Assignment of quantitative statistical methods

Quantitative Statistical Methods Semester 2

Westminster International College

Contents

1.0 Introduction22.0 Question 122.1 Net Present Value (NPV)32.2 Calculation of net present value (Project: A)42.3 Calculation of net present value (Project: B)42.4 Discussion on first question53.0 Question 253.1 Calculation64.0 Question 374.1 Calculation of product moment correlation coefficient84.2 Calculation of spearman rank correlation coefficient94.3 Discussion on third question105.0 Question 4105.1 Calculation of Mean115.2 Calculation of Standart and Variance Deviation126.0 Bibliography13

1.0 Introduction

Statistics are selection of several methods for planning tests, summarizing, analyzing, presenting, and drawing conclusions. Today they are used by governments, financial companies, social researches, business, community decisions and they have already pervaded our life. There are two main parts of statistics: Descriptive statistics and Inferential statistics. About descriptive statistics mean, median, mode can be talked. Inferential statistics is used for making educated guesses about something. This assignment also will provide information about several terms of quantitative and statistical methods. 2.0 Question 1

In this question there are two projects are given that company is considering investing in a project. First of all we have to define which the best project for company to recommend is. In order to select better investment I will use Net Present Value analysis. Now I am going to define what net present value is and why is it important for considering investing. 2.1 Net Present Value (NPV)

Net Present Value (NPV) is the difference between the present values of the future cash flows investment the amount of investment. It gives the best acceptable investment rule according to time value measure of true profitability and shareholder value. And also it gives permission to the company to find out in the future how much of income is worth today, taking to account inflation. For instance, $20 K for 20 years is equal to less than $200 K today still inflation will slowly to be ruined worth of your money in the future. If NPV of prospective project will be positive, it can be recommended for the company. And they will accept. Moreover, NPV is negative; it will be rejected definitely by the company because cash flow also will be negative. (Lane, 2013)The NPV is designed: the present value of cash flows lack of the mission the present value of the risks cash outflows. It is showed clearly by following formula.

2.2 Calculation of net present value (Project: A)

Period (years)Net Cash FlowsDiscount Factor @ 18 %Present Value

027.0001

1 17800.847 1507.66

2 2750 0.718 1974.5

3 42500.609 2557.8

4 45700.516 2358.12

5 8600 0.437 3758.2

Total 12156.28

Less Investment 27000

NPV

-14843.72

Comments : In this project it can be seen it proves which net presenr value is considered 18 % and project is not beneficial because of negative Net Present Value. Consequently this project is not acceptable. 2.3 Calculation of net present value (Project: B)

Period (years)Net Cash FlowsDiscount Factor @ 12 %Present Value

118700 0.893 16699.1

219512 0.797 15551.064

320900 0.712 14880.8

422978 0.636 14614.008

523838 0.567 13516.146

Total 75261.118

Less Investment 48000

NPV 27261.118

Comments : Project B has proved that net present value is 12 % , answer is positive and project is beneficial.It should be accepted by the company.

2.4 Discussion on first question

The projects were analyzed in terms of Net Present Value. Moreover project A was not as our expected, but project B gave result that was expected. Therefore, company will reject the project A and it will accept the project B. The reason for project A why will it be rejected is project has got negative Net Present Value for the taken discount rate 18 % . In here investment should not be taken. The reason is negative Net Present Value provides financial loss for company.On the other hand, the profitability index of the project B is enough. If company accept this project it can make a profit, can achieve success and company will not lose the money investing in this project. 3.0 Question 2

In this question it was given that an accountant derivered the below data on production costs and units output for the passed twelve month.For calculation we have to plot a scatter diagram and find out the least regression equation of production on output. Now I am going to describe the least squares regression.The Least Squares Regression is a statistical system recycled to controller a streak of top fitting via diminishing squares sum organized through a mathematical mission. A "square" is acute in organizing the detached between a statistics argument and the regression link. The least squares attitude boundaries the accumulating between a meaning and the figures facts which an occupation is endeavoring to define. It is charity in regression enquiry, nonsinglely in nonlinear regression shows in that a turn is fit into a adjusted of statistics (Francis, 2004)

The formula: Y = a + bx; 2) b = 3) a = b ; x = 223; y = 1289; xy = 27635

B = == =3.418 a = 3.418 = 107.417 3.418 18.58 = 107.417- 63.52 = 43.8; y = 43.8+3.418x y = 43.8+3.41830; y = 146.3

3.1 Calculation

Y X XY

160 29 4640 841

64 4 256 16

65 7 455 49

166 35 5810 1225

127 28 3556 784

125 23 2875 529

93 16 1488 256

63 8 504 64

105 21 2205 441

94 14 1316 196

98 12 1176 144

129 26 3354 676

1289 223 27635 5221

4.0 Question 3

In this question there are given gas and electricity sales between 2002 and 2009 years by the public supply system.In order to calculate the coefficient of correlation between them two method : the product moment and spearmen rank correlation coefficient will be used.

