Welcome to
PMBA0608:
Economics/Statistics
Foundation
Fall 2006
Session 4: September 6
Study
 Chapters 1 through 4 of Mankiw
 Chapters 1 through 3 of Mendenhall,
Beaver and Beaver
 Send me your questions
 I will do one or all of the following
 Answer you privately
 Publish the answer to your question on line
 Answer your question in our next class
Discuss Assignment 1
1) Problem 5, Page 16 of Mankiw
$5 million is sunk cost
MC = $1 million
MB = $3 million
MB>MC should complete the
project
 As long as MB >MC, the answer is
the same
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


Discuss Assignment 1
2) Problem 8, Page 17 of Mankiw
 The new bill will increase the incentive for
economic activity.
 Efficiency may increase for two reasons
 Resources are not wasted as much as before
 If tax rates go down  current work force will
have an incentive to work harder
 Equity may decline as
 Current workers’ tax rate may go down
 Some current welfare recipients may not be
able to find jobs the pay a much as welfare.
Discuss Assignment 1
3)
The discussion on the
connection between the
article and the economic
principle should be well
developed.
Discuss Assignment 1
4) Question 1.2, Page 10 of Mendenhall,
Beaver and Beaver
 Population of interest is the population of the
measurements of the appraisals of the land by
all experienced appraisers.
 Population is large but it does exist, so it is not
conceptual.
 Populations are different
 Buyers may underestimate. Sellers may over
estimate….
 More than one appraisal should be used.
Discuss Assignment 1
5) Question 1.7, Page 10 of Mendenhall,
Beaver and Beaver
 Population of shopper opinions (in favor or
opposed background music)
 Not possible to examine the entire population as
future shoppers are not known.
 No, sample percentages will not be the same as
population percentage but it will serve as an
estimate as population percentage.
Back to Chapter 2 of Mankiw:
Macro/micro economics
 Macro = big Picture = Forest
 Focuses on the aggregate
markets
 Micro = small picture = tree
 Focuses on individual markets
Which of the following is a
macro/micro topic?
 The effect of tax policy on the price of gas
in Ohio.
 The effect of tax policy on the general
price level in Ohio.
 The effect of agricultural subsides on the
income of farmers.
 The effect of agricultural subsidies on
income tax rates in the U.S.
Which of these topics will be covered in
a macro/micro economics course?
 The impact of the 1987 market crash on
consumers’ spending.
 How a higher rate of inflation alters the
distribution of wealth and income.
 The effect of war in Iraq on the price of
oil.
 The effect of the increase in the price of
oil on the overall unemployment rate.
Normative/Positive Statements
 Positive Statement




is descriptive
But not necessarily true
can be tested for validity
Example
 Normative statement
 is an opinion
 can not be tested for validity
 Example
Note
A normative economic
statement that is not backed
up by positive statement is
worthless.
Chapter 2 of Mendenhall, Beaver &
Beaver (Stat)
 Which of the following is (are) a Variable?
1.
2.
3.
4.
Interest rates
My name
My weight
Price of gasoline
 1, 3 and 4.
 Variable = characteristics that change over
time or across different objects.
Which of the following is (are)
experimental unit (s)?
1.
2.
3.
4.


Jackie
United States
Unemployment rate
A PMBA student
1, 2 and 4
Experimental unit = an individual or
object on which a variable is
measured.
Which of the following variables is
(are) qualitative?
1.
2.
3.
4.


Gender of students in this class
Height of students in this class
Seasons
Cost of production
1 and 3
Qualitative variables can be
categorized but not measured.
Which of the following variables is
continuous?
1. The number of your children over
time.
2. Your weight over time.
3. The year
 2
 Continuous variable can assume all
of the infinitely many values
corresponding to a line interval.
Can a qualitative variable be
continuous?
No.
Gender
Male = 1
Female = 2
Budget deficit in billions of dollars.
(What kind of graph is this?)
100
0
-100
-200
-300
-400
-500
-600
2000
2001
2002
2003
2004
2005
Prime rate in the US
(What type of graph is this?)
Make sure
You know how to create a
graph using Excel or any
other program.
 Highlight your columns that contain data
and click on Chart Wizard.
You know what type of graph
is more appropriate in
different scenarios and why?
Histograms are used to show
relative frequencies: Example
Individual
Mark
Number of
children
1
Jan
0
Mary
0
Jackie
3
Total
4
Histograms are used to show
relative frequencies: Example
Number of children
Relative frequency
0-1
¾ = 75%
2-3
¼ = 25%
Histograms are used to show
relative frequencies: Example
Relative
frequency
75%
25%
0
1
2
3
Number of kids
Do you use a bar graph or a histogram
in each of the following situations?
1. You want to compare heights of 10
individuals in this class.
 Bar
2. You want to compare total revenues of five
different companies.
 Bar
3. You want to compare numbers of
companies that make from 0 to $10,000;
from $10,000 to $20,000; from $20,000 to
$30,000 and so on.
 Histogram
Check out the following interactive
site for creating histograms
 http://www.shodor.org/interactivate/a
ctivities/histogram/?jv=1.4.1_02&jb=
MSIE
The arithmetic mean
 Helps us describe the sample (xbar)or the
population (μ)
 The sample mean, xbar is
 xbar = (x1 + x2 + . . . + xn) / n .
 Mean member of US households
 = total population /number of households
 In 2003 =2.57
 Mean household income in the US
 = total income/households
 In 2003 =$59,067
What is median?
 50% of observations fall below
median and 50% of observations fall
above median
 In 2003 median income of a
household in the US was $43,318
 50% of households received less than
$43,318.
 50% of households made over $43,318.
Mean /median
Note: Area under the curve is 100%
 What does this tell you about income
equality in the US?
Relative
frequency
50% of
households
$43,318 =
median
50% of
households
$59,067 =
mean
Income
household
Which nation has more poor
households?
 Mean income is the same
Relative
frequency
Relative
frequency
$60,000
Nation A
income
60,000
Nation B
income
Need a measure of dispersion in
order to describe our data better
1. Range
 Maximum value – minimum
value
 Makes more sense for small
samples
Are these two samples the same?
 Weight sample 1




