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1
FEEDBACK TUTORIAL LETTER
ASSIGNMENT 2
SEMESTER 1 ‐ 2018
QUANTITATIVE METHODS
[QTM511S]
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
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
Dr. D. Ntirampeba
Tel. +26461 207 2808
Email: [email protected]
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
2
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]
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
3
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
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
4
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]
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
5
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]
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
6
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]
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
7
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]
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
8
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
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
9
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
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
10
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
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
11
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.
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
12
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
TUTORIAL LETTER MEMO
SEMESTER 1/2018
QUANTITATIVE METHODS
QTM511S
13
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]