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DBM30033 (Engineering Mathematics 3)Case Study ReportStatistical DataPrepared By :Ahmad Suhair Ariffin Bin Tajul Ariffin02DKM19FMuhammad Mustaqim Bin Ahmad Surin02DKM19FMuhammad Syurafaq Afifi Bin Rashid02DKM19F(DKM3C)1 Introduction 32 Data 33 Frequency Table 4 – 54 Measures of Central Tendency And ...

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DBM30033 (Engineering Mathematics 3)

Case Study Report Statistical Data Prepared By : Ahmad Suhair Ariffin Bin Tajul Ariffin 02DKM19F1144 Muhammad Mustaqim Bin Ahmad Surin 02DKM19F1134 Muhammad Syurafaq Afifi Bin Rashid 02DKM19F1123 (DKM3C) 1

1

Introduction

3

2

Data

3

3 4

Frequency Table

4–5

Measures of Central Tendency And Dispersion - Mean - Median - Mode - Mean Deviation - Variance - Standard Daviation - Percentile

6 – 11

5

Graph Histogram And Ogive - Histogram - Ogive

12 – 15

6

Measure Quartile and Decile Using Graph - Quartile o First Quartile o Third Quartile - Decile o 8th Decile o 5th Decile

16 – 19

7

Conclusion & Discussion

20

8

References

21

2

1.0 Introduction Statistics is a mathematical science including methods of collecting, organizing and analyzing data in such a way that meaningful conclusions can be drawn from them. In general, its investigations and analyses fall into two broad categories called descriptive and inferential statistics.

Descriptive statistics deals with the processing of data without attempting to draw any inferences from it. The data are presented in the form of tables and graphs. The characteristics of the data are described in simple terms. Events that are dealt with include everyday happenings such as accidents, prices of goods, business, incomes, epidemics, sports data, population data.

Inferential statistics is a scientific discipline that uses mathematical tools to make forecasts and projections by analyzing the given data. This is of use to people employed in such fields as engineering, economics, biology, the social sciences, business, agriculture and communications.

2.0 Data 2.1

Data below show the Total Demand of the Energy Supply and Demand For Fuel Oil

709

807

846

489

529

883

938

1088 1293 1392 1506 1770 1978 1678

598

1875 1498 1589 1255 1463 1954 1901 2203 1792

785

1964 1290

478

734

414

422

769

604

329

528

246

554

498

512

3

3.0 Frequency Table i. Number of class, k

𝑘 = 1 + 3.33𝑙𝑜𝑔𝑛

𝑘 = 1 + 3.33𝑙𝑜𝑔39 𝑘 = 6.30 → 7

ii. Class width, c

𝒌=𝟕

𝑟𝑎𝑛𝑔𝑒 𝑘 2203 − 246 𝑐= 7 𝑐=

𝑐 = 279.6 → 280 iii. Starting Point

𝒄 = 𝟐𝟖𝟎 =246

iv. Frequency Table Number of

Tally

Frequency

246 – 525

|||| |||

8

526 – 805

|||| ||||

9

806 – 1085

||||

4

1086 – 1365

||||

4

1366 – 1645

||||

5

1646 – 1925

||||

5

1926 – 2205

||||

4

Total Demand

𝚺𝒇 = 𝟑𝟗

4

Number of

Frequency

Total Demand

Lower

Upper

Boundary

Boundary

Midpoint

Comulative Frequency

246 – 525

8

245.5

525.5

385.5

8

526 – 805

9

525.5

805.5

665.5

17

806 – 1085

4

805.5

1085.5

945.5

21

1086 – 1365

4

1085.5

1365.5

1225.5

25

1366 – 1645

5

1365.5

1645.5

1505.5

30

1646 – 1925

5

1645.5

1925.5

1785.5

35

1926 – 2205

4

1925.5

2205.5

2065.5

39

5

4.0 Measures of Central Tendency And Dispersion (Mean, Median, Mode, Mean Deviation, Variance, Standart Deviation, And Percentile) 4.1

