# Quantitative Statistical Methods Test Essay A
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Quantitative Statistical Methods

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Question 1

The undermentioned informations are the tonss obtained by 40 kids in a Quantitative Methods trial

100 92 96 91 81 110 70 119 94 88 104 115 97 108 93 116 86 89 78 108 127 91 114 84 101 121 95 105 112 102 124 92 76 105 90 81 109 116 96 107

a. Draw the root secret plan

B. Find average, Q1 and Q3

c. Draw the box secret plan

d. Find the mean and standard divergence for the tonss

e. Discussion the restriction of utilizing stem secret plans and box secret plans

a ) The Stem Plot

 Root Leafs 7 0,6,8 8 1,1,4,6,8,9 9 0,1,1,2,2,3,4,5,6,6,7 10 0, 1, 2, 4,5,5,7,8,8,9 11 0,2,4,5,6,6,9 12 1,4,7

B )

 Time interval Tally Frequency ( degree Fahrenheit ) Mid-point ( x ) Accumulative Frequency ( F ) fx  70-79 ||| 3 74.5 3 223.5 5550.25 16650.7 80-89 |I?|I?|I?|| 6 84.5 9 507 7140.25 42841.5 90-99 |I?|I?|I?||I?|I?|I?|| 11 94.5 20 1039.5 8930.25 98232.7 100-109 |I?|I?|I?||I?|I?|I?| 10 104.5 30 1045 10920.25 109202.5 110-119 |I?|I?|I?||| 7 114.5 37 801.5 13110.25 91771.75 120-129 ||| 3 124.5 40 373.5 15500.25 46500.75 40 597 3990 61151.5 405199.9

N=40 ( even ) = =90+ =90+ =90+10 =100 =90+ =90+ =90+ =90+ = =  90.90 =100+ =100+ =100+ =100+10 110

degree Celsius ) The Box Plot is given below vitamin D ) Mean and the standard divergence

Mean, = = =99.75

S.D = = = = =13.41 =134.1

vitamin E ) Here is the Restrictions of Stem secret plans and Box Plots:

Root and Leaf Plots

Stem.and Leaf Plot.is.a.way.of.briefing.a.set.of.data.dignified.on.an.interlude.scale. It.is.often.used.inexperimental.data.analysis.to.illustrate.the.key.features.of.the.circulation.of.data.in.an appropriate.and.easy.way. Stem.plots.record.data.values.in.rows, and.easily.can.be.made.into.a histogram. Huge.data.sets.can.be.billeted.by.splitting.stems.

( Purplemath, 2014 ) ( Statistics Canada, 2014 ) ( Math is for merriment, 2014 )

Restrictions of utilizing Stem Plots

Besides a batch of advantages there has besides some Restrictions of utilizing Stem and Leaf Plots.

Root secret plan is non visually appealing. Does non easy indicate steps of centrality for

Large informations sets. Root and Leaf Plots can non be used for categorical informations and Difficult with big figure of observations. It’s really hard if there are a batch of roots with no foliages. And sometimes outlier might be a job. Preferably have need of foliages to be well-ordered on each root – difficult work. It’s tricky to utilize ( though non impossible ) if denary stem/leaf are non the optimum solution.

( Purplemath, 2014 ) ( Statistics Canada, 2014 ) ( Math is for merriment, 2014 )

Box Plot

Box Plot is a one sort of graph which used to expose the array of quantitative informations. It is besides known as Box and Whisker Plot.

Box Plot fragmented the information set into quartiles. It is often used in analyzing informations analysis. It is a sort of graph used to demo the signifier of the distribution, its cardinal value, and variableness. A box secret plan is specially utile for meaning whether a distribution is tilted and whether there are any infrequent observations ( outliers ) in the information set. Box and hair’s-breadth secret plans are besides really helpful when immense sum of readings are convoluted and when two or more informations sets are being associated.

Restrictions of utilizing Box Plot

It’s non as visually attractive as other graphs, & A ; exact values non retained.

( Purplemath, 2014 ) ( Statistics Canada, 2014 ) ( Math is for merriment, 2014 )

Question 2

A company is sing puting in a undertaking it has two options ( Project X and Y ) . You have been called to urge to better of the two options. The information in the below is available for your analysis.

Undertaking Ten

Initial investing = ?27000

Cost of Capital =16 %

Expected net hard currency flows for 5 old ages:

 Year 1 2 3 4 5 Net hard currency flows 1780 2750 4200 4570 8600

Undertaking Y

Initial investing = ?48000

Cash of Capital =10 %

Expected net hard currency flows for 5 old ages:

 Year 1 2 3 4 5 Net hard currency flows 18700 19512 20900 22978 23838
1. Using NPV analysis, select the better investing
2. What are the other factor that need to be considered in your concluding determination?

