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### Estdesc(2)

1. 1. www.esmaschido.com Estadística sergiodls@yahoo.com A X F Fa FX X2 FX2 rango modas 1 36 6 6 216 1296 7776 1 --- 6 52 4 10 208 2704 10816 7 --- 10 68 6 16 408 4624 27744 11 --- 16 84 5 21 420 7056 35280 17 --- 21 100 6 27 600 10000 60000 22 --- 27 116 3 30 348 13456 40368 28 --- 30 132 5 35 660 17424 87120 31 --- 35 148 5 40 740 21904 109520 36 --- 40 164 2 42 328 26896 53792 41 --- 42 180 7 49 1260 32400 226800 43 --- 49 Moda = 180 n = 49 ΣX = 5188 ΣX 2 = 659216 36 0 52 0 X0 = 36 n = 49 68 0 DX= 16 MEDIA= 105.88 84 0 MODA= 180 100 0 mediana MEDIANA= 100 116 0 Dato a buscar s = 47.85 132 0 25 σ = 47.36 148 0 180 F. Max s = 2290.07 2 164 0 7 σ2 = 2243.33 180 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 36 52 68 84 100 116 132 148 164 180 DATOS ING. Sergio De Los Santos. 1 México D.F.
2. 2. www.esmaschido.com Estadística sergiodls@yahoo.com A X F Fa FX X2 FX2 rango modas 36 6 --- 52 4 --- 68 6 --- 84 5 --- 100 6 --- 116 3 --- 132 5 --- 148 5 --- 164 2 --- 180 7 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Dato a buscar F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 36 52 68 84 100 116 132 148 164 180 x DATOS ING. Sergio De Los Santos. 2 México D.F.
3. 3. www.esmaschido.com Estadística sergiodls@yahoo.com B X F Fa FX X2 FX2 rango modas 3 35 5 5 175 1225 6125 1 --- 5 47 2 7 94 2209 4418 6 --- 7 59 7 14 413 3481 24367 8 --- 14 Moda = 59 71 1 15 71 5041 5041 15 --- 15 83 7 22 581 6889 48223 16 --- 22 Moda = 83 95 3 25 285 9025 27075 23 --- 25 107 2 27 214 11449 22898 26 --- 27 119 7 34 833 14161 99127 28 --- 34 Moda = 119 131 3 37 393 17161 51483 35 --- 37 143 1 38 143 20449 20449 38 --- 38 n = 38 ΣX = 3202 ΣX 2 = 309206 35 0 47 0 X0 = 35 n = 38 59 0 DX= 12 MEDIA= 84.26 71 0 MODA= multimodal 83 0 mediana MEDIANA= 83 95 0 Promedio de datos s = 32.63 107 0 19 20 σ = 32.2 119 0 261 F. Max s = 1064.74 2 131 0 7 σ2 = 1036.72 24 143 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 35 47 59 71 83 95 107 119 131 143 DATOS ING. Sergio De Los Santos. 3 México D.F.
4. 4. www.esmaschido.com Estadística sergiodls@yahoo.com B X F Fa FX X2 FX2 rango modas 35 5 --- 47 2 --- 59 7 --- 71 1 --- 83 7 --- 95 3 --- 107 2 --- 119 7 --- 131 3 --- 143 1 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Promedio de datos F. Max s = 2 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N i =1 σ2 = σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 35 47 59 71 83 95 107 119 131 143 x DATOS ING. Sergio De Los Santos. 4 México D.F.
