# Analyzing Random Numbers

Neva and I are waiting in Simon’s bedroom to do the traditional bedtime reading, but he is stuck at his computer. When I go to fetch him I see he is in the flow, I can almost see him glow with that special kind of joyful energy that one radiates when immersed into one’s favorite activity and discovering new ways to play with it. He was analyzing random numbers. After finally joining us in the bedroom, he jumped out of bed again a few times, saying he just had another good idea. It was after midnight. One of the greatest blessings of homeschooling is that you don’t have to rush your evenings or your mornings. Below is Simon’s little analysis log:

```List of random numbers (1000 random numbers 0-100 exclusive):

17 36 6 47 24 84 14 33 40 28 61 91 16 51 28 53 87 35 12 39 3 92 36 80 24 77 22 73 70 36 53 15 6 73 16 11 42 12 49 90 81 99 90 10 13 34 22 16 93 56 33 79 9 59 69 84 23 87 34 80 40 5 26 62 69 93 22 23 20 36 79 42 26 7 60 27 8 87 60 16 65 81 20 96 85 94 8 3 63 70 89 16 98 92 65 18 69 95 0 0 76 22 43 54 71 94 27 79 13 81 84 94 42 20 15 94 18 95 5 73 55 28 52 86 16 88 67 53 58 86 15 81 65 26 50 97 29 73 91 84 47 61 31 13 15 3 62 67 52 17 15 76 10 1 92 19 21 94 43 49 68 81 25 18 80 54 64 89 0 56 73 37 70 61 66 2 59 99 41 32 59 33 85 59 83 53 34 53 58 8 5 8 27 11 18 84 23 63 12 63 28 78 24 16 19 77 73 6 87 20 64 69 9 79 9 7 82 42 79 64 32 45 16 23 89 90 61 37 57 14 33 48 26 0 28 50 64 96 75 87 18 17 57 86 55 61 18 6 98 1 32 23 49 5 54 82 84 97 47 49 4 98 98 57 45 50 43 20 33 51 45 99 63 67 66 10 55 60 59 77 80 78 46 40 49 10 14 52 73 83 91 27 2 89 17 75 22 86 42 80 55 99 83 10 64 76 71 70 89 51 24 30 77 23 81 38 48 26 23 61 66 35 78 24 79 18 83 37 8 42 95 26 62 77 48 30 90 84 11 8 94 86 42 83 42 23 83 40 24 96 59 0 94 51 4 66 36 69 58 89 30 89 26 53 26 92 57 34 41 91 23 88 94 35 3 20 35 59 80 37 24 61 32 38 55 3 47 33 52 53 46 13 6 56 86 53 38 90 41 81 28 4 26 33 62 76 21 19 48 87 60 51 84 59 18 1 22 20 89 55 34 95 76 6 40 29 75 78 96 83 38 67 97 61 61 13 35 65 41 49 70 76 51 48 4 97 21 6 36 91 70 46 40 30 98 75 93 3 10 80 34 45 38 73 57 28 37 33 70 67 47 20 97 21 31 77 52 10 5 85 63 0 66 26 48 73 69 74 38 40 50 18 80 86 39 4 36 43 35 57 90 84 74 36 53 1 72 33 27 39 44 82 94 23 73 42 84 85 45 47 83 60 6 74 49 40 35 77 73 47 99 94 22 35 68 49 61 9 90 96 27 16 18 54 5 13 35 23 6 14 86 15 65 71 2 50 83 55 1 0 86 70 11 28 15 51 26 61 17 92 82 61 90 4 80 88 47 60 5 57 66 67 14 71 0 70 72 12 43 8 33 11 80 19 54 0 51 22 18 32 33 42 33 12 1 22 67 86 79 16 22 61 76 66 77 90 52 16 13 79 17 38 24 70 81 78 97 91 96 11 32 41 70 11 2 61 48 22 63 90 88 80 88 59 48 45 45 12 10 8 21 16 18 45 80 54 49 1 67 16 44 41 74 48 91 0 46 63 46 34 28 90 22 70 87 47 29 83 18 82 80 60 79 52 27 9 96 27 13 75 19 34 45 71 94 83 17 95 4 68 82 84 5 57 5 47 42 66 19 21 46 38 96 32 13 57 91 78 7 97 21 93 81 89 25 68 14 16 45 95 17 72 30 41 37 69 8 38 81 86 45 51 48 22 32 43 85 55 51 0 13 56 53 66 44 21 98 68 22 86 90 54 20 84 15 1 17 96 95 5 52 91 75 4 8 4 12 91 68 76 25 51 83 23 33 41 43 65 55 78 3 20 61 82 96 85 42 97 24 25 19 65 8 82 15 3 30 77 80 66 77 28 31 0 64 53 33 28 46 78 95 52 0 58 30 10 25 50 86 72 46 40 60 79 38 57 50 31 1 93 27 81 80 93 29 44 69 29 95 43 2 55 62 8 85 62 62 22 93 96 86 29 62 53 65 17 53 79 39 11 75 35 53 58 98 6 8 91 87 84 38 23 6 45 65 89 82 31 37 84 2 61 63 39 98 92 89 97 5 79 84 79 64 94 67 43 66 75 69 86 87 64 68 33 32 20 9 61 98 87 19 87 76 62 53 34 37 52 7 28 48 3 94 69 68 88 70 45 40 71 40 1 76 81 16 32 86 16 67 44 6 37 82 65 67 43 21 4 79 37 25 71 68 31 63 70 25 97 86 61 84 33 91 86 11 2 91 89 21 39 39 25 89 43 71 9 2 90 6 46 91 70 38 50 4 38 47 54 67 93