Mean

Total Demand

𝒇

𝒙

𝒇𝒙

246 – 525

8

385.5

3084

526 – 805

9

665.5

5989.5

806 – 1085

4

945.5

3782

1086 – 1365

4

1225.5

4902

1366 – 1645

5

1505.5

7527.5

1646 – 1925

5

1785.5

8927.5

1926 – 2205

4

2065.5

8262

Number of

𝚺𝒇 = 𝟑𝟗 𝑥 𝑥

 𝒙

= = =

∑ 𝑓𝑥 ∑𝑓

𝚺𝒇𝒙 = 𝟒𝟐𝟒𝟕𝟒. 𝟓

42474.5 39 1089.1

6

4.2

Median, m

Total Demand

𝒇

𝑭

Boundary

246 – 525

8

8

245.5

526 – 805

9

17

525.5

806 – 1085

4

21

805.5

1086 – 1365

4

25

1085.5

1366 – 1645

5

30

1365.5

1646 – 1925

5

35

1645.5

1926 – 2205

4

39

1925.5

Number of

Lower

Determine the class which median lies: = =

𝑵 𝒕𝒉 ( ) 𝟐 𝐿𝑚

𝟏𝟗. 𝟓

𝑁

=

𝑐

=

𝐹

𝑓𝑚

(

=

= =

=

39 ) 2

𝑡ℎ

805.5 39 17 4

280

𝑁 −𝐹 𝐿𝑚 + ( 2 )𝑐 𝑓𝑚

𝑀𝑒𝑑𝑖𝑎𝑛, 𝒎

=

𝑀𝑒𝑑𝑖𝑎𝑛, 𝒎

=

39 − 17 805.5 + ( 2 ) 280 4

=

980.5

𝑴𝒆𝒅𝒊𝒂𝒏, 𝒎

7

4.3

Mode

Total Demand

𝒇

𝑭

Boundary

246 – 525

8

8

245.5

526 – 805

9

17

525.5

806 – 1085

4

21

805.5

1086 – 1365

4

25

1085.5

1366 – 1645

5

30

1365.5

1646 – 1925

5

35

1645.5

1926 – 2205

4

39

1925.5

Number of

Lower

(Highest

𝐿𝑚𝑜

=

𝑑1

= =

𝑑2

= =

𝑐

𝑀𝑜𝑑𝑒 𝑀𝑜𝑑𝑒

𝑴𝒐𝒅𝒆

=

= = =

Frequency)