Year Gas sales (000) Electricity (000)

2002 2.7 1.9

2003 3.1 1.8

2004 4.0 2.1

2005 4.6 2.7

2006 5.3 3.0

2007 6.5 4.1

2008 6.7 2.9

2009 6.6 2.7

Correlation: is relevant with defining the strength of the relationship among two variables over measuring degree of scatter of the data values. (Math is Fun, 2013)The Coefficient of Correlation: The way of measuring the strength of the correlation is needded between two variables. This is reached thru a correlation coefficient , simply it is expressed by symbol r. (Francis, 2004) This is the number that can be found between -1 and +1 /inclusive/. This is equal: -1 < = r < = + 1. (William, 2006)

4.1 Calculation of product moment correlation coefficient

Year Gas sales (X)Electricity (Y) XY

2002 2,7 1.9 5.13 7.29 3.61

2003 3.1 1.8 5.58 9.61 3.24

2004 4.0 2.1 8.4 16 4.41

2005 4.6 2.7 12.42 21.16 7.29

2006 5.3 3.0 15.9 28.09 9

2007 6.5 4.1 26.65 42.25 16.81

2008 6.7 2.9 19.43 44.89 8.41

2009 6.6 2.7 17.82 43.56 7.29

39.5 21.2 111.33 212.85 60.06

The product moment correlation coefficient: The standart measure of correlation correlation which has got the features defined in section 4 is named the product moment correlation coefficient. And also /x, y/ has already given. In order to calculate formula that is below is used. r = n is the number of bivariate /x,y/ value

Solution: r = = = = 0.8 Answer is r = 0.8Spearman rank correlation coefficient: is used to find out the strength of relationship among two variables. The measure of rank correlation often used as Spearmans rank correlation coefficient and the plan for achieving. (Francis, 2004)The formula: R = 1

Solution: r = 1- = 1- = 1- = 1- = = 0.755 answer is 0.755

4.2 Calculation of spearman rank correlation coefficient X Y

2.7 1 1.9 2 1

3.1 2 1.8 1 1

4.0 3 2.1 3 0

4.6 4 2.7 4.5 0.25

5.3 5 3.0 7 4

6.5 6 4.1 8 4

6.7 8 2.9 6 4

6.6 7 2.7 4.5 6.25

=20.50

4.3 Discussion on third question

After calculation and consideration this is realized that product moment and spearman rank correlation coefficient, they are close each other. But people spend more money for gas than electricity.

5.0 Question 4

The table below shows recorded ages of social club members. For calculation Mean, Median, Variance and Standard Deviation will be used. Age (Years)Frequency

18 24 20

25 31 35

32 38 25

39 45 18

46 52 12

53 59 7

60 73 3

Mean: the arithmetic mean of sets values is described like the sum of the values divided by number of values. (Glosser, 2013)Formula : Solution: = = 35.088 it is 35.088 Age/Years 5.1 Calculation of Mean

Age (Years)Frequency (F)Midpoint (X)FX

18-24 2021420

25-313528980

32-382535875

39-451842756

46-521249588

53-59756392

60-73366.5199.5

Total = 120 Total = 4210.5

Median: The middle value when the original data values are arranged in order of improving or decreasing magnitude.The formula: Median= LM+ lm=lower bound of median class; fm-1=cumulative frequency of class immediately prior to median class; fm=actual frequency of median class; cm=median class width. (Stapel, 2013) Solution: Median = LM+= 24.5+ = 24.5+*7 = 24.5+3 = 27.5 Median is 27.5Variance and Standart Deviation: They are both measures of the average scatter around the mean. Another names measure fluations of data values below and above its mean.The formula S= = = 124.43 answer is standard deviation and variance = 12.43 5.2 Calculation of Standart and Variance Deviation

Age (Years)Frequency (F)(X)FX

18-2420214208820

25-31352898027440

32-38253587530625

39-45184275631752

46-52124958828812

53-5975639221952

60-73366.5199.513266.75

120 4210.5

Bibliography

1. Francis, A., 2004. Business Mathematics and Statistics. Nottingham UK : Thomson Learning.2. Francis, A., 2004. Business Mathematics and Statistics. In Francis, A. Business Mathematics and Statistics. Nottingham: Thomson Learning. pp.191-206.3. Francis, A., 2004. Business Mathematics and Statistics. Nottingham: Thomson learning.4. Glosser, 2013. Arithmetic Mean. [Online] (1.15) Available at: http://www.mathgoodies.com/ [Accessed 12 April 2013].5. Lane, M.A., 2013. Net Present Value. [Online] Available at: http://www.zenwealth.com/BusinessFinanceOnline/CB/NetPresentValue.html [Accessed 04 April 2013].6. Math is Fun, 2013. Correlation. [Online] (1.15) Available at: http://www.mathsisfun.com/ [Accessed 09 april 2013].7. Stapel, E., 2013. Mean, Median,Mode and Range. [Online] (1.15) Available at: http://www.purplemath.com/modules/meanmode.htm [Accessed 15 April 2013].8. William, T., 2006. Correlation. [Online] (1.15) Available at: http://www.socialresearchmethods.net/ [Accessed 10 april 2013].

Mavlonbek Soliev UZB/WIC/BABS/0086MWMW061213