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1

FEEDBACK TUTORIAL LETTER

ASSIGNMENT 2

SEMESTER 1 ‐ 2018

QUANTITATIVE METHODS

[QTM511S]

TUTORIAL LETTER MEMO

SEMESTER 1/2018


QTM511S

1

COURSE: QUANTITATIVE METHODS

COURSE CODE: QTM511S

FEEDBACK TUTORIAL LETTER: 05/2018

DATE: 05/ 2018

Dear Student

Congratulations on the successful completion of your first assignment for semester 1 2018.

We are convinced the study guide gave you enough exposure to applications of Quantitative

methods skills in daily financial transactions.

We have no doubts that working through the questions must have in no small way improved

on your statistical, analytical and other calculation skills.

SOME COMMON MISTAKES

WE wish to point out the following general mistake in this assignment:

The attached memoranda are for you to see the step by step methods of realising the final

calculations and will also prepare you towards the end of June examinations.

Regards,

Dr. I. Ajibola

Tel. +26461 207 2157

[email protected]

Dr. D. Ntirampeba

Tel. +26461 207 2808

Email: [email protected]

mailto:[email protected]

mailto:[email protected]


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Question 1 [20 marks]

1.1.

1.1.1.

0.180 [3]

1.1.2.

0.029 0.011 0.016 0.056 [3]

1.1.3.

0.029 0.011 0.016 0.014 0.180 0.034 0.284 [3]

1.1.4.

0.18 0.24 0.3940.7216

0.014 0.180 ... 0.016 0.546

[4]

1.2. [4]

A= “children under 2 years old who sleep with the light”

B = “children under 16 is myopic are independent”

| 0.36, | 0.21, ( ) 0.28, ( ) 0.72

( ) | ( ) | ( )

=0.36 0.28+0.21 0.72=0.252

P B A P B A P A P A

P B P B A P A P B A P A

1.3.

[2]

1.4. exhaustive events [1]


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Question 2 [30 marks]

Distance (in Km)

Number of days

0 up to 5 4 2.5 10 25

5 up to 10

15 7.5 112.5 843.75

10 up to 15

27 12.5 337.5 4218.75

15 up to 20

18 17.5 315 5512.5

20 up to 25

6 22.5 135 3037.5

Tot 70 62.5 910 13637.5

2.1.

1370

i if xx

n

On average, the distance from NamWater headquarter and employee home is 13 km

[5]

Distance (in Km)

Number of days

0 up to 5 4 4

5 up to 10 15 19

10 up to 15 27 46

15 up to 20 18 64

20 up to 25 6 70


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2.2.

f

Fn

c

LMedian

2

Median class =70

352 2

n , 35 falls within interval 10 - < 15

705 19

210 12.963

27Median

For 50% of the employees, distance between the headquarter and their homes is less

than 12.963 km, whereas for the other 50% of the employees distance between the

headquarter and their homes is greater than 12.963 km . [5]

2.3.

1 0

1 0 22

27 15 =10 5

2 27 15 18

=12.857

oo M

f fM l h

f f f

[4]

2.4.

33

3

4q

nc F

Q Lf

Upper quartile class : 3

52.54

n , 52.5 falls within interval 15 - < 20

3

5 52.5 4615 16.806

18Q

[4]


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2.5.

11

1

4q

nc F

Q Lf

Lower quartile class : 70

17.54 4

n , 17.5 falls within interval 5 - < 10

1

5 17.5 45 9.5

15Q

3 1 16.806 9.5 7.306Q Q

[5]

2.6.

22

2

2

91013637.5

70 26.1961 69

i i

i i

f xf x

nsn

26.196

5.118

s

100 100 39.37%

13

sCV

x [8]


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Question 3[16 marks]

2015 2017

Cartridge

Unit price (NS) (

Quantity ordered

Unity price

Quantity ordered

Front 4500 24 6500 36 156000 108000 234000

Side 2450 37 4600 44 170200 90650 202400

Rear 6500 12 7850 14 94200 78000 109900

Tot 420400 276650 546300

3.1

Price relative for front screen= 1

0

6500100% 100% 144.44

4500

p

p

The price index for a front screen stands at 144.44.

This shows that the price of a front screen has increased by 44.44% since 2015.

[2]

3.2

Quantity relative for rear screen= 1

0

14100% 100% 116.67%

12

q

q .

This shows that the quantity of a rear screen has increased by 16.67 % since 2015

[2]

3.3

Laspeyres price index = 1 0

0 0

420400100% 100% 151.96%

276650

p q

p q

[5]

If quantities are held constant at 2015(base period) levels , the composite cost index

is 151.96. This means that the cost of of screens have increased by, on average, by

51.96 % since 2015.

[5]


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3.4

Paasche’s quantity index= 1 1

1 0

546300100% 100% 129.95%

1420400

p q

p q

[5]

If prices are held constant at current period levels (2015) , the quantities of screens

ordered have increased by 29.95 % since 2015. [5]

3.5

1 18950100% 100% 140.89%

0 13450

p

p

This means that on aggregate, cost of 2017 are 40.89 % higher than those of 2015 .

