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math portfolio

Extracts from this document...

Introduction

MATHEMATICS HL

PORTFOLIO (TYPE II: MODELLING) PART 1

Data Collection, Representation and Calculations

EXPERIMENT: Distribution of People Waiting for Services.

Choice: Post Office

Raw Data

  1. The Number of People Arriving at Entrance during the 3 Minutes Intervals

3

5

3

2

2

3

14

4

3

8

2

2

5

4

3

9

5

5

1

7

5

5

4

5

2

4

4

2

3

5

3

1

5

3

6

12

3

9

3

8

5

4

3

2

4

8

9

5

6

9

2

8

6

7

4

9

7

2

9

5

6

3

5

4

3

3

5

2

9

6

6

10

5

2

6

5

4

9

7

5

13

10

7

5

4

4

10

1

4

8

2

5

5

4

5

10

6

4

4

5

  1. The
...read more.

Middle

The Number of People Arriving at Entrance during the 3 Minutes Intervals

Number Entrance, x

x2

Frequency, f

Cumulative Frequency, F

1

1

3

3

2

4

12

15

3

9

14

29

4

16

16

45

5

25

22

67

6

36

8

75

7

49

5

80

8

64

5

85

9

81

8

93

10

100

4

97

11

121

0

97

12

144

1

98

13

169

1

99

14

196

1

100

  1. The Time Interval between Successive Clients (seconds)

125

156

162

36

62

144

236

71

39

66

82

15

153

18

226

107

152

163

218

160

151

81

97

30

140

426

597

64

69

401

138

63

113

85

277

126

341

67

95

354

148

136

174

81

216

232

276

125

178

110

61

62

88

118

32

226

346

120

188

219

90

146

84

97

276

44

77

112

85

362

129

188

271

414

109

66

77

170

122

272

25

159

210

550

74

166

152

247

73

346

150

98

136

262

76

79

299

162

127

126

Time Interval

x

x2

Frequency, f

F

f(x)

0 – 59

29.5

870.25

8

8

236

60 - 119

89.5

8010.25

34

42

3043

120 – 179

149.5

22350.25

30

72

4485

180 – 239

209.5

43890.25

10

82

2095

240 – 299

269.5

72630.25

8

90

2156

300 – 359

329.5

108570.3

4

94

1318

360 – 419

389.5

151710.3

3

97

1168.5

420 – 479

469.5

220430.3

1

98

469.5

480 – 539

509.5

259590.3

0

98

0

540 – 599

569.5

324330.3

2

100

1139

Total

100

100

16110


...read more.

Conclusion

  1. The Time Interval between Successive Clients
  1. Waiting Time for Each Client to Be Served

6.5 – 3 = 3.5

197.5 – 89.5 = 108

414.7 – 283.1 = 131.6

  • Variance image14.pngimage14.png
  1. The Number of People Arriving at Entrance during the 3 Minutes Intervals
  1. The Time Interval between Successive Clients
  1. Waiting Time for Each Client to Be Served

image15.png

image16.png

image17.png

image18.png

image20.png

image21.png

  • Standard Deviation = image22.pngimage22.png
  1. The Number of People Arriving at Entrance during the 3 Minutes Intervals
  1. The Time Interval between Successive Clients
  1. Waiting Time for Each Client to Be Served

image23.png

image24.png

image25.png

...read more.

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