QMgroupproject

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HTM 2203 QUANTITATIVE METHODS

GROUP ASSIGNMENT

BH4

GROUP MEMBERS:

Chantika Zilda Arifin (0303772)

Elizabeth Stella Alverina (0302621)

Kevin Gosal (0302138)

Rudi Halim (

0303771)

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Resort and Casino Service Data on their Debt to Equity

0.359 3.366 32.412 48.693 60.119 66.63 82.238 94.004 167.17

602.35 5 0.917 7.801 32.737 48.693 63.882 67.906 87.407 99.096

178.00 5

803.95 8 3.161 13.914 35.764 49.528 63.882 68.506 87.407 99.096

280.10 1

803.95 8 3.161 16.517 37.445 50.216 65.499 68.506 90.081

149.21 4 282.81 8 803.95 8 3.161 19.38 37.515 56.619 65.763 72.309 90.231

149.21 4 282.81 8 2933.4 7 3.366 28.833 42.809 59.048 66.552 81.697 90.231

149.21 4 297.74 6 18400. 6 0.359 28.833 48.66 59.992 66.63 82.238 90.231

155.94 4 297.74 6 Mean 432.078382 4 Median 66.63 Mode 3.161 Standard Deviatio n 2244.53932 7 Variance 5037956.79 2 Max 18400.6 Min 0.359 n 68 Frequency Table Step 1 2k _{> n} 2k_{> 68} k = 7

Step 2 i  (H-L)/k

i  (18400.6-0.359)/7 i  2628.6

i = 2629

Debt to Equity Tally No of Frequency Cumulative Frequency

% of Cumulative Frequency 0.359 up to

2629.359

|||| |||| |||| |||| |||| |||| ||||

|||| |||| |||| |||| |||| |||| | 66 66 97.06%

2629.359 up to 5258.359

|

1 67 98.53%

5258.359 up to

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7887.359 up to

10516.36 0 67 98.53%

10516.36 up to

13145.36 0 67 98.53%

13145.36 up to 15774.36

0 67 98.53%

15774.36 up to 18403.36

| 1 68 100.00%

0.359 up to

2629 .359

2629 .359 u

p to 5 258.3

59

5258 .359 u

p to 7 887.3

59

7887 .359 u

p to 1 0516

.36

1051 6.36 u

p to 1 3145

.36

1314 5.36 u

p to 1 5774

.36

1577 4.36 u

p to 1 8403 .36 0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Coefficient of skewness = 3(mean-median)/Std. Deviation = 3(432.0783824-66.63)/ 2244.539327

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= 0.4884 (positively skewed)

0.772 4.003 16.36 21.481 28.675 48.921 49.999 64.437 104.424 113.173 367.141 0.883 10.066 16.36 27.829 29.613 48.921 49.999 84.816 104.424 159.023 367.141 3.632 11.07 19.624 28.121 30.608 49.137 53.233 84.816 109.854 207.394 560.209 4.003 14.016 21.481 28.121 31.297 49.137 57.899 91.684 109.854 234.288

Gaming Activities Service Data on their Debt to Equity

Mean 81.81253

Median 48.921

Mode 4.003

Standard Deviatio

n 112.7133

Variance 12704.3

Max 560.209

Min 0.772

n 43

Frequency Table

Step 1 2k _{> n} 2k_{> 43} k = 6

i  (560.209-0.772)/6 i  93.23

i = 94

Debt to Equity Tally No of Frequency Cumulative

Frequency % of CumulativeFrequency

0.772 up to 94.772

|||| |||| |||| |||| ||||

|||| || 32 32 74.42%

94.772 up to 188.772

|||| |

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188.772 up to 282.772

||

2 40 93.02% 282.772 up to

376.772

||

2 42 97.67% 376.772 up to

470.772 0 42 97.67%

470.772 up to 564.772

|

1 43 100.00%

0.772 up to

94.77 2

94.77 2 up t

o 188 .772

188.7 72 up

to 28 2.772

282.7 72 up

to 37 6.772

376.7 72 up

to 47 0.772

470.7 72 up

to 56 4.772

0 5 10 15 20 25 30 35

0 100 200 300 400 500 600

Coefficient of skewness = 3(mean-median)/Std. Deviation = 3(81.81253-48.921)/ 112.7133

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= 0.875 (Positively skewed)

Drug Stores Service Data on their Debt to Equity

9.523 29.568 79.869 131.077

14.394 33.286 92.106 138.839

27.197 55.751 111.372 269.323

Mean 81.85875

Median 67.81

Mode N/A

Standard

Deviation 71.78873774 Variance 5153.622867

Max 259.323

Min 9.523

n 12

Step 1 2k _{> n} 2k_{> 12} k = 4

i  (259.323-9.523)/4 i  62.45

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FREQUENCY TABLE

9.523 - 71.5

23

71.52 3 - 13

3.523

133.5 23 - 1

95.52 3

195.5 23 - 2

57.52 3

257.5 23 - 3

19.52 3 0 1 2 3 4 5 6 7

0 50 100 150 200 250 300 350

0 1 2 3 4 5 6 7 Debt to Equity Tally FREQUENCY CULMULATIVE FREQUENCY

% of Cumulative Frequency

9.523 - 71.523 llllll 6 6 50%

71.523 -133.523

llll

4 10 83.33%

133.523

-195.523 l 1 11 91.67%

195.523

-257.523 0 11 91.67%

257.523 -319.523

l

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Coefficient of skewness = 3(Mean – Median) / Std. Deviation = 3(81.85875 - 67.81) /71.78873774 = 0.587 (Positively Skewed)

