Datos Agrupados

A)

36 65 46 27 60 28 53 50 58 33 70 45 59 48

54 30 49 63 42 54 17 57 39 55 29 56 31

A.V = 70 – 17 = 53 N.C= 1 + 3.3 x 1.4313 = 6 IC= 9

Clases fi fac fr fr % fr%ac Xi Lím verd Xi . fi

17 - 25 1 1 0.037 3.7 3.7 21 16.5–25.5 21

26 – 34 6 7 0.2222 22.22 25.92 30 25.5-34.5 180

35 – 43 3 10 0.1111 11.11 37.03 39 34.5-43.5 117

44 – 52 5 15 0.1852 18.52 55.55 48 43.5-52.5 240

53 – 61 9 24 0.3333 33.33 88.88 57 52.5-61.5 513

62 - 70 3 27 0.1111 11.11 99.99 66 61.5-70.5 198

_

X= 47 Me= 49.8 Mo = 56.1 ∑ 1269

B)

31 55 26 49 57 34 45 58 30 51 24 61 42 34 43

60 37 59 32 44 39 61 28 56 35 58 40 33 60 46

A.V = 61-24=37 N.C= 1 + 3.3 x 1.4771= 6 IC= 6

Clases fi fac fr fr % fr%ac Xi Lím verd Xi . fi

24-29 3 3 0.1 10 10 26.5 23.5-29.5 79.5

30-35 7 10 0.2333 23.33 33.33 32.5 29.5-35.5 227.5

36-41 3 13 0.1 10 43.33 38.5 35.5-41.5 115.5

42-47 5 18 0.1667 16.67 60 44.5 41.5-47.5 222.5

48-53 2 20 0.0667 6.67 66.67 50.5 47.5-53.5 101

54-59 6 26 0.2 20 86.67 56.5 53.5-59.5 339

60-65 4 30 0.1333 13.33 100 62.5 59.5-65.5 250

_

X= 44.5 Me= 43.9 Mo = 32.5 ∑ 1335

C)

72 47 71 42 72 58 49 72 68 69 42 51 44 72 49 72 60 46

43 69 63 48 45 72 43 67 50 72 70 59 50 53 72 45 56

A.V = 72-42=30 N.C= 1 + 3.3 x 1.5441= 6 IC= 5

Clases fi fac fr fr % fr%ac Xi Lím verd Xi . fi

42-46 8 8 0.2286 22.86 22.86 44 41.5-46.5 352

47-51 7 15 0.2 20 42.86 49 46.5-51.5 343

52-56 2 17 0.0571 5.71 48.57 54 51.5-56.5 108

57-61 3 20 0.0857 8.57 57.14 59 56.5-61.5 177

62-66 1 21 0.0286 2.86 60 64 61.5-66.5 64

67-71 6 27 0.1714 17.14 77.14 69 66.5-71.5 414

72-76 8 35 0.2286 22.86 100 74 71.5-76.5 592

_

X= 58.57 Me= 57.33 Mo1 = 45.94 y Mo2 = 72.5 ∑ 2050

D)

85 86 70 84 81 94 59 82 94 71 79 75 81 92 77 87 83 80 82 55 81 63 82

90 68 94 53 83 72 94 74 91 94 61 91 76 57 87 58 90 84 79 88 78 85

A.V = 94-53=41 N.C= 1 + 3.3 x 1.6532= 6 IC= 7

Clases fi fac fr fr % fr%ac Xi Lím verd Xi . fi

53-59 5 5 0.1111 11.11 11.11 56 52.5 - 59.5 280

60-66 2 7 0.0444 4.44 15.55 63 59.5 - 66.5 126

67-73 4 11 0.0889 8.89 24.44 70 66.5 - 73.5 280

74-80 8 19 0.1778 17.78 42.22 77 73.5 - 80.5 616

81-87 15 34 0.3333 33.33 75.55 84 80.5 - 87.5 1260

88-94 11 45 0.2444 24.44 99.99 91 87.5 - 94.5 1001

_

X= 79.18 Me= 82.13 Mo1 = 84.95 ∑ 3563

E)

45 61 48 68 31 79 57 65 77 36 53 76 37 80 64 79 47 42 40 49 75

70 34 78 56 51 72 40 80 35 59 45 60 79 52 74 36 73 50 78 37 44

A.V = 80-31=49 N.C= 1 + 3.3 x 1.6232= 6 IC= 8

Clases fi fac fr fr % fr%ac Xi Lím verd Xi . fi

31-38 7 7 0.1667 16.67 16.67 34.5 30.5-38.5 241.5

39-46 6 13 0.1428 14.28 30.95 42.5 38.5-46.5 255

47-54 7 20 0.1667 16.67 47.62 50.5 46.5-54.5 353.5

55-62 5 25 0.1190 11.90 59.52 58.5 54.5-62.5 292.5

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