Transcript Document 7540519

Math 1476: Business Calculus II
The Path Without A Beginning
Or End Is Symbolic Of The
Learning Process...
Math 1476: Business Calculus II!
Science: The Foundation of Technical Knowledge
“Knowledge is the only instrument of production that
is not subject to diminishing returns ”
J.M. Clark
Math 1476: Business Calculus II
The indispensable condition for creating a
world-class economy in a democratic
society is the creation of world-class
schools.
Lester Thurow
Math 1476: Business Calculus II
Lester C. Thurow - Is the current Lemelson Professor
of Management and Economics at MIT, where he has taught
since 1968. From 1987-1993 he was Dean of MIT’s Sloan
School of Management.
Books: The Zero-Sum Society, Head to Head, The Future of
Capitalism All New York Times bestsellers
Most Recent: Building
Wealth: The New Rules for
Individuals, Companies, and Nations in a
Knowledge-Based Economy
The Wealth Pyramid
Math 1476: Business Calculus II
“Knowledge is the New Basis for
Wealth”
Lester Thurow
“ What is important about any pyramid is not
found by climbing to the top, but by
locating the tunnels that lead to the hidden
treasures within.”
Math 1476: Business Calculus II
Total Quality
Math 1476: Business Calculus II
Lester Thurow
“Rule One:”
“ No one has ever become very rich by saving their money.
The rich see opportunities where large disequilibriums exist.
This was as true for John D. Rockefeller as it is for Bill
Gates. In both cases their lifetime savings constitute a small
fraction of their total wealth. Carefully savings one’s money
and investing in normal equilibrium situations can make one
comfortable in one’s old age, but never really wealthy.”
Math 1476: Business Calculus II
Lester Thurow
“Rule Two:”
“Rule Two: Successful businesses must be willing
to cannibalize themselves to save themselves. They
must be willing to destroy the old while it is still
successful if they wish to build the new before it is
successful. If they won’t destroy themselves, others
will destroy them.”
Math 1476: Business Calculus II
Lester Thurow
“Rule Three:”
“Rule Three: Businesses that would grow rapidly
with high profit margins must take advantage of
technological disequilibriums, exploit
developmental disequilibriums, or create
sociological disequilibriums. All other activities are
slow-growth, low-rate-of-return commodity
businesses. ”
Math 1476: Business Calculus II
Total Quality
"There is no "magic bullet" that will transform companies
into world class competitors. The best companies sometimes
make it seem as though there is. They choose one or two
simple, easy to understand goals as a rallying point: 6 sigma
quality at Motorola. "Leadership Through Quality" and
"Employee Involvement" at Xerox. Usually quality is the
organizing principle, because of its power as a driver for
achieving other key things - productivity, customer
satisfaction, cost reduction, and so on.
Math 1476: Business Calculus II
Total Quality
Quality, as defined by world class companies, is not
what we often understand the concept to be. Rather
when you look at what these best-practice
companies actually do to implement these quality
goals, virtually every task, function and department
in the company is affected." - Extract from Made
In America - MIT
Math 1476: Business Calculus II
THE MATHEMATICS OF FREQUENCY DISTRIBUTION
To apply the four statistical tools in modern quality control
it to essential that the basic mathematics of statistics be
understood because it is possible to misapply sound
practices through insufficient knowledge.
Math 1476: Business Calculus II
The average or arithmetic mean of any set of data is a
measure of its central tendency. It is only a theoretical
concept and does not necessarily describe any of the
measurements from which it is computed. For example,
the average height of ten people measured is 68.2 inches.
This average value divides the data into five
measurements above the average and five measurements
below it; therefore, it is a measurement of central
tendency but may be different from any of the
measurements actually recorded
Math 1476: Business Calculus II
In statistics an average ( ) is
denoted by
F x I
G
J
X , where X  G J
n J
G
G
J
H K
n
i
i 1
Math 1476: Business Calculus II
Course Materials
In statistics an average ( ) is
denoted by
F x I
G
J
 , where   G J
n J
G
G
J
H K
n
i
i 1
Math 1476: Business Calculus II
There are two other terms sometimes used to express the
central tendency of a set of data other than the average.
These terms, which often cause confusion in the minds of
management personnel, are ”median" and ”mode"; they
are usually different from the average value in industrial
data.
The median of a set of data is the middlemost value, or
that value which divides the data into two equal
portions, one with values higher that the median. the
other with values lower than the median. The mode of a
set of date is that value which occurs most frequently.
Measures of Central Tendency
Age (years)
64
61
56
51
49
47
46
43
42
40
37
35
31
26
21
Total Employees
Total Years
Number of Employees
1
4
3
4
4
5
9
12
13
21
12
10
8
2
1
109
4542
Measures of Central Tendency
Age (years)
Number of Employees
64
61
56
51
49
47
46
43
42
40
37
35
31
26
21
Mean
Median
Mode
1
4
3
4
4
5
9
12
13
21
12
10
8
2
1
41.7
42
40
Measures of Central Tendency
Age (years)
Number of Employees
64
61
56
51
49
47
46
43
42
40
37
35
31
26
21
1
4
3
4
4
5
9
12
13
21
12
10
8
2
1
The difference between the highest and lowest value in a set of
data is referred to as the "range" and is denoted by the
symbol R. In this example the range of ages is 64 minus 21
or 43 years. lowest
Math 1476: Business Calculus II
Math 1476: Business Calculus II
The normal curve has a standard deviation which for
practical purposes may be said to divide the range of
the set of date represented into areas under the curve
which will contain specific percentages of the data
represented. These areas under the curve are defined
in terms of distances measured from the average
value in increments of the standard deviation .
The most commonly quoted areas under the normal
curve are as follows:
Math 1476: Business Calculus II
Course Materials 2/24/99
Specified Limits
Percent of Total Area
µ ± 1
68.26
µ ± 2
95.46
µ ± 3
99.73
Math 1476: Business Calculus II
In addition, the standard deviation may be computed
for a population using following equation
n
=
 (x
i
 )
i=1
n
2
Math 1476: Business Calculus II
As compared to a subset of a population which uses
n
=
 (x
i
 )
i=1
n 1
2
Math 1476: Business Calculus II
Math 1476: Business Calculus II
Do you understand
that you are responsible for
your own success or
failure?