QUANTITATIVE TECHNIQUES

Quantitative Techniques for Business

Quantitative Techniques for Business

Portfolio One: Task One

Table One:

 

Per person employed

(EU-27=100)

 

 

 

2000

2002

2004

2006

2008

2010

Euro area

112

111

109

109

109

109

Germany

107

106

108

109

107

105

Greece

94

100

101

99

100

96

Spain

104

105

103

103

105

110

France

126

126

121

121

120

120

United Kingdom

111

113

114

113

109

108

Japan

99

99

100

98

96

96

United States

143

141

144

141

138

144

Percentage change between each year for per person employed shown from 2000 through to 2010 for the Euro area, Germany, Greece, France, Spain, Uk, Japan, & USA:

 

Percentage change between

 

 

 

2001 & 2002

2003 & 2004

2005 & 2006

2007 & 2008

2009 & 2010

Euro area

-1%

-2%

0%

0%

0%

Germany

-1%

2%

1%

-2%

-2%

Greece

6%

1%

-2%

1%

-4%

Spain

1%

-2%

0%

2%

5%

France

0%

-4%

0%

-1%

0%

United Kingdom

2%

1%

-1%

-4%

-1%

Japan

0%

1%

-2%

-2%

0%

United States

-1%

2%

-2%

-2%

4%

Overall percentage change from 2000 to 2010 for the same countries:

Percentage Change between

Percentage Change between

2000-2010

2000-2010

Eu -27

0%

Netherlands

-100%

Euro area

-3%

Austria

-100%

Belgium

-7%

Poland

-100%

Bulgaria

35%

Portugal

-100%

Czech Republic

16%

Romania

-100%

Denmark

-2%

Slovenia

-100%

Germany

-2%

Slovakia

-100%

Estonia

49%

Finland

-100%

Ireland

5%

Sweden

-100%

Greece

2%

United Kingdom

-100%

Spain

6%

Iceland

-100%

France

-5%

Norway

-100%

Italy

-15%

Switzerland

-100%

Cyprus

3%

Croatia

-100%

Latvia

38%

FYR of Macedonia

-100%

Lithuania

47%

Turkey

-100%

Luxembourg

1%

Japan

-100%

Hungary

22%

United States

-100%

Malta

-4%

Country with highest growth in percentage is Romania between the years 2001-2002

25%

Country with lowest growth in percentage is Turkey between the year 2001-2002

-9%

3.

(a)Line and Histogram Chart

 

2000

2002

2004

2006

2008

2010

 

1

2

3

4

5

6

Greece

94

100

101

99

100

96

 

2000

2002

2004

2006

2008

 

1

2

3

4

5

United Kingdom

111

113

114

113

109

 

2000

2002

2004

2006

2008

 

1

2

3

4

5

Japan

99

99

100

98

96

 

2000

2002

2004

2006

2008

 

1

2

3

4

5

United States

143

141

144

141

138

(b). Impact after Minimum y-axis value of 80:

Excel Formulas

= 2002 value / 2000value -1

= MAX (A:A)

=MIN (A:A)

Comments

Eurostat data shown that comments made in BBC article was proper regarding Greece. The calculations confirmed the comments and explain us how they attributes.

Portfolio One: Task Two

Answer the following questions based on the numbers of people travelling from a particular village on the daily bus to town was recorded for a period of 30 days.

Draw up a frequency distribution table based on given data in Table 2.

6

3

2

7

4

0

5

1

3

2

6

2

4

4

3

0

5

2

1

2

4

3

5

2

4

6

3

0

7

1



Frequency Distribution Table is as follow:

S. No.

Class Intervals

Frequency

1

0-2

12

2

3-5

13

3

6-8

5

? f = 30

For Table 2, determine/ calculate the following measures of central tendency and spread of data for the above data.

Minimum

Min

0

Maximum

Max

7

Range

Formula:

Maximum value - Minimum Value 7-0

Range = 7

Arithmetic Mean

Formula: = (6+3+2+7+4………..0+7+1) / 30

= 97 / 30

= 3.233

Median 3

Mode 2

Standard Deviation 2.02881541

Formula: = (6-3.23)2 + (3-3.23) 2 + (2-3.23) 2 + (7-3.23) 2….. (7-3.23) 2 + (1-3.23) 2 /30

= 2.0288

Coefficient of Variance 4.11609195

Formula: v

Use of Standard deviation and variance

Coefficient of variance and standard deviation is mainly use to measures variation in the values of any data set which revolves around the average mean of the data.

Portfolio One: Task Three

The following table gives quarterly actual sales ('000 units) for a drug used to treat colds and flu.

Obtain and estimate the underlying trend using a four-point moving average and the Additive model.

Plot the actual sales and estimate trend values on a graph.

Obtain estimates of the average seasonal factor for each quarter.

Project the trend for 2011 Q4 & 2012 Q1-Q4 and obtain the resulting sales forecasts.

What assumptions have you made here?

Sales

1

2

3

4

2008

121

78

65

107

2009

150

105

99

142

2010

188

132

123

177

2011

211

166

155

209

When examine the given values qualitatively, it shows that the rising sales is one of the common trend. Putted on top, this data shows ...