3 3
• Multiply Stem.Leaf by 10

10
Stem-Leaf Example

• Problem 2.5 (revised stem-leaf)
• Stem Leaf
• 2 2 3 8
• 3 0 1 2 2 3 4 4 5 6 6 6 6 6 7 7 7 7 7 8 9 9 9 9
• 4 0 0 0 0 0 0 1 1 2 2 3 3 3 3 4 4 4 4 4 5 6 6 9
• 5 0
• Multiply Stem.Leaf by 100

11
Frequency DistributionsDetermining Frequency
Groups

• Start by breaking the data range into k equal
  width intervals
• Let n represent the number of observations
• Number of intervals such that 2k gt n
• Interval width
• Start with (Max - Min) / k
• Use convenient breakpoints for intervals
• 91.0 through 97.4 (OK)
• 90.0 through 95.0 (Better)
• Intervals no overlap no gaps

12
Frequency DistributionsDetermining Frequencies

• Absolute frequencies
• Count number of observations in each interval
• Relative frequencies
• Divide absolute frequency by total number of
  observations
• Cumulative frequencies
• Add frequencies for all previous intervals (note
  difference from manner done in text)
• Cumulative relative frequencies
• Add relative frequencies for all previous
  intervals

13
Histograms

• What are they?
• Just graphical displays of frequency
  distributions
• Absolute frequencies
• Relative frequencies
• Cumulative frequencies
• Provide picture of the variation in the data
• Basics
• Horizontal axis values for variable of concern
• Vertical axis indicates corresponding
  frequencies

14
Ogives

• What are they?
• Line plots of cumulative relative frequencies
• Often displayed in conjunction with absolute or
  relative frequency histograms
• Provide quick means of identifying critical break
  points
• Quartiles
• 80/20 analyses

15
Categorical Data Charts Tables

• Frequency table is basis for chart
• Same as with numerical data, except data already
  are broken into frequency groups (categories)
• Bar chart
• Pie chart
• Pareto chart

16
Bar Charts and Pie Charts

• Bar chart
• Two formats
• Vertical (preferred)
• Horizontal
• Analogous to histograms, but
• Bars dont touch each other
• Ordering of bars doesnt matter
• Pie chart
• Often preferable to bar charts
• Must identify slices

17
Pareto Charts

• Special form of bar chart
• Bars arranged from largest to smallest
• Ogive is superimposed
• May need secondary vertical axis
• Aid quick identification of
• Vital few
• Trivial many

18
Summary

• Weve overviewed the basic informal means of
  describing data
• Tables
• Charts
• Type of exhibit depends on data type
• Numeric
• Categorical
• Whats next numerical summary measures for
  numeric data