Four observations: 100, 110, 170, 200
Mean = 145
Median = 140
Range = 100
 Weight sample 2
 Eight observations: 100, 115, 125, 130, 150,
160, 180,200
 Mean = 145
 Median = 140
 Range= 100
 According to mean, median and range, yes.
Measures of dispersion:
(2) Mean Absolute Deviation (MAD)

= mean of absolute values of deviation of each observation
from mean
Weight of individual (wi) in Sample 1
|wi- wbar|
100
45
110
35
170
25
200
55
•MAD = (Σ |wi- wbar|)/n) =(45+35+25+55)/4= 40
What is MAD for Sample 2?
 Weight sample 2
 100, 115, 125, 130, 150, 160, 180,200
 Mean = 145




MAD = 27.5
MAD in sample 2 < MAD in sample 1
What does this mean?
The distribution of Sample 2 is tighter
Measures of dispersion:
(3) Variance
 In population = Σ(wi- wbar)2/n
 In sample = Σ(wi- wbar)2/n-1
 Calculate the variance in Sample 1
and Sample 2
 Variance in Sample 1 = 2300
 Variance in Sample 2 =1150
 Standard deviation is the square root
of variance.
Empirical Rule
 If the sample is very large
population
 If the relative frequency distribution
is bell shaped
 Then
 68% of observations fall within one
standard deviation from the mean
 95% of observations fall within two
standard deviation from the mean
Empirical Rule
 Suppose standard deviation is 30
Rela.
frequency
68%
95%
8
5
1
1
5
145
1
7
5
2
0
5
weight
In our example, both samples had the
same mean and Sample 1 had a higher
standard deviation
 So, Sample 1 was more variable.
 But what if two samples have different
means?
 How do we measure which one is more
variable?
 Coefficient of variation = (standard
deviating/mean) * 100
 The higher the mean, the ______ the CV.
 The higher the standard deviation, the _____
the CV.
Bivariate data
 Sometimes we want to focus on two
variables at the same time
 Example 1
 Are women earning less than men for
doing the same job?
 One of my students wanted to answer
this question
 Collected a sample of area attorneys at
different stages of their careers
Bivariate data
 The study of earning gap
Earnings
Male
Female
Years after
graduation
Bivariate data: relationship
 There is economic theory suggesting
that there is a negative relationship
(trade off) between inflation and
unemployment
 Collect data on both variables
Bivariate data: relationship
 Plot your points
Unemployment
rate
1990
1991
1993
1992
1994
•What type of relationship is there between inflation
and unemployment?
Inflation
Is there a measure of correlation
between two variables (x and y)?
 Yes?
 Correlation coefficient (r)
 Takes a value between -1 to +1
 If r =0  x and y are not correlated
 If r = -1  x and y are perfectly and
indirectly correlated
 If r = +1 x and y are perfectly and
directly correlated
How do we calculate r?
 Formula on Page 66 of stat book
 Excel calculates it automatically
 Under fx type
=CORREL (A2:A10;B2:B10)
Suppose you are told that your salary is at
70th percentile in the distribution of salaries in
your organization. What does this mean?
70% of other salaries in your
organization are lower than
your salary and 30% are
higher than your salary.
Another measure of relative
standing is z-score
 Measures the number of standard
deviations between an observation an
the mean of the set.
 Example
 If z = 2
 Then your salary is lies 2 standard
deviations above the mean
 Formula on page 71 of Stat Book
Note:
 Sections 2.5 and 2.13 of this Chapter
are dropped.
Assignment 2
Due: On or before September 16
Problem 3, Page 59 of Mankiw
Problem 6. Page 60 of Mankiw
Application 2.6, Page 24 of Mendenhall, Beaver and
Beaver (Use Excel or similar program. Explain why one
presentation is more effective.)
4. Application 2.12, Page 33 of Mendenhall, Beaver and
Beaver (Use Excel or similar program.)
5. Exercise 2.47, Page 67 of Mendenhall, Beaver and
Beaver (Use Excel or similar program.)
Notes:
1) Each question has 4 points.
2) Don’t hesitate to contact me.
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