JOHOR ADDITIONAL MATHEMATICS PROJECT WORK 2015 SUGGESTED ANWSER BY www.addmathsprojectwork2015.blogspot.com

BAHAGIAN 2 SECTION 2 1. Jadual 1 / Table 1

Pelajar / Student Berat / Weight (kg) Tinggi / Height (cm)

1 35 152

2 38 144

3 42 160

4 42 154

5 43 154

6 45 167

7 45 173

8 45 159

9 46 167

10 46 172

11 46 135

12 48 178

13 48 167

14 48 138

15 51 177

16 51 142

17 51 157

18 52 168

19 52 166

20 52 160

21 53 166

22 53 164

23 54 180

24 54 165

25 54 173

26 54 160

27 54 170

28 55 148

29 55 172

30 55 166

31 55 155

32 56 167

33 58 172

34 58 163

35 59 164

36 60 185

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2. Jadual 2 : Taburan Kekerapan bagi berat yang diperoleh Table 2 : Frequecy distribution for the weight collected

(i) Data daripada taburan kekerapan diatas boleh diwakilkan dengan menggunakan 4 graf

statistic yang berlainan : Histogram, Poligon Kekerapan dan Ogif.

The data from the frequency distribution table can be represented by using three different

statistical graph : histogram, frequency polygons, and ogive.

Histogram

Poligon Kekerapan / Frequency Polygons

Bagi graf histogram dan polygon kekerapan, sempadan atas dan sempadan bawah

perlu dicari. Paksi y ialah Kekerapan dan paksi x ialah sempadan

Both histogram and frequency polygons are constructed by marking the boundaries

of each class along the horizontal axis and the frequencies along the vertical axis.

37 61 174

38 61 162

39 63 165

40 65 178

41 65 164

42 65 172

43 65 168

44 68 185

45 74 156

46 76 159

47 77 160

48 78 160

49 78 161

50 79 162

Berat / Weight (kg) Kekerapan / Frequency

30 - 34 0

35 - 39 2

40 - 44 3

45 - 49 9

50 - 54 13

55 - 59 8

60 - 64 4

65 - 69 5

70 - 74 1

75 - 79 5

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Ogif / Ogive

Ogif merupakan graf yang diplotkan dengan paksi y sebagai Kumulatif dan paksi x

sebagai sempadan atas.

Selain daripada itu, ogif juga boleh digunakan untuk mencari median, dan jarak

interquartile.

Ogive is a graph constructed by plotting the cumulative frequency of a set of data

against the corresponding upper boundary of each class.

Not only that, ogive is also the method of calculation, the median, and the

interquartile range of a set of data can also be estimated from its ogive.

Berat / Weight (kg)

Kekerapan / Frequency, f

Kumulatif / Cumulative frequency

Sempadan Atas / Upper boundary

30 - 34 0 0 34.5

35 - 39 2 2 39.5

40 - 44 3 5 44.5

45 - 49 9 14 49.5

50 - 54 13 27 54.5

55 - 59 8 35 59.5

60 - 64 4 39 64.5

65 - 69 8 47 69.5

70 - 74 2 49 74.5

75 - 79 1 50 79.5

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(ii) a) Min /Mean Min untuk berat 50 pelajar boleh dihitung dengan menggunakan formula : The mean weight of 50 students can be found by using the formula:

fx

f

f = 50

fx = 2795

Min/Mean 50

2795x

kgx 9.55

b) Sisihan Piawai / Standard deviation Sisihan piawai boleh dihitung dengan menggunakan formula berikut Standard deviation can be calculated by using formula stated below

22

xf

fx

Berat / Weight (kg)

Titik Tengah / Midpoint, x

Kekerapan / Frequency f

fx

35 - 39 37 2 74

40 - 44 42 3 126

45 - 49 47 9 423

50 - 54 52 13 676

55 - 59 57 8 456

60 - 64 62 4 248

65 - 69 67 5 335

70 - 74 72 1 72

75 - 79 77 5 385

f = 50 fx = 2795

Berat / Weight (kg)