Undertaking Ten

Initial investing = 27000

Cost of capital=16 %

 Ten Year Cash flow Discount factor ( 16 % ) Present value ( CF?DF ) 0 -27000 1 – 27000 1 1780 0.862068965 1534.48 2 2750 0.743162901 2043.69 3 4200 0.640657673 2690.76 4 4570 0.552291097 2523.97 5 8600 0.476113015 4094.57 Total= -5100 NPV=-14,112.53

Undertaking Y

Initial investing = 48000

Cost of capital= 10 %

 Yttrium Year Cash flow Discount factor ( 10 % ) Present value ( CF?DF ) 0 -48000 1 -48000 1 18700 0.909090909 17000 2 19512 O.82644624 16125.61 3 20900 0.7513148 15702.47 4 22978 0.683013455 15694.28 5 23838 0.620921323 14801.52 Total= 57928 NPV=17,223.88

( a ) Using NPV analysis the better investing is Project

B ) To do the concluding determination I have to see the Discount Factor.

Question 3

A leather industry has derived the following information on production costs ( ?Y ) and units of end product ( X ) for the last 12 months:

 Yttrium 16 6.4 6.5 16 12.7 12.5 9.3 6.3 10.5 9 9.8 12 Ten 29 4 7 35 28 23 16 8 21 14 12 26

You are required to:

1. Plot spread diagram of Y against X
2. Find the least squares regression equation of production costs on end product, and plot the line on the diagram
3. Predict production cost for the following month if it is able to bring forth 40 units of end product and discourse the likely dependability of this production

a ) Scatter diagram of Y against X

B ) The least squares regression equation of production costs on end product, and line on the diagram:

 ten Y ten Y  29 16 464 841 256 4 6.4 25.6 16 40.96 7 6.5 45.5 49 42.25 35 16 560 1225 256 28 12.7 355.6 784 161.29 23 12.5 287.5 529 156.25 16 9.3 148.8 256 86.49 8 6.3 50.4 64 39.69 21 10.5 220.5 441 110.25 14 9 126 196 81 12 9.8 117.6 144 96.04 26 12 312 676 144 ?x=223 ?y=127 ?xy=2713.5 ? =5221 ? =1470.22

The least squares regression equation

b= = = = =0.328

a = -b = -0.328 =10.583-6.095

=4.487

=4.49

Y=a+bx

=4.49+0.328x

X=0, Y=4.49+0.328?0=4.49

X=10, Y=4.49+0.328?10=7.77

X=20, Y=4.49+0.328?20=11.05

Question 4

The gas and electricity gross revenues between 2002 and 2009 by the public supply system are shown below:

 Year Oil and gas ( ‘000 ) Electricity ( ‘000 ) 2002 27 19 2003 31 18 2004 40 21 2005 46 27 2006 53 30 2007 65 41 2008 67 29 2009 66 27

a ) Calculate the coefficient of correlativity between oil & A ; gas and electricity gross revenues

( 1 ) The merchandise minute correlativity and coefficient

( 2 ) Spearman rank correlativity and coefficient

B ) Discuss the significance of both these steps.

a ) ( 1 )

 Year Oil & A ; gas ten Electricity Y Ten Y  2002 27 19 513 729 361 2003 31 18 558 961 324 2004 40 21 840 1600 441 2005 46 27 1242 2116 729 2006 53 30 1590 2809 900 2007 65 41 2665 4225 1681 2008 67 29 1943 4489 841 2009 66 27 1782 4356 729 ?x=395 ?y=212 ?xy=11133 ? =21285 ? =6006

R = = = = = = 0.80

The merchandise minute correlativity and coefficient is Strong.

( 2 )

 Year Oil & A ; Gas Electricity Ro Rhenium vitamin D 2002 27 19 8 6 2 4 2003 31 18 7 7 0 0 2004 40 21 6 5 1 1 2005 46 27 5 4.5 0.5 0.25 2006 53 30 4 2 2 4 2007 65 41 3 1 2 4 2008 67 29 1 3 -2 4 2009 66 27 2 4.5 2.5 6.25 n=8 395 212 ? P=1- =1- =1- =1- =1- =1-0.279

=0.720

=0.72

The Spearman Rank correlativity between oil & A ; gas and electricity is strong.

B )Significance of utilizing

The other steps of correlativity are parametric within the significance is upon possible relationship of a parameterized signifier, such as a additive relationship. This both two steps are much easier to utilize than other and since it doesn’t affair in which manner we rank the information, go uping or falling. It is less sensitive to bias due to the consequence of outliers. It can be used to cut down the weight of outliers. It does non necessitate of premise of normalcy. When the interval between informations points are debatable, it is advisable to analyze the rankings instead than the existent value.

( Laerd Statistics, 2014 )