Chapter Basic Mathematical Tools
Basic Statistics
December 2013
Keesuk KimStatistics consultant, GSO1
Chapter Basic Mathematical Tools2Chapter Basic Mathematical
ToolsMathematics;The language of quantitative methods in social
sciences such as economics, sociology and management sciencesThe
purpose of learning basic mathematics;To understand economic
theory/literature, presented in the form of mathematical
formula/statistical model To have robust knowledge on the theories
of statistics and econometric analysis. The topics of basic
mathematics covered in this lecture Summation operator, Linear and
certain nonlinear equations, Proportions and percentagesSome
special functions that often arise in statistics and applied
econometrics ;quadratic functions, natural logarithm and log
function,exponential function,Brief review of differential
calculus
3Section 1. The Summation Operator
4Section 1. The Summation Operator
5Section 1. The Summation Operator
6Section 1. The Summation Operator
7Section 1. The Summation Operator
8Section 1. The Summation Operator
99Section 2. Properties of Linear Functions
1010Section 2. Properties of Linear Functions
1111Section 2. Properties of Linear Functions
1212Section 2. Properties of Linear Functions
1313Section 3. Proportions and Percentages1414Section 3.
Proportions and Percentages
1515Section 3. Proportions and Percentages
1616Section 3. Proportions and Percentages
Changes in Labor Force and Employed Workers in Hanoi(2005 vs
2010)1717Section 3. Proportions and PercentagesDistinction between
percentage point change and percentage change is important, when
GSO statisticians communicate with press people and other users of
the statistics.
The percentage point change and the percentage change are very
different. The percentage point change is just the change absolute
in the percentages. The percentage change (or proportionate) is the
change relative to the initial value. Generally, we must pay close
attention to which number is being computed. The careful researcher
makes this distinction perfectly clear; unfortunately, in the
popular press as well as in academic research, the type of reported
change isoften unclear.
1818Section 3. Proportions and PercentagesE x a m p l e
1.2[Michigan Sales Tax Increase]In March 1994, Michigan voters
approved a sales tax increase from 4% to 6%. In political
advertisements, supporters of the measure referred to this as a
twopercentage point increase, or an increase of two cents on the
dollar. Opponents to the tax increase called it a 50% increase in
the sales tax rate. Both claims are correct; they are simply
different ways of measuring the increase in the sales tax.
Naturally, each group reported the measure that made its position
most favorable.
1919Section 4. Some Special Functions and Their
Properties2020Section 4. Some Special Functions and Their
Properties2121Section 4. Some Special Functions and Their
Properties
2222Section 4. Some Special Functions and Their
Properties2323Section 4. Some Special Functions and Their
Properties2424Section 4. Some Special Functions and Their
Properties
2525Section 4. Some Special Functions and Their Properties
2626Section 4. Some Special Functions and Their
Properties2727Section 4. Some Special Functions and Their
Properties2828Section 4. Some Special Functions and Their
Properties2929Section 4. Some Special Functions and Their
Properties3030Section 4. Some Special Functions and Their
Properties3131Section 4. Some Special Functions and Their
Properties3232Section 4. Some Special Functions and Their
Properties3333Section 4. Some Special Functions and Their
Properties
3434Section 5. Some of Differential Calculus3535Section 5. Some
of Differential Calculus3636Section 5. Some of Differential
Calculus3737Section 5. Some of Differential Calculus3838Section 5.
Some of Differential Calculus3939[Practice 1. Linear Consumption
Function of Vietnam Economy]4040K E Y T E R M SAverage / Ceteris
Paribus / Constant Elasticity Model / Derivative / Descriptive
Statistic / Diminishing Marginal Effect / Elasticity / Exponential
Function / Intercept / Linear Function /Log Function / Marginal
Effect / Median / Natural Logarithm / Nonlinear Function / Partial
Derivative / Partial Effect / Percentage Change / Percentage Point
Change /Proportionate Change / Relative Change / Semi-Elasticity /
Slope / Summation Operator
4141