Titik Tengah / Midpoint, x

Kekerapan / Frequency f

fx fx2

35 - 39 37 2 74 2738

40 - 44 42 3 126 5292

45 - 49 47 9 423 19881

50 - 54 52 13 676 35152

55 - 59 57 8 456 25992

60 - 64 62 4 248 15376

65 - 69 67 5 335 22445

70 - 74 72 1 72 5184

75 - 79 77 5 385 29645

f = 50 fx = 2795 fx2 = 161705

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29.5550

161705

kg45422.10

(iii) Merujuk kepada graf ogif yang dilukis, From the orgive plotted earlier,

Bilangan pelajar yang mempunyai berat badan melebihi 60 kg ialah The total number of student that weigh over 60 kg is 35.5 = 36 50 36 = 14 pelajar / student Peratusan pelajar yang melebihi 60kg Percentage of students weigh over 60kg

%3010050

15

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3) (i) = 55.9, = 10.45

P (X > 60) =

45.10

9.5560ZP

P = ( Z > 0.3923) P = 0.3473 Peratusan pelajar lebih daripada 60kg ialah Percentage of weigh more than 60 kg is 0.3473 x 100 = 34.742 % (ii) = 55.9, = 10.45

P (X < 45) =

45.10

9.5545ZP

P = ( Z > -1.0431) P = 0.1483 Peratusan pelajar lebih daripada 60kg ialah Percentage of weigh more than 60 kg is 0.1483 x 100 = 14.831 % (iii) 90 % = 0.9 P(M > m) = 0.9

9.045.10

9.55

m

ZP

282.145.10

9.55

m

m = 42.5 kg 4. Peratusan bilangan pelajar yang melebihi 60kg dengan menggunakan ogive menunjukkan sebanyak

30 peratus manakala melalui taburan normal, ialah 34.7 peratus. Terdapat berbezaan peratus sebanyak 4.7 peratus. Perbezaan ini berlaku kerana orgive merupakan pengiraan berdasarkan graf yang dilukis dengan menggunakan tangan yang berkemungkinan kurang tepat, berbanding dengan taburan normal yang menggunakan formula untuk pengiraan yang lebih tepat. Based on orgive, the percentage of students weigh more than 60kg is 30 percent. However, by using normally distributed formula, the percentage shows 34.7 percent. There is different by 4.7 percent. This different percentage occurs because orgive was drawn by using free hand which is less accurate compared to normally distributed formula, where the it is calculated theoretically using formula.

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5. n = 10, p = 0.3473 (dari soalan 3 / from question 3), q = 0.6527 Katakan X mewakili bilangan pelajar yang mempunyai berat 60kg Let X represent the number of student with 60kg weight. P(X=3)

73

3

10 )6527.0()3473.0(C = 0.2537 6. p = 0.3473 (dari soalan 3 / from question 3)

np = 50 n = 143.97 n = 144 [BERIKAN KOMEN ANDA SENDIRI] [PLEASE COMMENTS BY YOURSELF]