5. 5. www.esmaschido.com Estadística sergiodls@yahoo.com C X F Fa FX X2 FX2 rango modas 1 22 2 2 44 484 968 1 --- 2 39 5 7 195 1521 7605 3 --- 7 56 2 9 112 3136 6272 8 --- 9 73 4 13 292 5329 21316 10 --- 13 90 1 14 90 8100 8100 14 --- 14 107 2 16 214 11449 22898 15 --- 16 124 5 21 620 15376 76880 17 --- 21 141 7 28 987 19881 139167 22 --- 28 Moda = 141 158 1 29 158 24964 24964 29 --- 29 175 5 34 875 30625 153125 30 --- 34 n = 34 ΣX = 3587 ΣX 2 = 461295 22 0 39 0 X0 = 22 n = 34 56 0 DX= 17 MEDIA= 105.5 73 0 MODA= 141 90 0 mediana MEDIANA= 124 107 0 Promedio de datos s = 50.11 124 0 17 18 σ = 49.37 141 0 141 F. Max s = 2511.11 2 158 0 7 σ2 = 2437.25 18 175 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 22 39 56 73 90 107 124 141 158 175 DATOS ING. Sergio De Los Santos. 5 México D.F.
6. 6. www.esmaschido.com Estadística sergiodls@yahoo.com C X F Fa FX X2 FX2 rango modas 22 2 --- 39 5 --- 56 2 --- 73 4 --- 90 1 --- 107 2 --- 124 5 --- 141 7 --- 158 1 --- 175 5 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Promedio de datos F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 22 39 56 73 90 107 124 141 158 175 x DATOS ING. Sergio De Los Santos. 6 México D.F.
7. 7. www.esmaschido.com Estadística sergiodls@yahoo.com D X F Fa FX X2 FX2 rango modas 1 34 3 3 102 1156 3468 1 --- 3 50 4 7 200 2500 10000 4 --- 7 66 1 8 66 4356 4356 8 --- 8 82 7 15 574 6724 47068 9 --- 15 Moda = 82 98 3 18 294 9604 28812 16 --- 18 114 3 21 342 12996 38988 19 --- 21 130 4 25 520 16900 67600 22 --- 25 146 5 30 730 21316 106580 26 --- 30 162 6 36 972 26244 157464 31 --- 36 178 6 42 1068 31684 190104 37 --- 42 n = 42 ΣX = 4868 ΣX 2 = 654440 34 0 50 0 X0 = 34 n = 42 66 0 DX= 16 MEDIA= 115.9 82 0 MODA= 82 98 0 mediana MEDIANA= 122 114 0 Promedio de datos s = 46.91 130 0 21 22 σ = 46.35 146 0 82 F. Max s = 2200.38 2 162 0 7 σ2 = 2147.99 41 178 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 34 50 66 82 98 114 130 146 162 178 DATOS ING. Sergio De Los Santos. 7 México D.F.
8. 8. www.esmaschido.com Estadística sergiodls@yahoo.com D X F Fa FX X2 FX2 rango modas 34 3 --- 50 4 --- 66 1 --- 82 7 --- 98 3 --- 114 3 --- 130 4 --- 146 5 --- 162 6 --- 178 6 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Promedio de datos F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 34 50 66 82 98 114 130 146 162 178 x DATOS ING. Sergio De Los Santos. 8 México D.F.
9. 9. www.esmaschido.com Estadística sergiodls@yahoo.com E X F Fa FX X2 FX2 rango modas 2 23 5 5 115 529 2645 1 --- 5 43 6 11 258 1849 11094 6 --- 11 Moda = 43 63 6 17 378 3969 23814 12 --- 17 Moda = 63 83 5 22 415 6889 34445 18 --- 22 103 4 26 412 10609 42436 23 --- 26 123 3 29 369 15129 45387 27 --- 29 143 5 34 715 20449 102245 30 --- 34 163 1 35 163 26569 26569 35 --- 35 183 4 39 732 33489 133956 36 --- 39 203 4 43 812 41209 164836 40 --- 43 n = 43 ΣX = 4369 ΣX 2 = 587427 23 0 43 0 X0 = 23 n = 43 63 0 DX= 20 MEDIA= 101.6 83 0 MODA= multimodal 103 0 mediana MEDIANA= 83 123 0 Dato a buscar s = 58.46 143 0 22 σ = 57.77 163 0 106 F. Max s = 3417.05 2 183 0 6 σ2 = 3337.59 38 203 0 x 6 HISTOGRAMA DE FRECUENCIA 7 6 F 5 R E 4 C U E 3 N C 2 I A 1 0 23 43 63 83 103 123 143 163 183 203 DATOS ING. Sergio De Los Santos. 9 México D.F.
