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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

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

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

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