1       2       3       4       5       6       7       8       9      10      11      12      13      14      15      16      17      18      19      20
1    2.813   2.784   2.807   2.810   2.787   2.846   2.794   2.761   2.823   2.761   2.796   2.824   2.771   2.815   2.789   2.826   2.781   2.817   2.759   2.823
2    2.833   2.793   2.813   2.801   2.802   2.803   2.748   2.818   2.814   2.783   2.838   2.802   2.801   2.814   2.789   2.781   2.766   2.826   2.804   2.795
3    2.783   2.790   2.862   2.816   2.765   2.796   2.829   2.840   2.793   2.779   2.804   2.806   2.796   2.792   2.800   2.759   2.775   2.812   2.776   2.813
4    2.817   2.800   2.813   2.808   2.785   2.805   2.805   2.791   2.827   2.818   2.808   2.790   2.818   2.808   2.801   2.764   2.839   2.807   2.829   2.798
5    2.802   2.789   2.793   2.769   2.830   2.805   2.784   2.779   2.800   2.799   2.850   2.783   2.836   2.766   2.769   2.836   2.775   2.810   2.798   2.797
6    2.795   2.770   2.764   2.773   2.813   2.829   2.768   2.797   2.761   2.774   2.755   2.797   2.777   2.793   2.843   2.778   2.753   2.779   2.828   2.839
7    2.797   2.794   2.810   2.797   2.803   2.801   2.786   2.781   2.840   2.826   2.810   2.816   2.813   2.833   2.788   2.805   2.797   2.800   2.772   2.796
8    2.789   2.803   2.797   2.766   2.801   2.796   2.764   2.826   2.765   2.795   2.837   2.821   2.828   2.773   2.804   2.788   2.814   2.800   2.746   2.785
9    2.825   2.752   2.808   2.827   2.812   2.795   2.800   2.792   2.875   2.786   2.818   2.804   2.776   2.798   2.759   2.828   2.821   2.785   2.825   2.776
10   2.865   2.760   2.804   2.789   2.805   2.771   2.794   2.825   2.820   2.809   2.768   2.823   2.860   2.781   2.791   2.785   2.801   2.845   2.791   2.833
11   2.815   2.781   2.827   2.755   2.828   2.800   2.817   2.793   2.797   2.766   2.800   2.846   2.820   2.813   2.794   2.802   2.836   2.820   2.796   2.789
12   2.785   2.789   2.785   2.768   2.829   2.750   2.774   2.777   2.795   2.789   2.803   2.803   2.773   2.812   2.792   2.848   2.795   2.786   2.782   2.798
13   2.771   2.807   2.795   2.788   2.774   2.840   2.828   2.806   2.789   2.779   2.830   2.817   2.757   2.771   2.815   2.797   2.817   2.836   2.793   2.788
14   2.755   2.772   2.809   2.790   2.810   2.812   2.802   2.821   2.765   2.818   2.834   2.805   2.825   2.788   2.802   2.807   2.760   2.811   2.821   2.774
15   2.809   2.795   2.773   2.778   2.797   2.757   2.796   2.774   2.803   2.759   2.797   2.767   2.766   2.836   2.790   2.795   2.772   2.808   2.782   2.803
16   2.848   2.780   2.797   2.789   2.830   2.779   2.805   2.811   2.810   2.818   2.751   2.802   2.818   2.747   2.799   2.817   2.809   2.840   2.771   2.798
17   2.782   2.786   2.826   2.830   2.793   2.795   2.807   2.774   2.818   2.795   2.849   2.840   2.808   2.766   2.754   2.757   2.790   2.815   2.787   2.795
18   2.790   2.834   2.808   2.829   2.764   2.852   2.801   2.803   2.808   2.790   2.780   2.821   2.777   2.810   2.819   2.779   2.792   2.814   2.826   2.779
19   2.838   2.788   2.773   2.785   2.781   2.823   2.852   2.787   2.802   2.809   2.795   2.787   2.832   2.768   2.797   2.823   2.801   2.814   2.817   2.777
20   2.849   2.821   2.825   2.793   2.769   2.823   2.816   2.817   2.789   2.836   2.807   2.789   2.792   2.806   2.823   2.790   2.766   2.788   2.783   2.820
21   2.781   2.824   2.785   2.802   2.785   2.802   2.806   2.796   2.774   2.782   2.795   2.774   2.844   2.805   2.771   2.746   2.818   2.804   2.787   2.801
22   2.741   2.808   2.794   2.814   2.813   2.768   2.796   2.756   2.817   2.790   2.795   2.748   2.811   2.795   2.802   2.817   2.780   2.816   2.892   2.791
23   2.832   2.778   2.752   2.771   2.770   2.797   2.807   2.789   2.861   2.814   2.774   2.845   2.804   2.794   2.827   2.774   2.752   2.802   2.789   2.819
24   2.768   2.815   2.821   2.820   2.746   2.809   2.810   2.802   2.806   2.803   2.802   2.782   2.808   2.787   2.793   2.780   2.817   2.811   2.796   2.792
25   2.807   2.811   2.774   2.753   2.788   2.806   2.816   2.769   2.802   2.791   2.782   2.768   2.804   2.835   2.783   2.810   2.774   2.823   2.814   2.792
Máximo
2.892
Mínimo
2.741
Rango
0.151
Numero de
intervalos


0.010
Marca
                                     de
Inferior Superior Inferior Superior Clase   fi   fia    fr           fra         (fi)(xi)    |Xi-Xm|Fi    |Xi-Xm|^2Fi