10. 10. www.esmaschido.com Estadística sergiodls@yahoo.com E X F Fa FX X2 FX2 rango modas 23 5 --- 43 6 --- 63 6 --- 83 5 --- 103 4 --- 123 3 --- 143 5 --- 163 1 --- 183 4 --- 203 4 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Dato a buscar F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 7 6 F 5 R E 4 C U E 3 N C 2 I A 1 0 23 43 63 83 103 123 143 163 183 203 x DATOS ING. Sergio De Los Santos. 10 México D.F.
11. 11. www.esmaschido.com Estadística sergiodls@yahoo.com F X F Fa FX X2 FX2 rango modas 1 2 7 7 14 4 28 1 --- 7 Moda = 2 15 6 13 90 225 1350 8 --- 13 28 2 15 56 784 1568 14 --- 15 41 5 20 205 1681 8405 16 --- 20 54 2 22 108 2916 5832 21 --- 22 67 6 28 402 4489 26934 23 --- 28 80 1 29 80 6400 6400 29 --- 29 93 6 35 558 8649 51894 30 --- 35 106 2 37 212 11236 22472 36 --- 37 119 4 41 476 14161 56644 38 --- 41 n = 41 ΣX = 2201 ΣX 2 = 181527 2 0 15 0 X0 = 2 n = 41 28 0 DX= 13 MEDIA= 53.68 41 0 MODA= 2 54 0 mediana MEDIANA= 54 67 0 Dato a buscar s = 39.8 80 0 21 σ = 39.31 93 0 2 F. Max s = 1584.27 2 106 0 7 σ2 = 1545.63 18 119 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 2 15 28 41 54 67 80 93 106 119 DATOS ING. Sergio De Los Santos. 11 México D.F.
12. 12. www.esmaschido.com Estadística sergiodls@yahoo.com F X F Fa FX X2 FX2 rango modas 2 7 --- 15 6 --- 28 2 --- 41 5 --- 54 2 --- 67 6 --- 80 1 --- 93 6 --- 106 2 --- 119 4 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Dato a buscar F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 2 15 28 41 54 67 80 93 106 119 x DATOS ING. Sergio De Los Santos. 12 México D.F.
13. 13. www.esmaschido.com Estadística sergiodls@yahoo.com G X F Fa FX X2 FX2 rango modas 1 20 7 7 140 400 2800 1 --- 7 Moda = 20 31 6 13 186 961 5766 8 --- 13 42 1 14 42 1764 1764 14 --- 14 53 1 15 53 2809 2809 15 --- 15 64 5 20 320 4096 20480 16 --- 20 75 2 22 150 5625 11250 21 --- 22 86 4 26 344 7396 29584 23 --- 26 97 6 32 582 9409 56454 27 --- 32 108 2 34 216 11664 23328 33 --- 34 119 6 40 714 14161 84966 35 --- 40 n = 40 ΣX = 2747 ΣX 2 = 239201 20 0 31 0 X0 = 20 n = 40 42 0 DX= 11 MEDIA= 68.68 53 0 MODA= 20 64 0 mediana MEDIANA= 69.5 75 0 Promedio de datos s = 36 86 0 20 21 σ = 35.55 97 0 20 F. Max s = 1296.17 2 108 0 7 σ2 = 1263.77 19 119 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 20 31 42 53 64 75 86 97 108 119 DATOS ING. Sergio De Los Santos. 13 México D.F.
