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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.

Estdesc(2)

  • 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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.