[2]


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QUESTION 4 [34 marks]

4.1

Year Quarter Visitors (in 000)

UCMT CMT 4-Period MA

1999 Winter 117

Spring 80.7

403.4

Summer 129.6

808.4 101.05

405

Fall 76.1

811.8 101.475

406.8

2000 Winter 118.6

805.4 100.675

398.6

Spring 82.5

798.1 99.7625

399.5

Summer 121.4

794.4 99.3

394.9

Fall 77

791.6 98.95

396.7

2001 Winter 114

791.9 98.9875

395.2

Spring 84.3

788.4 98.55

393.2

Summer 119.9

793.1 99.1375

399.9

Fall 75

795.1 99.3875

395.2

2002 Winter 120.7

801.2 100.15

406

Spring 79.6

806.6 100.825

400.6

Summer 130.7

Fall 69.6


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4.2

First we compute the seasonal ratios:

Year Quarter Y MA

Seasonal

Ratio=

100%Actual y

MA

1999 Winter 117

Spring 80.7

Summer 129.6 101.05 128.2533

Fall 76.1 101.475 74.99384

2000 Winter 118.6 100.675 117.8048

Spring 82.5 99.7625 82.6964

Summer 121.4 99.3 122.2558

Fall 77 98.95 77.81708

2001 Winter 114 98.9875 115.1661

Spring 84.3 98.55 85.54033

Summer 119.9 99.1375 120.9431

Fall 75 99.3875 75.46221

2002 Winter 120.7 100.15 120.5192

Spring 79.6 100.825 78.94867

Summer 130.7

Fall 69.6


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Secondly, we compute average seasonal ratios

Averaging seasonal ratios

Total

Year Winter Spring Summer Fall

1999 128.253 74.994

2000 117.805 82.696 122.256 77.817

2001 115.166 85.54 120.943 75.462

2002 120.519 78.949

Seasonal median 117.805 82.696 122.256 75.462 398.219

Third, we compute the adjustment factor

100 400 1.0045

398.219

kAdjustment factor

Median seasonal index

seaonal index cAdjusted meadian seasonal index adjustment fa tor

Median

seasonal

index

Adjustment

factor

Adjusted

seasonal

index

Winter 117.81 1.0045 118.34

Spring 82.696 1.0045 83.068

Summer 122.26 1.0045 122.81

Fall 75.462 1.0045 77.802


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4.3

Year Quarter Y Seasonal Index Deseasonalized

1999 Winter 117 118.34 98.868

Spring 80.7 83.068 97.14932

Summer 129.6 122.81 105.5289

Fall 76.1 75.802 100.3931

2000 Winter 118.6 118.34 100.2197

Spring 82.5 83.068 99.31622

Summer 121.4 122.81 98.85189

Fall 77 75.802 101.5804

2001 Winter 114 118.34 96.3326

Spring 84.3 83.068 101.4831

Summer 119.9 122.81 97.63049

Fall 75 75.802 98.94198

2002 Winter 120.7 118.34 101.9943

Spring 79.6 83.068 95.82511

Summer 130.7 122.81 106.4246

Fall 69.6 75.802 91.81816

Interpretation:

Year 1999 Winter visitors would have been lower at 98.868, instead of the actual visitors of 117, had

seasonal influences not been present.


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4.4

Zero-sum method: 1 ( 1) (16 1) 15x n

Year Quarter ( )y )(x 2( )x ( )xy

1999 Winter 117 -15 225 -1755

Spring 80.7 -13 169 -1049.1

Summer 129.6 -11 121 -1425.6

Fall 76.1 -9 81 -684.9

2000 Winter 118.6 -7 49 -830.2

Spring 82.5 -5 25 -412.5

Summer 121.4 -3 9 -364.2

Fall 77 -1 1 -77

2001 Winter 114 1 1 114

Spring 84.3 3 9 252.9

Summer 119.9 5 25 599.5

Fall 75 7 49 525

2002 Winter 120.7 9 81 1086.3

Spring 79.6 11 121 875.6

Summer 130.7 13 169 1699.1

Fall 69.6 15 225 1044

Tot 1596.7y 0x 2 1360x 402.1xy

Trend Line formula: abxy

2

402.10.296

1360

1596.7int 99.794

16

xySlope b

x

yy ercept a

n

Trend Line: 0.296 99.794y x

4.5 [2 marks]

Estimate the trend value of the time series for Fall 2004 in year 6.

Fall 2004: ˆ 0.296(31 99.794 90.618T y


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4.6

The seasonally-adjusted trend estimate is calculated usingT S .

where the S is the seasonal index for the specific period (Q2)

Thus, 77.575

90.618 70.297100

T S

Total: [100 marks]

-1- · title-1- author. created date: 5/30/2018 7:55:11 am

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