14. 14. www.esmaschido.com Estadística sergiodls@yahoo.com G X F Fa FX X2 FX2 rango modas 20 7 --- 31 6 --- 42 1 --- 53 1 --- 64 5 --- 75 2 --- 86 4 --- 97 6 --- 108 2 --- 119 6 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Promedio de datos F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 20 31 42 53 64 75 86 97 108 119 x DATOS ING. Sergio De Los Santos. 14 México D.F.
15. 15. www.esmaschido.com Estadística sergiodls@yahoo.com H X F Fa FX X2 FX2 rango modas 1 9 3 3 27 81 243 1 --- 3 22 1 4 22 484 484 4 --- 4 35 3 7 105 1225 3675 5 --- 7 48 3 10 144 2304 6912 8 --- 10 61 6 16 366 3721 22326 11 --- 16 74 6 22 444 5476 32856 17 --- 22 87 7 29 609 7569 52983 23 --- 29 Moda = 87 100 6 35 600 10000 60000 30 --- 35 113 1 36 113 12769 12769 36 --- 36 126 4 40 504 15876 63504 37 --- 40 n = 40 ΣX = 2934 ΣX 2 = 255752 9 0 22 0 X0 = 9 n = 40 35 0 DX= 13 MEDIA= 73.35 48 0 MODA= 87 61 0 mediana MEDIANA= 74 74 0 Promedio de datos s = 32.24 87 0 20 21 σ = 31.84 100 0 87 F. Max s = 1039.57 2 113 0 7 σ2 = 1013.58 6 126 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 9 22 35 48 61 74 87 100 113 126 DATOS ING. Sergio De Los Santos. 15 México D.F.
16. 16. www.esmaschido.com Estadística sergiodls@yahoo.com H X F Fa FX X2 FX2 rango modas 9 3 --- 22 1 --- 35 3 --- 48 3 --- 61 6 --- 74 6 --- 87 7 --- 100 6 --- 113 1 --- 126 4 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Promedio de datos F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 9 22 35 48 61 74 87 100 113 126 x DATOS ING. Sergio De Los Santos. 16 México D.F.
17. 17. www.esmaschido.com Estadística sergiodls@yahoo.com I X F Fa FX X2 FX2 rango modas 2 8 4 4 32 64 256 1 --- 4 28 5 9 140 784 3920 5 --- 9 48 2 11 96 2304 4608 10 --- 11 68 4 15 272 4624 18496 12 --- 15 88 5 20 440 7744 38720 16 --- 20 108 4 24 432 11664 46656 21 --- 24 128 1 25 128 16384 16384 25 --- 25 148 6 31 888 21904 131424 26 --- 31 Moda = 148 168 1 32 168 28224 28224 32 --- 32 188 6 38 1128 35344 212064 33 --- 38 Moda = 188 n = 38 ΣX = 3724 ΣX 2 = 500752 8 0 28 0 X0 = 8 n = 38 48 0 DX= 20 MEDIA= 98 68 0 MODA= multimodal 88 0 mediana MEDIANA= 88 108 0 Promedio de datos s = 60.58 128 0 19 20 σ = 59.78 148 0 336 F. Max s = 3670.27 2 168 0 6 σ2 = 3573.68 41 188 0 x 6 HISTOGRAMA DE FRECUENCIA 7 6 F 5 R E 4 C U E 3 N C 2 I A 1 0 8 28 48 68 88 108 128 148 168 188 DATOS ING. Sergio De Los Santos. 17 México D.F.
18. 18. www.esmaschido.com Estadística sergiodls@yahoo.com I X F Fa FX X2 FX2 rango modas 8 4 --- 28 5 --- 48 2 --- 68 4 --- 88 5 --- 108 4 --- 128 1 --- 148 6 --- 168 1 --- 188 6 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Promedio de datos F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 7 6 F 5 R E 4 C U E 3 N C 2 I A 1 0 8 28 48 68 88 108 128 148 168 188 x DATOS ING. Sergio De Los Santos. 18 México D.F.