Histogram (how many times every number occours in the list):

{0: 13, 1: 10, 2: 8, 3: 9, 4: 11, 5: 11, 6: 13, 7: 4, 8: 13, 9: 7, 10: 9, 11: 9, 12: 7, 13: 10, 14: 6, 15: 9, 16: 16, 17: 10, 18: 13, 19: 8, 20: 11, 21: 10, 22: 15, 23: 13, 24: 9, 25: 8, 26: 11, 27: 9, 28: 12, 29: 6, 30: 7, 31: 6, 32: 10, 33: 16, 34: 9, 35: 10, 36: 8, 37: 10, 38: 13, 39: 7, 40: 11, 41: 8, 42: 12, 43: 11, 44: 5, 45: 13, 46: 9, 47: 11, 48: 11, 49: 9, 50: 8, 51: 11, 52: 10, 53: 15, 54: 8, 55: 10, 56: 4, 57: 10, 58: 5, 59: 9, 60: 8, 61: 18, 62: 9, 63: 9, 64: 8, 65: 10, 66: 11, 67: 12, 68: 9, 69: 10, 70: 15, 71: 8, 72: 4, 73: 11, 74: 4, 75: 8, 76: 10, 77: 10, 78: 8, 79: 14, 80: 15, 81: 12, 82: 10, 83: 12, 84: 16, 85: 7, 86: 18, 87: 11, 88: 6, 89: 13, 90: 13, 91: 14, 92: 6, 93: 8, 94: 13, 95: 9, 96: 11, 97: 10, 98: 9, 99: 5}

Number of even numbers: 500
Number of odd numbers: 500
Number of low numbers (<50): 496
Number of high numbers (>=50): 504

Yeah I was just as surprised as you when I noticed exactly half of the numbers are even

Sum of all the numbers: 49920
Average number: 49.92

Yes there are less low numbers but somehow the average is still less than 50

For the next set of experiments, I split this big list of 1000 numbers into 100 smaller runs of 10 numbers

I tried to think of something good to do with these for a bit

Sum of all the numbers in each run:

[329, 473, 513, 367, 514, 557, 396, 412, 585, 542, 560, 540, 589, 611, 368, 420, 535, 540, 525, 314, 428, 504, 464, 507, 417, 522, 499, 601, 525, 531, 668, 431, 470, 531, 613, 526, 539, 474, 398, 510, 404, 459, 612, 527, 500, 545, 482, 445, 497, 448, 509, 619, 544, 623, 211, 428, 457, 574, 423, 320, 391, 552, 603, 440, 483, 367, 487, 556, 518, 530, 428, 555, 547, 479, 432, 527, 477, 481, 497, 535, 445, 438, 478, 495, 590, 547, 494, 595, 500, 625, 727, 559, 455, 596, 459, 441, 597, 547, 420, 552]

Then I got an idea

For every run we play this game:
- You go through every number until you find one that's >= 80
- Your score = the number of numbers you have gone through until the big one

Results for each run (-1 if there is no number >= 80 in the run):

[5, 1, 1, 9, 0, 5, 5, 7, 1, 0, 5, 0, 3, 1, -1, 4, 1, 7, 2, 5, 8, 6, 4, 7, 3, 5, 1, 1, 0, 0, 1, 4, 6, 0, 0, 2, 1, 1, -1, 4, 9, 2, 1, 2, 5, 4, -1, 2, -1, 2, 0, 1, 0, 0, -1, 0, 0, 0, -1, 2, 7, 5, 4, 9, 0, 4, 4, 1, 0, 4, 0, 2, 1, 8, 6, 6, 0, 1, 2, 3, 3, -1, 0, 9, 1, 4, 0, 4, 5, 4, 0, 0, 1, 2, 3, 2, 7, 0, 2, 0]

Histogram of the results:

{0: 23, 1: 17, 2: 12, 3: 5, 4: 12, 5: 9, 6: 4, 7: 5, 8: 2, 9: 4, -1: 7}

Average of all the results which aren't -1: 2.6

One more experiment, this one has to do with the original histogram of the original list:

What if we take the histogram OF THE HISTOGRAM? (I mean of the values of the histogram not of the keys)

{4: 4, 5: 3, 6: 5, 7: 5, 8: 13, 9: 15, 10: 16, 11: 13, 12: 5, 13: 10, 14: 2, 15: 4, 16: 3, 18: 2}

Alright, that's all I have thought of for now