Broadcasting TV Service Data on their Debt to Equity

Mean 157.3481494

Median 39.341

Mode 82.086

Standard Deviation 559.0424178

Variance 312528.4249

Max 5054.7

Min 0.152

n 87

Frequency Table

Step 1 Step 2

0.152 2.958 19.692 33.798 51.264 85.309 157.586 476.829 0.152 3.327 19.692 36.524 57.605 85.309 181.554 1297.04 0.203 3.398 24.104 36.524 57.605 93.003 188.266 5054.7 0.203 3.398 24.104 37.309 57.605 93.003 188.266

0.969 4.12 24.905 37.309 58.333 101.189 289.745 1.112 4.12 24.905 39.21 58.333 107.334 289.745 1.112 5.721 28.409 39.341 68.184 117.746 358.191 1.232 5.721 29.034 39.341 79.031 117.746 358.191 1.401 10.003 30.79 39.383 82.086 142.277 409.376 1.605 14.992 31.02 39.383 82.086 142.277 410.275 2.779 14.992 31.02 49.46 82.086 142.277 449.543 2.958 16.65 33.798 49.46 82.086 157.586 476.829

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2k _{> n} 2k_{> 87} k = 7

i  (H-L)/k

i  (5054.7-0.152)/7 i  722.08

i = 722

Debt to Equity Interval

Tally No of Frequency Cumulative Frequency

% of Cumulative Frequency 0.152 up to

722.152

||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| ||||| |||||

||||| ||||| ||||| ||||| ||||| 85 85 97.70%

722.152 up to 1444.152

|

1 86 98.85%

1444.152 up to

2166.152 0 86 98.85%

2166.152 up to

2888.152 0 86 98.85%

2888.152 up to

3610.152 0 86 98.85%

3610.152 up to

4332.152 0 86 98.85%

4332.152 up to

5054.152 0 86 98.85%

5054.152 up to

5776.152 | 1 87 100%

0.152 - 722

.152

722.1 52 - 1

444.1 52

1444 .152

2166 .152

2888 .152

3610 .152

4332 .152

5054 .152

5776 .152 0 10 20 30 40 50 60 70 80 90

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Coefficient of Skewnewss = 3(Mean – Median)/ Std. Deviation = 3(157.3481494 - 39.341)/ 559.0424178 = 0.633 (Positively Skewed)

0 1000 2000 3000 4000 5000 6000

0 10 20 30 40 50 60 70 80 90

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SUMMARY

For this data analysis, we have chosen the Service Industry sector as our data. In the service sector itself, we have chosen 4 data that consist of Resort and Casino Service, Gaming Activities Service, Drug Stores Service, and Broadcasting TV Services. For this analysis, we have decided to analyze the

Debt to Equity ratio of each services, which is also defined as financial ratio

indicating the relative proportion of shareholders' equity and debt used to

finance a company's assets.

As we all can see, the data all have different numbers of samples, which is shown by the variety of n for each service data. However, we found some similarities in most of the data. In Resort and Casino Service, the debt equity numbers are quite similar as few numbers are repeated for about 2-3times, which means that the debt to equity ratio is progressing slowly and are quite stable. The same thing also happens for the Gaming Service data and Broadcasting TV data of their debt to equity, as the numbers are quite often to be repeated around 2-3 times. However, for the Drug Stores Debt to Equity, no similar or same numbers stated in the data, which not allows us to find any Mode for the data. The numbers of debt to equity data of Drug Stores are

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increasing in quite big gap from each other, from 9 to 14 to 27 and so on, which means that the numbers are increasing rapidly.

After calculating the mean of each data, we found that Gaming Activities data and Drug Stores data means are quite similar, with the numbers of 81.81253 and 81.85875 to be exact. This means that for the Gaming Activities Service Data and Drug Stores Service Data, the range of numbers are similar to each other, although the increase of the numbers of Gaming Activities Service are increasing more slowly than the Drug Store Activities, which makes the Gaming Activities Service has more numbers than Drug Store Activities in the process.

Usually, if the means of all data are bigger than all medians and all medians are bigger than all modes, the shape of distribution would be positively skewed. However, even though the Broadcasting TV Service data has bigger mode than median, the shapes of distribution of these four data are still positively skewed even though they are more to stable. We could also see proves of positive skewness from the scatter diagrams from each data. After calculating the coefficient skewness of each data, we found that the numbers are quite similar, as all coefficients are around 0. For the Resort and Casino Service, the shape of distribution is positively skewed in 0.4884, while for the Gaming Activities Service the shape of distribution is positively skewed in 0.857. The Drug Stores Service Industry is also positively skewed in 0.587, as well as the Broadcasting TV Service Industry that is positively skewed in 0.633. This means that the data are all quite symmetrical and almost have no skewness, because the mean and median of all data are quite equal with

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each other. The one that shows most positive skewness among these 4 data is only the Gaming Activities Service that almost has 1 as its value.

From all the calculations and analysis, we conclude that the data don’t have much variability in the numbers except for Drug Stores Service, as the three other data have many similar numbers that shows how stable their debt to equity ratios are. This also means that the proportions of shareholder’s equity and debt of these industries are quite proportional to be used as finance to companies’ assets, while for the Drug Stores Service debt and equity are not stable and not really proportional.