19. 19. www.esmaschido.com Estadística sergiodls@yahoo.com J X F Fa FX X2 FX2 rango modas 1 1 5 5 5 1 5 1 --- 5 8 5 10 40 64 320 6 --- 10 15 5 15 75 225 1125 11 --- 15 22 5 20 110 484 2420 16 --- 20 29 5 25 145 841 4205 21 --- 25 36 5 30 180 1296 6480 26 --- 30 43 1 31 43 1849 1849 31 --- 31 50 7 38 350 2500 17500 32 --- 38 Moda = 50 57 5 43 285 3249 16245 39 --- 43 64 4 47 256 4096 16384 44 --- 47 n = 47 ΣX = 1489 ΣX 2 = 66533 1 0 8 0 X0 = 1 n = 47 15 0 DX= 7 MEDIA= 31.68 22 0 MODA= 50 29 0 mediana MEDIANA= 29 36 0 Dato a buscar s = 20.52 43 0 24 σ = 20.3 50 0 50 F. Max s = 420.87 2 57 0 7 σ2 = 411.92 11 64 0 x 7 HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 1 8 15 22 29 36 43 50 57 64 DATOS ING. Sergio De Los Santos. 19 México D.F.
20. 20. www.esmaschido.com Estadística sergiodls@yahoo.com J X F Fa FX X2 FX2 rango modas 1 5 --- 8 5 --- 15 5 --- 22 5 --- 29 5 --- 36 5 --- 43 1 --- 50 7 --- 57 5 --- 64 4 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Dato a buscar F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 8 7 6 F R 5 E C U 4 E N 3 C I 2 A 1 0 1 8 15 22 29 36 43 50 57 64 x DATOS ING. Sergio De Los Santos. 20 México D.F.
21. 21. www.esmaschido.com Estadística sergiodls@yahoo.com K X F Fa FX X2 FX2 rango modas 3 28 6 6 168 784 4704 1 --- 6 Moda = 28 37 4 10 148 1369 5476 7 --- 10 46 6 16 276 2116 12696 11 --- 16 Moda = 46 55 3 19 165 3025 9075 17 --- 19 64 5 24 320 4096 20480 20 --- 24 73 6 30 438 5329 31974 25 --- 30 Moda = 73 82 3 33 246 6724 20172 31 --- 33 91 1 34 91 8281 8281 34 --- 34 100 5 39 500 10000 50000 35 --- 39 109 1 40 109 11881 11881 40 --- 40 n = 40 ΣX = 2461 ΣX 2 = 174739 28 0 37 0 X0 = 28 n = 40 46 0 DX= 9 MEDIA= 61.53 55 0 MODA= multimodal 64 0 mediana MEDIANA= 64 73 0 Promedio de datos s = 24.46 82 0 20 21 σ = 24.15 91 0 147 F. Max s = 598.1 2 100 0 6 σ2 = 583.15 44 109 0 x 6 HISTOGRAMA DE FRECUENCIA 7 6 F 5 R E 4 C U E 3 N C 2 I A 1 0 28 37 46 55 64 73 82 91 100 109 DATOS ING. Sergio De Los Santos. 21 México D.F.
22. 22. www.esmaschido.com Estadística sergiodls@yahoo.com K X F Fa FX X2 FX2 rango modas 28 6 --- 37 4 --- 46 6 --- 55 3 --- 64 5 --- 73 6 --- 82 3 --- 91 1 --- 100 5 --- 109 1 --- n= ΣX = ΣX 2 = 2 n n= n  ∑xi  ∑xi MEDIA= n   x= n i =1 MODA= ∑xi 2 − i =1n i =1 s= mediana MEDIANA= n −1 Promedio de datos F. Max s = 2 F. Max σ = n  ∑ xi  n i =1  s2 = ∑ xi 2 − N σ2 = i =1 σ= N HISTOGRAMA DE FRECUENCIA 7 6 F 5 R E 4 C U E 3 N C 2 I A 1 0 28 37 46 55 64 73 82 91 100 109 x DATOS ING. Sergio De Los Santos. 22 México D.F.