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BAHAGIAN 3 SECTION 3

PELAJAR / STUDENT PENGIRAAN BMI /

CALCULATION OF BMI

KATEGORI /

CATEGORY

1 35

= 1.52 x 1.52

= 15.1

Underweight

2 38

= 1.44 x 1.44

= 18.3

Underweight

3 42

= 1.60 x 1.60

= 16.4

Underweight

4 42

= 1.54 x 1.54

= 17.7

Underweight

5 43

= 1.54 x 1.54

= 18.1

Underweight

6 45

= 1.67 x 1.67

= 16.1

Underweight

7 45

= 1.73 x 1.73

= 15.0

Underweight

8 45

= 1.59 x 1.59

= 17.8

Underweight w

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9 46

= 1.67 x 1.67

= 16.5

Underweight

10 46

= 1.72 x 1.72

= 15.5

Underweight

11 46

= 1.35 x 1.35

= 25.2

Overweight

12 48

= 1.78 x 1.78

= 15.1

Underweight

13 48

= 1.67 x 1.67

= 17.2

Underweight

14 48

= 1.38 x 1.38

= 25.2

Overweight

15 51

= 1.77 x 1.77

= 16.3

Underweight

16 51

= 1.42 x 1.42

= 25.3

Overweight

17 51

= 1.57 x 1.57

= 20.7

Norma

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18 52

= 1.68 x 1.68

= 18.4

Underweight

19 52

= 1.66 x 1.66

= 18.9

Normal

20 52

= 1.60 x 1.60

= 20.3

Normal

21 53

= 1.66 x 1.66

= 19.2

Normal

22 53

= 1.64 x 1.64

= 19.7

Normal

23 54

= 1.80 x 1.80

= 16.7

Underweight

24 54

= 1.65 x 1.65

= 19.8

Normal

25 54

= 1.73 x 1.73

= 18.0

Underweight

26 54

= 1.60 x 1.60

= 21.1

Normal

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27 54

= 1.70 x 1.70

= 18.7

Normal

28 55

= 1.48 x 1.48

= 25.1

Overweight

29 55

= 1.72 x 1.72

= 18.6

Normal

30 55

= 1.66 x 1.66

= 20.0

Normal

31 55

= 1.55 x 1.55

= 22.9

Normal

32 56

= 1.67 x 1.67

= 20.1

Normal

33 58

= 1.72 x 1.72

= 19.6

Normal

34 58

= 1.63x 1.63

= 21.8

Normal

35 59

= 1.64 x 1.64

= 21.9

Normal

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36 60

= 1.85 x 1.85

= 17.5

Underweight

37 61

= 1.74 x 1.74

= 20.1

Normal

38 61

= 1.62 x 1.62

= 23.2

Normal

39 63

= 1.65 x 1.65

= 23.1

Normal

40 65

= 1.78 x 1.78

= 20.5

Normal

41 65

= 1.64 x 1.64

= 24.2

Normal

42 65

= 1.72 x 1.72

= 22.0

Normal

43 65

= 1.68 x 1.68

= 23.0

Normal

44 68

= 1.85 x 1.85

= 19.9

Normal

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45 74

= 1.56 x 1.56

= 30.4

Obese

46 76

= 1.59 x 1.59

= 30.1

Obese

47 77

= 1.60 x 1.60

= 30.1

Obese

48 78

= 1.60 x 1.60

= 30.5

Obese

49 78

= 1.61 x 1.61

= 30.1

Obese

50 79

= 1.62 x 1.62

= 30.1

Obese

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2. (i)

BMI Pelajar / BMI of students

Titik Tengah / Midpoint, x

Kekerapan / Frequency, f

fx fx2

13.0 - 15.9 14.45 4 57.80 835.21

16.0 - 18.9 17.45 16 279.20 4872.04

19.0 - 21.9 20.45 14 286.30 5854.835

22.0 - 24.9 23.45 6 140.70 3299.415

25.0 - 27.9 26.45 4 105.80 2798.41

28.0 - 30.9 29.45 4 117.80 3469.21

31.0- 33.9 32.45 2 64.90 2106.005

f= 50 fx = 1052.50 fx2 = 23235.13

Min / Mean = 05.2150

50.1052

f

fx

Sisihan Piawai / Standard Deviation

22

xf

fx

205.2150

13.23235

= 4.65 (ii)

BMI Pelajar /

BMI of students

Kekerapan /

Frequency

Kumulatif / Cumulative

Frequency

Sempadan Atas /

Upper boundary

10.0 - 12.9 0 0 9.95

13.0 - 15.9 4 4 15.95

16.0 - 18.9 16 20 18.95

19.0 - 21.9 14 34 21.95

22.0 - 24.9 6 40 24.95

25.0 - 27.9 4 44 27.95

28.0 - 30.9 4 48 30.95

31.0- 33.9 2 50 33.95

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a) Berdasarkan ogif, bilangan pelajar yang kurang berat badan ialah 17 pelajar Based on the ogive, the number of student with low body weight is 17 students Peratusan bilangan pelajar yang kurang berat badan ialah Percentage of student with low body weight is 17 students is

%3410050

17

b) Berdasarkan ogif, bilangan pelajar yang mempunyai berat badan melebihi BMI 25 ialah 10 pelajar Based on the ogive, the number of student with BMI higher than 25 is 10 students. Peratusan bilangan pelajar yang mempunyai berat badan melebihi BMI 25 ialah Percentage of student with BMI higher than 25 is

%2010050

10

3. (i)

= 21.05, = 4.65

P (25

(iii) 5 % = 0.05 P(K > k) = 0.05

05.065.4

05.21

k

ZP

644.165.4

05.21

k

k = 42.5 kg k = 28.7

4. p = 0.1693 (dari soalan 3 / from question 3)

np = 50 n = 295.33 n = 295 295 pelajar/students. [BINCANGKAN SENDIRI] [DISCUSS BY YOURSELF]

5. CARI DI GOOGLE / FIND IT FROM GOOGLE PENEROKAAN LANJUTAN / FURTHER EXPLORATION CARI DI GOOGLE / FIND IT FROM GOOGLE REFLEKSI / REFLECTION TULIS REFLEKSI ANDA / WRITE YOU OWN REFLECTION

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