SEB.10.11. (01)

Analytical Tools

Business Statistics Study

October 11, 2001

Susan Blouin

ATHABASCA UNITVERISTY, Centre for Innovative Management – MBA Program, Analytical Tools Final Project

PART I ANALYSIS: Quantitative and Qualitative Statistical Business Analysis:

European Management Consultancy Firms

PART II ANALYSIS: Quantitative Assessment: Statistical Summary

A. Stem and Leaf Integers as Stems

B. Probability Theory Analysis

C. Population Parameters Estimating and Confidence Intervals

D. Correlation Analysis

Page 1.

PART I ANALYSIS

Quantitative and Qualitative Statistical Business Analysis:

European Management Consultancy Firms

INTRODUCTION:

The management consultancy landscape is a promising industry for European

management consultancy firms deploying their services across the European

marketplace. Consolidation in the European management consultancy field shows to

be in a positive position for business end users as the consultancy firms have a strong

core expertise in areas such as information technology, human resources, operations

and strategy. Business end users are at an advantage through the use of a consultancy

firms that can provide a variety of expertise in business management.

This report examines and provides various key strategic observations based on the

collection of quantitative data. Businesses and the general economy manage

processes for influencing quantitative data and rely on statistics and analysis as a

fundamental part of their business development. Sr. Operating Teams of

organizations rely on data results to make critical decisions about company direction

or strategic initiative. Statistics has sometimes caused a misconception in the display

of data. The importance that statistics has is beyond the results of the data. It’s what

the data tells us that is key in making management decisions and in analyzing current

trends and situational objectives. This analysis is focused on the data results of

European management consultant firms and provides an evaluation that draws

conclusions about its current global business, through the summary and interpretation

of graphical data.

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STATISTICAL BUSINESS ANALYSIS:

Percentage Breakdown of the Turnover generated by European Management

Consultancy Firms

Figure 1 is a pie graph that shows the percentage breakdown of the revenue

generated by European management consultancy firms Internationally. The

classifications for Western Europe, Eastern Europe and Rest of World represent

qualitative variables that show a quantitative observation on the percentage of

revenue generation. European management consultancy firms show a primary focus

in Western Europe. There is very little business in Eastern Europe and Rest of

World. For example, European management consultancy firms generate 87%

revenue in Western Europe, 5% generation of revenue in Eastern Europe and 8%

revenue generation throughout the rest of the world.

Figure 1

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Market by Industry Sector Analysis: Strategy for Market Penetration

The market by industry sector analysis shows the deployment of business

development relative to industry focus by European management consultancy

firms in the European marketplace.

The communications and business services share similar focus of market

penetration, where the penetration of communications is 12.1% and business

services 11.1% of European management consultancy firms business focus. The

primary focus is in financial services and insurance, which represents 24.7% of

management consultancy business. Subsequent to its primary focus, is

manufacturing which represents 21.2% of management consultancy business.

Collectively, the manufacturing and the financial services and insurance

industries make up almost half of the management consultancy business in the

industry sector.

Figure 2

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The percentage of Market Penetration by Region

The findings in figure 3 indicate that both Germany and the UK provide the

greatest percentage of management consultancy. However, it does not

conclusively indicate that a greater percentage of revenue is derived from these

regions. Additional information would be required in order to conclude

statements on global spend. Figure 3 shows a market by region that is spread

unusually thin. Its shows consultancy firms operating in many markets.

Management consultancy firms could lower their distribution in the areas that

have a smaller percentage of business in order to strengthen the more economical

markets similar to Germany and the U.K. However this is not limited to the

economical growth of France which represents 8.9% of management consultancy

and Nordic at 8%. Both of these regions have more of a demand than Eastern

Europe, Belgium, Austria, Swiss, Spain, Portugal, Netherlands, Greece and the

percentage shown for other. However if European management consultancy

firms continue to grow and provide new initiatives, the smaller percentage

market regions could be a vital part of their business growth and stability.

There is a demand fore European management consultancy firms in Germany

where 32% is representative of the market and in the U.K. 27.2%. Germany has a

powerful economy and provides a need for outside business consulting. The

effect of European management consulting shows a critical economic

requirement for Germany and the U.K. This could be an indication of a good

economy or it could suggest that it is strong since European management

consultancy firms could be driving the economy of both Germany and the U.K.

The percentage of the management consultancy market demands of the four

highest regions, Germany, U.K. France and Nordic, suggests that there is more Page 5.

enlightened management requirements for outside consulting which therefore

increases economic spending.

Figure 3

Market Breakdown by Key Consulting Areas

European management consultancy firms are showing to have an established set

of services in Human Resource Management, Strategy Planning, Information

Technology and Operations. The findings of Figure 4 indicate that Information

Technology is the primary strategic focus, representing 44% of consulting

services based on the aggregated findings of the 4 key consulting areas. Second,

Strategy Planning shows a 27% strategic focus, followed by Operations at 23%

and Human Resources Management at 6%.

