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What is the expected value of this data set at 14 days.


sam conifer

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I am wondering if someone like me who likes math would like to work this problem out for me since it has been about 10 years since I have done much calculus. I am just playing a clash of clans clone game and would like to know the expected value of the premium currency it would take to knock off 14 days of build time. The game is Galaxy Control. The name given to the premium currency is redmin. I have taken 132 data samples, or in other words I have recorded 132 instances of time in minutes which are each associated with a value of redmin. It would however be more accurate to say that each value of redmin is associated with a range of time. For example, while the time lies between 6 to 8 minutes, it is 2 redmin which is associated with this range of time. It may be that between 9 and 11 minutes, 3 value is associated with this range. The value of redmin is always an integer, but to make this more complicated, the value of time is not so clean (rounded) as this example. The time range of a redmin value is actually a value of seconds rather than minutes. Even worse (or better if you appreciate the challenge of it), the value of seconds is rarely known. There is a rule as to the display of time. Only one pair of time numbers are ever displayed. What I mean is that if days are greater than 0, than hours are also displayed, but minutes and seconds are not. If the real value of an instance of time is 2 days, 4 hours, 13 minutes, 10 seconds, what you actually see is 2 days, 4 hours. This means that within that known 2 days 4 hours, multiple time ranges which correspond to different redmin values may exist, so while I have recorded time values associated with redmin values, there are other redmin values which are associated to that 2 days, 4 hours other than what is recorded. If it isn't apparent, a real time such as 12 hours, 5 minutes, 20 seconds would display as 12 hours 5 minutes which also creates opportunity for redmin overlap, though not as wildly as when the minutes are not known. If the redmin associations were linear, the problem would be very easy - just a matter of knowing the slope, but I see from the data that the range of time for each redmin value increases as time increases. Where the function begins, redmin values claim a range of 3 minutes or so, but by the time the function reaches 7 days, the range of time associated with a value of redmin has grown to almost 13 minutes. I feel like this is a calculus problem because I remember calculus dealing with slopes, but I don't think I can remember enough to actually finish the problem and have an answer. In any case, if someone would like to have some fun, here is the data I have collected. T is the value of time in minutes or D* 24 * 60 + H* 60 + M. Where D is days, H is hours, M is minutes. The G column is just T / R where R is the value of Redmin.

 