525.5 9−8 1

9−4 5

280

𝐿𝑚𝑜 + (

𝑑1 )𝑐 𝑑1 + 𝑑2

1 525.5 + ( ) 280 1+5 572.17

8

4.4

Mean Deviation, E

Total demand

𝒇

𝒙

𝒇𝒙

|𝒙−𝒙 |

| 𝒙 − 𝒙|𝒇

246 – 525

8

385.5

3084

703.6

5628.8

526 – 805

9

665.5

5989.5

423.6

3812.4

806 – 1085

4

945.5

3782

143.6

574.4

1086 – 1365

4

1225.5

4902

136.4

545.6

1366 – 1645

5

1505.5

7527.5

416.4

2082

1646 – 1925

5

1785.5

8927.5

696.4

3482

1926 – 2205

4

2065.5

8262

976.4

3905.6

Number of

𝚺𝒇

= 𝟑𝟗

𝚺𝒇𝒙

= 𝟒𝟐𝟒𝟕𝟒. 𝟓 𝐸 𝐸

𝑬

= = =

∑ |𝑥 − 𝑥 |𝑓 ∑𝑓

𝚺| 𝒙 −  𝒙|

= 𝟑𝟒𝟗𝟔. 𝟒

𝚺| 𝒙 − |𝒇 𝒙

= 𝟐𝟎𝟎𝟑𝟎. 𝟖

20030.8 39 𝟓𝟏𝟑. 𝟔𝟏

9

4.5

Variance, S2

Total demand

𝒇

𝒙

| 𝒙 − 𝒙|

| 𝒙 − 𝒙|𝟐

|𝒙− 𝒙|𝟐𝒇

246 – 525

8

385.5

703.6

495052.96

3960423.68

526 – 805

9

665.5

423.6

179436.96

1614932.64

806 – 1085

4

945.5

143.6

20620.96

82483.84

1086 – 1365

4

1225.5

136.4

18604.96

74419.84

1366 – 1645

5

1505.5

416.4

173388.96

866944.8

1646 – 1925

5

1785.5

696.4

484972.96

2424864.8

1926 – 2205

4

2065.5

976.4

953356.96

3813427.84

= 𝟑𝟒𝟗𝟔. 𝟒

= 𝟐𝟑𝟐𝟓𝟒𝟑𝟒. 𝟕𝟐

= 𝟏𝟐𝟖𝟑𝟕𝟒𝟗𝟕. 𝟒𝟒

Number of

𝚺𝒇

𝚺| 𝒙 −  𝒙|

= 𝟑𝟗

𝑆2 𝑆2 𝑆2 4.6

= = =

𝚺| 𝒙 −  𝒙|𝟐

∑ |𝑥 − 𝑥 |2 𝑓 ∑𝑓

𝚺| 𝒙 − 𝒙|𝟐𝒇

12837497.44 39 𝟑𝟐𝟗𝟏𝟔𝟔. 𝟔

Standart Deviation, S 𝑆

=

𝑆

=

𝑆

=

√𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒

√329166.6 𝟓𝟕𝟑. 𝟕𝟑

10

4.7

85th Percentile

Total demand

𝒇

𝑭

246 – 525

8

8

526 – 805

9

17

806 – 1085

4

21

1086 – 1365

4

25

1366 – 1645

5

30

1646 – 1925

5

35

1926 – 2205

4

39

Number of

Determine the class which median lies: 𝑘𝑁 𝑡ℎ ( ) 100

𝑃𝑘 =

𝑷𝟖𝟓 =

𝐿𝑃𝐾

𝑘𝑁

=

𝐶

=

𝐹

𝑓𝑃𝑘

= =

=

= (

𝟑𝟑. 𝟏𝟓𝒕𝒉

85(39) ) 100

𝑡ℎ

1645.5

85(39) 30 5

280 𝑘𝑁 −𝐹 𝐿𝑃𝑘 + ( 100 )𝐶 𝑓𝑃𝑘

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒

=

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒

=

85(39) − 30 ) 280 1645.5 + ( 100 5

=

1821.9

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒

11

5.0 Graph Histogram And Ogive 5.1

Histogram Number of

Total Demand

Frequency

Lower

Upper

Boundary

Boundary

Midpoint

246 – 525

8

245.5

525.5

385.5

526 – 805

9

525.5

805.5

665.5

806 – 1085

4

805.5

1085.5

945.5

1086 – 1365

4

1085.5

1365.5

1225.5

1366 – 1645

5

1365.5

1645.5

1505.5

1646 – 1925

5

1645.5

1925.5

1785.5

1926 – 2205

4

1925.5

2205.5

2065.5

Group of The Total Demand

12

Group of The Total Demand

13

5.2

Ogive Number of

Upper

Comulative

Boundary

Frequency

Frequency

Total Demand -34 – 245

0

245.5

0

246 – 525

8

525.5

8

526 – 805

9

805.5

17

806 – 1085

4

1085.5

21

1086 – 1365

4

1365.5

25

1366 – 1645

5

1645.5

30

1646 – 1925

5

1925.5

35

1926 – 2205

4

2205.5

39

Ogive 45 39 40 35

Cumulative Frequency

35 30 30 25 25

21

20

17

15 8

10 5 0 0 0

500

1000

1500

2000

2500

Upper Class Boundary

14

15

6.0 Measures Quartile And Decile Using Graph 6.1 Quartile

16

6.1.1 First Quartile 𝑄1 𝑄1 𝑄1 𝑄1

= = = =

6.1.2 Third Quartile 𝑄3 𝑄3 𝑄3 𝑄3

= = = =

1(𝑁)𝑡ℎ 4

1(39)𝑡ℎ 4

9.75𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 581.5

3(𝑁)𝑡ℎ 4

3(39)𝑡ℎ 4

29.25𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 1603.5

17

6.2 Decile

18

6.2.1 8th Decile 𝐷𝑘

𝐷8 𝐷8 𝐷8

= = = =

(

𝐷5

31.2𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 1708.5

𝐷5 𝐷5

= = = =

𝑡ℎ

) 10 𝑡ℎ 8(39) ) ( 10

6.2.2 5th Decile 𝐷𝑘

𝑘𝑁

(

(

𝑘𝑁 𝑡ℎ ) 10

5(39) ) 10

𝑡ℎ

19.5𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 959.5

19

7.0 Conclusion And Discussion

20

8.0 References 8.1

https://www.analyzemath.com/statistics/introduction_statistics.html#:~:text= Statistics%20is%20a%20mathematical%20science,can%20be%20drawn%2 0from%20them.&text=Descriptive%20statistics%20deals%20with%20the,d raw%20any%20inferences%20from%20it

8.2

https://www.data.gov.my/data/en_US/dataset/energy-supply-and-demandfor-fuel-oil

21...