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Figure 4

The data results of both IT and Operations could show an indication of overlap.

IT consulting is known to bring in technology such as business application tools

or a network expansion with varying degrees of new technology. The statistics

may possibly be unclear due to the role operations plays in operationalizing new

technology. A company’s new IT application development could also cause the

development of operational techniques, process development and operations

management. Recent IT networks that consultant firms formulate for a business

plan, could require new provisioning planing activities within operations. A more

detailed analysis would need to be provided in order to develop more clear

definitions that scope out the elements of IT versus Operations to prevent

vagueness in the statistics.

Traditionally, companies have handled HR internally and have relied very little

on outside consulting services. The percentage of European management

consultancy firms providing Human Resources Management consulting is shown

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to be 6% of the 4 key consulting areas. Although this number appears low,

businesses are continuing to rely on outside consulting for Human Resources

planning. It could possibly become a key area of growth that evolves in the

European business market. Strategic planning is seen as a critical business skill

required by the European business markets. It shows that outside knowledge is

appropriately required for business firms, and that the European market finds

outside knowledge to be essential and useful in providing management

techniques in consulting.

CONCLUSION:

European management consultancy firms are best positioned in the European

market. Possible expansion towards Eastern Europe would be more adaptable for

business opportunities than in the rest of the world, since the European

consultancy firms have more than likely established practices that are related to

the European market. Expansion in Eastern Europe represents a good opportunity

for continuous emergence of outsourced services for consulting practices where

these practices could be transferable and remodeled. The rest of world presents

unclear statistics as to the different global areas. Although it only has 8% of

European consultancy efforts, many European firms have a greater opportunity to

expand their practice globally. Germany and the U.K. represent a long-term

demand for outside firms to engage in consulting. These two regions are

economically stable in by means of the management consultant firms. Companies

will continue to develop in Europe as the world economy continues to evolve.

European management consultancy firms will require evolving their business

however; they will need to pose some concern on what the impact of the global

economy might have on their business.

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PART II ANALYSIS Quantitative Assessment: Statistical Summary on Business Examples

1. Stem and Leaf “Integers as Stems”

The price earning ratios for 21 stocks in the retail trade category are:

8.3 9.6 9.5 9.1 8.8 11.2 7.710.1 9.9 10.8 10.2 8.0 8.4 8.111.6 9.6 8.8 8.0 10.4 9.8 9.2

The following analysis will show the above information organized into a stem-and-leaf display. The analysis will also show the following principles:

(a) Values that are there less than 9.0 (b) A list of values in the 10.0 up to 10.9 category (c) The middle value (d) What the largest and the smallest price-earnings ratio are

Stem and Leaf Display:

The following table displays the above information into an organized stem and leaf display.

STEM LEAF

7 .7

8 .0,.0,.1,.3,.4,.8,.8

9 .1,.2,.5,.6,.8,.9

10 .1,.2,.4,.8

11 .2,.6

The above data has only one value that is less than 9.0. That value is 8.

The list of values in the 10.0 up to 10.9 category are 10.1, 10.2, 10.4 and 10.8 respectively.

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The numeric middle value that is also the 11th or median value in the data set, is 9.5. The smallest

price earnings shown in the data set is 7.7 and the largest is 11.6.

2. Probability Theory Analysis

Routine physical examinations are conducted annually as part of a health program for General Cement employees. It was discovered that 8 percent of the employees needed corrective shoes, 15 percent need major dental work, and 3 percent need both corrective shoes and major dental work.

The following analysis will show probability methods to justify the following measures:(a) The probability that an employee selected at random will need either corrective shoes or

major dental work (b) Venn Diagram.

(a) The probability that an employee selected at random will need either corrective shoes or

major dental work

The following formulas are described to outline the probability theory that an employee selected

at random, where “P” represents a random event. These methods are used to calculate the

probability of a particular outcome happening (the probability of an employee selected at random

needing either shoes or major dental work), and represents a ratio of the number of times it can

happen to the total number of possible outcomes. The probability is expressed as a fraction (or

decimal) and is between zero and one. These formulas are considered for one event occurring.

P (need corrective shoes) = 0.08

P (need major dental work) = 0.15

P (need shoes and dental work) = 0.03

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In order to find the probability that an employee is selected at random for either corrective shoes

or major dental work, the following formula is used:

P (need shoes and dental work)

= P (need shoes) + P (need dental work) – P (shoes and dental work)

= 0.08 + 0.15 – 0.03

= 0.2

Therefore, the probability factor is 0.2 that an employee is selected at random for either corrective

shoes or major dental work.

(b) Venn Diagram.

The following illustration is a Venn diagram that shows the unison of two events, A and B. The

surrounding area of the circles represent the sample space. Circle A represents “corrective shoes”

and circle B represents “ the need for major dental work”. The intersection of A and B (shown as

A and B), represents the event that both A and B occur.