5 M 1 R 5 T 5.00 G
6 M 2 R 6 T 3.00 G
7 M 2 R 7 T 3.50 G
8 M 2 R 8 T 4.00 G
11 M 3 R 11 T 3.67 G
12 M 4 R 12 T 3.00 G
13 M 4 R 13 T 3.25 G
14 M 4 R 14 T 3.50 G
15 M 4 R 15 T 3.75 G
16 M 4 R 16 T 4.00 G
17 M 4 R 17 T 4.25 G
18 M 4 R 18 T 4.50 G
19 M 5 R 19 T 3.80 G
20 M 5 R 20 T 4.00 G
24 M 6 R 24 T 4.00 G
26 M 7 R 26 T 3.71 G
30 M 8 R 30 T 3.75 G
34 M 9 R 34 T 3.78 G
43 M 12 R 43 T 3.58 G
1 H 50 M 23 R 110 T 4.78 G
2 H 9 M 25 R 129 T 5.16 G
2 H 59 M 32 R 179 T 5.59 G
4 H 0 M 40 R 240 T 6.00 G
4 H 20 M 44 R 260 T 5.91 G
5 H 14 M 51 R 314 T 6.16 G
6 H 15 M 60 R 375 T 6.25 G
7 H 35 M 71 R 455 T 6.41 G
9 H 57 M 91 R 597 T 6.56 G
12 H 53 M 115 R 773 T 6.72 G
13 H 9 M 117 R 789 T 6.74 G
14 H 33 M 129 R 873 T 6.77 G
16 H 43 M 147 R 1003 T 6.82 G
17 H 58 M 157 R 1078 T 6.87 G
18 H 50 M 164 R 1130 T 6.89 G
20 H 27 M 178 R 1227 T 6.89 G
21 H 50 M 190 R 1310 T 6.89 G
22 H 40 M 196 R 1360 T 6.94 G
1 D 0 H 208 R 1440 T 6.92 G
1 D 1 H 215 R 1500 T 6.98 G
1 D 2 H 219 R 1560 T 7.12 G
1 D 5 H 230 R 1740 T 7.57 G
1 D 10 H 251 R 2040 T 8.13 G
1 D 11 H 256 R 2100 T 8.20 G
1 D 12 H 259 R 2160 T 8.34 G
1 D 14 H 266 R 2280 T 8.57 G
1 D 16 H 274 R 2400 T 8.76 G
1 D 17 H 281 R 2460 T 8.75 G
1 D 19 H 288 R 2580 T 8.96 G
1 D 21 H 296 R 2700 T 9.12 G
1 D 23 H 304 R 2820 T 9.28 G
2 D 1 H 312 R 2940 T 9.42 G
2 D 2 H 316 R 3000 T 9.49 G
2 D 3 H 323 R 3060 T 9.47 G
2 D 7 H 338 R 3300 T 9.76 G
2 D 8 H 340 R 3360 T 9.88 G
2 D 9 H 346 R 3420 T 9.88 G
2 D 10 H 351 R 3480 T 9.91 G
2 D 11 H 356 R 3540 T 9.94 G
2 D 13 H 361 R 3660 T 10.14 G
2 D 15 H 371 R 3780 T 10.19 G
2 D 20 H 392 R 4080 T 10.41 G
3 D 0 H 405 R 4320 T 10.67 G
3 D 9 H 444 R 4860 T 10.95 G
3 D 10 H 448 R 4920 T 10.98 G
3 D 11 H 451 R 4980 T 11.04 G
3 D 16 H 472 R 5280 T 11.19 G
3 D 17 H 477 R 5340 T 11.19 G
3 D 18 H 482 R 5400 T 11.20 G
3 D 19 H 484 R 5460 T 11.28 G
3 D 22 H 499 R 5640 T 11.30 G
4 D 0 H 506 R 5760 T 11.38 G
4 D 3 H 519 R 5940 T 11.45 G
4 D 4 H 523 R 6000 T 11.47 G
4 D 5 H 525 R 6060 T 11.54 G
4 D 7 H 532 R 6180 T 11.62 G
4 D 8 H 540 R 6240 T 11.56 G
4 D 9 H 543 R 6300 T 11.60 G
4 D 10 H 548 R 6360 T 11.61 G
4 D 11 H 549 R 6420 T 11.69 G
4 D 12 H 556 R 6480 T 11.65 G
4 D 14 H 564 R 6600 T 11.70 G
4 D 16 H 571 R 6720 T 11.77 G
4 D 17 H 576 R 6780 T 11.77 G
4 D 18 H 581 R 6840 T 11.77 G
4 D 19 H 583 R 6900 T 11.84 G
4 D 20 H 589 R 6960 T 11.82 G
4 D 21 H 591 R 7020 T 11.88 G
4 D 22 H 598 R 7080 T 11.84 G
5 D 0 H 604 R 7200 T 11.92 G
5 D 1 H 607 R 7260 T 11.96 G
5 D 2 H 612 R 7320 T 11.96 G
5 D 3 H 617 R 7380 T 11.96 G
5 D 4 H 622 R 7440 T 11.96 G
5 D 5 H 624 R 7500 T 12.02 G
5 D 6 H 630 R 7560 T 12.00 G
5 D 7 H 633 R 7620 T 12.04 G
5 D 8 H 637 R 7680 T 12.06 G
5 D 9 H 640 R 7740 T 12.09 G
5 D 10 H 645 R 7800 T 12.09 G
5 D 12 H 652 R 7920 T 12.15 G
5 D 14 H 660 R 8040 T 12.18 G
5 D 15 H 668 R 8100 T 12.13 G
5 D 16 H 668 R 8160 T 12.22 G
5 D 18 H 678 R 8280 T 12.21 G
5 D 19 H 681 R 8340 T 12.25 G
5 D 20 H 685 R 8400 T 12.26 G
5 D 22 H 694 R 8520 T 12.28 G
5 D 23 H 696 R 8580 T 12.33 G
6 D 0 H 703 R 8640 T 12.29 G
6 D 1 H 708 R 8700 T 12.29 G
6 D 2 H 712 R 8760 T 12.30 G
6 D 3 H 716 R 8820 T 12.32 G
6 D 4 H 719 R 8880 T 12.35 G
6 D 6 H 728 R 9000 T 12.36 G
6 D 7 H 730 R 9060 T 12.41 G
6 D 8 H 736 R 9120 T 12.39 G
6 D 9 H 740 R 9180 T 12.41 G
6 D 10 H 744 R 9240 T 12.42 G
6 D 11 H 750 R 9300 T 12.40 G
6 D 15 H 764 R 9540 T 12.49 G
6 D 16 H 768 R 9600 T 12.50 G
6 D 17 H 772 R 9660 T 12.51 G
6 D 18 H 777 R 9720 T 12.51 G
6 D 19 H 782 R 9780 T 12.51 G
6 D 20 H 786 R 9840 T 12.52 G
6 D 21 H 791 R 9900 T 12.52 G
6 D 22 H 792 R 9960 T 12.58 G
6 D 23 H 797 R 10020 T 12.57 G
7 D 6 H 825 R 10440 T 12.65 G
7 D 9 H 838 R 10620 T 12.67 G
7 D 16 H 867 R 11040 T 12.73 G

 

I apologize for the lack of readability. I can't seem to paste a nice table into this post. I have all this data on an Open Office spreadsheet.

Edited by sam conifer
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