2000 words economic assignment due 13 hours
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EQAWeek13.ppt8220 Economics and Quantitative Analysis
Week 13
Learning Outcome 4:
Analyze business and economic data and interpret quantitative analysis to inform business decisions using quantitative analytic techniques.
Lecturer: Dr. Dayal Talukder
ICL Business School, Auckland
Key elements:
Introduction to statistics for business and economics
- Central tendency, variation and shape of numerical data
- Covariance and coefficient of correlation
LO 4 :
Analyze business and economic data and interpret quantitative analysis to inform business decisions using quantitative analytic techniques.
*
Introduction to statistics for business and economics
Objectives
On completion of this topic students should be able to:
- calculate and interpret measures of central tendency, variation and the shape of numerical data
- calculate and interpret the covariance and the coefficient of correlation.
*
Topic overview
In this topic you will be introduced to some statistics that are designed to measure the:
- central tendency (i.e. the mean, median, and mode)
- variation (i.e. the variance and standard deviation)
- shape of a distribution (i.e. how data are scattered from the central value)
- covariance and coefficient of correlation (i.e. the strength of association between two variables).
Summary Measures
Central Tendency
Mean
Median
Mode
Geometric Mean
Summary Measures
Variation
Variance
Standard Deviation
Coefficient of Variation
Measures of Central Tendency
Central Tendency
Mean
Median
Mode
Geometric Mean
Mean (Arithmetic Mean)
- Mean (Arithmetic Mean) of Data Values
- Sample mean
- Population mean
Sample Size
Population Size
Mean (Arithmetic Mean)
- The Most Common Measure of Central Tendency
- Affected by Extreme Values (Outliers)
(continued)
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12 14
Mean = 5
Mean = 6
- Approximating the Arithmetic Mean
Used when raw data are not available
Mean (Arithmetic Mean)
From a Frequency Distribution
(continued)
Median
- Robust Measure of Central Tendency
- Not Affected by Extreme Values
- In an Ordered Array, the Median is the ‘Middle’ Number
- If n or N is odd, the median is the middle number
- If n or N is even, the median is the average of the 2 middle numbers
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12 14
Median = 5
Median = 6
Chap 3-*
Mode
- A Measure of Central Tendency
- Value that Occurs Most Often
- Not Affected by Extreme Values
- There May Not Be a Mode
- There May Be Several Modes
- Used for Either Numerical or Categorical Data
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Mode = 9
0 1 2 3 4 5 6
No Mode
Geometric Mean
- Useful in the Measure of Rate of Change of a Variable Over Time
- Geometric Mean Rate of Return
- Measures the status of an investment over time
Measures of Variation
Variation
Variance
Standard Deviation
Coefficient of Variation
Population
Variance
Sample
Variance
Population
Standard
Deviation
Sample
Standard
Deviation
- Important Measure of Variation
- Shows Variation about the Mean
- Sample Variance:
- Population Variance:
Variance
Standard Deviation
- Most Important Measure of Variation
- Shows Variation about the Mean
- Has the Same Units as the Original Data
- Sample Standard Deviation:
- Population Standard Deviation:
- Approximating the Standard Deviation
Used when the raw data are not available and the only source of data is a frequency distribution
Standard Deviation
From a Frequency Distribution
(continued)
© 2004 Prentice-Hall, Inc.
Chap 3-*
Comparing Standard Deviations
Mean = 15.5
s = 3.338
11 12 13 14 15 16 17 18 19 20 21
11 12 13 14 15 16 17 18 19 20 21
Data B
Data A
Mean = 15.5
s = .9258
11 12 13 14 15 16 17 18 19 20 21
Mean = 15.5
s = 4.57
Data C
Coefficient of Variation
- Measure of Relative Variation
- Always in Percentage (%)
- Shows Variation Relative to the Mean
- Used to Compare Two or More Sets of Data Measured in Different Units
- Sensitive to Outliers
Comparing Coefficient of Variation
- Stock A:
- Average price last year = $50
- Standard deviation = $2
- Stock B:
- Average price last year = $100
- Standard deviation = $5
- Coefficient of Variation:
- Stock A:
- Stock B:
Shape of a Distribution
- Describe How Data are Distributed
- Measures of Shape
- Symmetric or skewed
Mean = Median =Mode
Mean < Median < Mode
Mode < Median < Mean
Right-Skewed
Left-Skewed
Symmetric
Coefficient of Correlation
- Measures the Strength of the Linear Relationship between 2 Quantitative Variables
Features of Correlation Coefficient
- Unit Free
- Ranges between –1 and 1
- The Closer to –1, the Stronger the Negative Linear Relationship
- The Closer to 1, the Stronger the Positive Linear Relationship
- The Closer to 0, the Weaker Any Linear Relationship
Scatter Plots of Data with Various Correlation Coefficients
Y
X
Y
X
Y
X
Y
X
Y
X
r = -1
r = -.6
r = 0
r = .6
r = 1
Pitfalls in Numerical Descriptive Measures and Ethical Issues
- Data Analysis is Objective
- Should report the summary measures that best meet the assumptions about the data set
- Data Interpretation is Subjective
- Should be done in a fair, neutral and clear manner
- Ethical Issues
- Should document both good and bad results
- Presentation should be fair, objective and neutral
- Should not use inappropriate summary measures to distort the facts
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