the path without a beginning or end is symbolic of the learning process... math 1476: business...

The Path Without A Beginning The Path Without A Beginning Or End Is Symbolic Of The Or End Is Symbolic Of The Learning Process...Learning Process...

Math 1476: Business Calculus IIMath 1476: Business Calculus II

Math 1476: Business Calculus II! Math 1476: Business Calculus II!

Science: The Foundation of Technical KnowledgeScience: The Foundation of Technical Knowledge

““Knowledge is the only instrument of production that Knowledge is the only instrument of production that is not subject to diminishing returns ”is not subject to diminishing returns ”

J.M. ClarkJ.M. Clark

The indispensable condition for creating a The indispensable condition for creating a world-class economy in a democratic world-class economy in a democratic society is the creation of world-class society is the creation of world-class schools.schools.

Lester ThurowLester Thurow


Lester C. ThurowLester C. Thurow - - Is the current Lemelson Professor Is the current Lemelson Professor of Management and Economics at MIT, where he has taught of Management and Economics at MIT, where he has taught since 1968. From 1987-1993 he was Dean of MIT’s Sloan since 1968. From 1987-1993 he was Dean of MIT’s Sloan School of Management. School of Management.

Books: Books: The Zero-Sum Society, Head to Head, The Future of The Zero-Sum Society, Head to Head, The Future of Capitalism Capitalism All New York Times bestsellers All New York Times bestsellers

Most Recent: Most Recent: Building Wealth: The New Rules for Building Wealth: The New Rules for Individuals, Companies, and Nations in a Individuals, Companies, and Nations in a Knowledge-Based EconomyKnowledge-Based Economy


The Wealth PyramidThe Wealth Pyramid

““Knowledge is the New Basis for Knowledge is the New Basis for Wealth”Wealth”

Lester ThurowLester Thurow“ “ What is important about any pyramid is not What is important about any pyramid is not

found by climbing to the top, but by found by climbing to the top, but by locating the tunnels that lead to the hidden locating the tunnels that lead to the hidden treasures within.”treasures within.”



Total QualityTotal Quality


““Rule One:”Rule One:” “ “ No one has ever become very rich by saving their money. No one has ever become very rich by saving their money.

The rich see opportunities where large disequilibriums exist. The rich see opportunities where large disequilibriums exist. This was as true for John D. Rockefeller as it is for Bill This was as true for John D. Rockefeller as it is for Bill Gates. In both cases their lifetime savings constitute a small Gates. In both cases their lifetime savings constitute a small fraction of their total wealth. Carefully savings one’s money fraction of their total wealth. Carefully savings one’s money and investing in normal equilibrium situations can make one and investing in normal equilibrium situations can make one comfortable in one’s old age, but never really wealthy.”comfortable in one’s old age, but never really wealthy.”



““Rule Two:”Rule Two:” “ “Rule Two: Successful businesses must be willing Rule Two: Successful businesses must be willing

to cannibalize themselves to save themselves. They to cannibalize themselves to save themselves. They must be willing to destroy the old while it is still 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 wish to build the new before it is successful. If they won’t destroy themselves, others successful. If they won’t destroy themselves, others will destroy them.”will destroy them.”



““Rule Three:”Rule Three:” “ “Rule Three: Businesses that would grow rapidly Rule Three: Businesses that would grow rapidly

with high profit margins must take advantage of with high profit margins must take advantage of technological disequilibriums, exploit technological disequilibriums, exploit developmental disequilibriums, or create developmental disequilibriums, or create sociological disequilibriums. All other activities are sociological disequilibriums. All other activities are slow-growth, low-rate-of-return commodity slow-growth, low-rate-of-return commodity businesses. ”businesses. ”



Total QualityTotal 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.


Total QualityTotal 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


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.


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


In statistics an average ( ) is denoted by

X Xx

n

ii

n

, where

F

H

GGGG

I

K

JJJJ

1


Course MaterialsCourse Materials

In statistics an average ( ) is denoted by

, where

F

H

GGGG

I

K

JJJJ x

n

ii

n

1


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 TendencyMeasures of Central Tendency

Age (years) Number of Employees

64 1

61 4

56 3

51 4

49 4

47 5

46 9

43 12

42 13

40 21

37 12

35 10

31 8

26 2

21 1

Total Employees 109

Total Years 4542

Measures of Central TendencyMeasures of Central Tendency Age (years) Number of Employees

64 1

61 4

56 3

51 4

49 4

47 5

46 9

43 12

42 13

40 21

37 12

35 10

31 8

26 2

21 1

Mean 41.7

Median 42

Mode 40

Measures of Central TendencyMeasures of Central Tendency Age (years) Number of Employees

64 1

61 4

56 3

51 4

49 4

47 5

46 9

43 12

42 13

40 21

37 12

35 10

31 8

26 2

21 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


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:


Course Materials 2/24/99Course Materials 2/24/99

Specified Limits Percent of Total Area

µ ± 1 68.26

µ ± 2 95.46

µ ± 3 99.73


In addition, the standard deviation may be computed for a population using following equation

=(xi

i=1

n

)2

n


As compared to a subset of a population which uses

=(xi

i=1

n

)2

1n

Do you understandDo you understand

that you are responsible for that you are responsible for your own success or your own success or

failure?failure?

the path without a beginning or end is symbolic of the learning process... math 1476: business...

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