The two full circles represent the “union”. Figure 5 – Venn Diagram

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P (shoes dental) = P (shoes) + P (dental) – P (shoes dental)

Need Dental Work

Need Shoes 0.08

Need Shoes and Dental Work 0.3= P ()

Sample Space

3. Population Parameters Estimating and Confidence Intervals

The wildlife department is feeding a special food to rainbow trout fingerlings in a pond. The sample of weights of 40 trout revealed that the sample mean is 402.7 grams and the sample standard deviation 8.8 grams.

The following analysis will show the following principals:

(a) The estimated mean weight of the population and its naming convention;(b) The 99% confidence interval; (c) The 99% confidence limits; (d) The degree of confidence being used; (e) Review on findings.

a. The estimated mean weight of the population and its naming convention

We are giving the following details in the study. Therefore let n= 40 , , = 402.7 grams

(sample mean), and S = 8.8 grams (sample standard deviation).

The estimate of the population mean is always the sample mean. Therefore the estimated

mean weight is shown as: û = = 402.7 grams.

b. The 99% confidence interval

If we took 100 samples, by this technique 99 out of 100 would capture the true mean 99% of

the time. A 99% confidence interval implies that the confidence coefficient = .01 and the

confidence coefficient divided by 2 = .005. The first measure is in finding the alpha over 2

(the confidence coefficient). The confidence coefficient line item and the Z score once found

in the Normal Curve Areas table, are used to calculate the confidence interval1

1

1 Terry Sinch. Business Statistics by Example. Fifth Edition (Upper Saddle River, NJ: Prentice Hall, 1996), p. 1198.table 5

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Figure 6 Standard Normal Curve

Since the sample size is large there is a 99% confidence interval. What we know in reference to

the formula shows the final confidence intervals:

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11 2 3

X= 402.7 (sample mean)S= 8.8 (sample standard. deviation)

S = 40

Confidence coefficient = .01, confid. Coefficient divided by 2 = .005

X + Ζ x S 2

402.7 + or - (2.575)(8.8)

402.7 + or - 3.583

n

40

0 1 2

Normal Curve and Probability Area

99 % Confidence

.495Area under curve

0 1 2 3-1

-2

-3

.005

Z confid. Coefficient / 2 = 2.575

SEH.10.11.(01)

c. The 99% confidence limits

The final 99% confidence limits are (399.117, 406.283). Therefore there is a confidence level

with a true mean 99% of the time, and it is between (399.117, 406.283).

d. The degree of confidence being used

The degree of confidence equals 99%, which is the confidence coefficient less “one” multiplied

by 100%. By using any different level of confidence intervals between 0 and 1, the degree of

confidence can be obtained.

e. Review on findings

Using this technique we can expect to capture the true mean in our confidence interval 99% of the

time.

4. Correlation Analysis

Reliable Furniture is a family business that has been selling to retail customers in the Chicago area for many years. They advertise extensively on radio and TV, emphasizing their low prices and easy credit terms. The owner would like to review the relationship between sales and the amount spent on advertising. Below is information on sales and advertising expense for the last 4 months.

Month Advertising Expense ($ million) Sales Revenue ($ million)July 2 7

August 1 3September 3 8October 4 10

The following analysis will answer the following key principals:(a) Forecast on sales based on advertising expense – Dependant/Independent Variables(b) Scatter diagram.

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(c) Determining the coefficient of correlation. (d) Interpreting the strength of the correlation coefficient.(e) Determining the coefficient of determination with Interpretation.

A. Forecast on sales based on advertising expense – Dependant/Independent Variables

In order for the owner to forecast sales based on advertising expense, the dependant variable

and independent variable are required. The dependant variable is “sales”. The independent

variable is “advertising”.

b. Scatter diagram

The following diagram shows the scattergram of advertising expense as X, for the dependant

sales revenue.

Figure 7, Scattergram

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C. Determining the coefficient of correlation

The following Sum of Squares table was used to gather the data for the formulas:

X Y X Squared Y Squared XY2 7 4 49 141 3 1 9 33 8 9 64 244 10 16 100 40

10X

28y

30x2

222y2

81Xy

Formula for coefficient of correlation:

2

2

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SSxx SSyy

SSxy

R =

= xy - ( x) (y) n [x - (x) ][ y - (y) ] 2

n n

2 2 2

2

= 81 - (10) (28) 4

[ 30 - (10 ) ] [ 222 - (28 ) 2

44

= 81 - 70

(5) (26)

R = 0.9647

=11

130

D. Interpreting the strength of the correlation coefficient.

The results of the above coefficient of correlation show a strong linear relationship between sales

and advertising expense.

E. Determining the coefficient of determination with Interpretation

R = (.9647) = .93062 2

R squared is the percentage of the variability in sales that can be explained by the explanatory

variable advertising expense.

Analytical Tools, Business Statistics Study October 11, 2001S. Blouin

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