 2.741   2.751    2.7405   2.7515   2.746   9     9    0.018       0.018         24.714      0.478170     0.008468
 2.752   2.762    2.7515   2.7625   2.757   22   31 0.044          0.062         60.654      0.926860     0.005325
 2.763   2.773    2.7625   2.7735   2.768   43   74 0.086          0.148        119.024 1.338590          0.002907
 2.774   2.784    2.7735   2.7845   2.779   55   129 0.11          0.258        152.845 1.107150          0.001216
 2.785   2.795    2.7845   2.7955   2.79    93   222 0.186         0.444        259.470 0.849090          0.000250
 2.796   2.806    2.7955   2.8065   2.801   94   316 0.188         0.632        263.294 0.175780          0.000010
 2.807   2.817    2.8065   2.8175   2.812   79   395 0.158         0.790        222.148 1.016730          0.000497
 2.818   2.828    2.8175   2.8285   2.823   53   448 0.106         0.896        149.619 1.265110          0.001709
 2.829   2.839    2.8285   2.8395   2.834   28   476 0.056         0.952         79.352 0.976360          0.003648
 2.840   2.850    2.8395   2.8505   2.845   16   492   0.032       0.984         45.520      0.733920     0.006312
 2.851   2.861    2.8505   2.8615   2.856    4   496   0.008       0.992         11.424      0.227480     0.009703
 2.862   2.872    2.8615   2.8725   2.867    2   498   0.004       0.996         5.734       0.135740     0.013819
 2.873   2.883    2.8725   2.8835   2.878    1   499   0.002       0.998         2.878       0.078870     0.018661
 2.884   2.894    2.8835   2.8945   2.889    1   500   0.002         1           2.889       0.089870     0.024230
                                                                   Suma         1399.565     9.399720      0.096756
                                                               Media Aritmética 2.799130
                                                                                Desviación
                                                                 Mediana          Media      0.018799
                                                                    2.798        Moda        Varianza     0.0001935
                                                                                             Desviación
                                                                                  2.795         Std       0.0139108
Media
     2.799        0
     2.799        99
Media - Desviación Std
     2.785        0
     2.785        99
Media + Desviación Std
     2.813        0
     2.813        99
Media -2 Desviación Std   Desviación   2 Desviación   3 Desviación
     2.771        0          STD           Std            Std
     2.771        99
                            0.014         0.028          0.042
Media +2 Desviación Std
     2.827        0
     2.827        99
Media +3 Desviación Std
     2.841        0
     2.841        99
Media -3 Desviación Std
     2.757        0
     2.757        99
2.7405    0
2.7405    9   2.8285    0
2.7515    9   2.8285   28
2.7515    0   2.8395   28
2.7515   22   2.8395    0
2.7625   22   2.8395   16
2.7625    0   2.8505   16
2.7625   43   2.8505    0
2.7735   43   2.8505    4
2.7735    0   2.8615    4
2.7735   55
              2.8615    0
2.7845   55
              2.8615    2
2.7845    0
2.7845   93
              2.8725    2
2.7955   93   2.8725    0
2.7955    0   2.8725    1
2.7955   94   2.8835    1
2.8065   94   2.8835    0
2.8065    0   2.8835    1
2.8065   79   2.8945    1
2.8175   79   2.8945    0
2.8175    0
2.8175   53
2.8285   53
Grafica
                                                            Media
100
                                                       93      94


                                                                                           Media +3 Desviacion Std
      Media -3 Desviacion Std               Media - DesviacionMedia + Desviacion Std
                                                              Std
                                                                     79
 80                               Media -2 Desviacion Std               Media +2 Desviacion Std




 60
                                               55
                                                                            53


                                        43

 40

                                                                                        28
                             22

 20                                                                                          16

                  9
                                                                                                         4
                                                                                                             2      1    1
  0
  2.73                2.75              2.77         2.79           2.81         2.83             2.85       2.87       2.89

Ejercicio 9

  • 2.
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2.813 2.784 2.807 2.810 2.787 2.846 2.794 2.761 2.823 2.761 2.796 2.824 2.771 2.815 2.789 2.826 2.781 2.817 2.759 2.823 2 2.833 2.793 2.813 2.801 2.802 2.803 2.748 2.818 2.814 2.783 2.838 2.802 2.801 2.814 2.789 2.781 2.766 2.826 2.804 2.795 3 2.783 2.790 2.862 2.816 2.765 2.796 2.829 2.840 2.793 2.779 2.804 2.806 2.796 2.792 2.800 2.759 2.775 2.812 2.776 2.813 4 2.817 2.800 2.813 2.808 2.785 2.805 2.805 2.791 2.827 2.818 2.808 2.790 2.818 2.808 2.801 2.764 2.839 2.807 2.829 2.798 5 2.802 2.789 2.793 2.769 2.830 2.805 2.784 2.779 2.800 2.799 2.850 2.783 2.836 2.766 2.769 2.836 2.775 2.810 2.798 2.797 6 2.795 2.770 2.764 2.773 2.813 2.829 2.768 2.797 2.761 2.774 2.755 2.797 2.777 2.793 2.843 2.778 2.753 2.779 2.828 2.839 7 2.797 2.794 2.810 2.797 2.803 2.801 2.786 2.781 2.840 2.826 2.810 2.816 2.813 2.833 2.788 2.805 2.797 2.800 2.772 2.796 8 2.789 2.803 2.797 2.766 2.801 2.796 2.764 2.826 2.765 2.795 2.837 2.821 2.828 2.773 2.804 2.788 2.814 2.800 2.746 2.785 9 2.825 2.752 2.808 2.827 2.812 2.795 2.800 2.792 2.875 2.786 2.818 2.804 2.776 2.798 2.759 2.828 2.821 2.785 2.825 2.776 10 2.865 2.760 2.804 2.789 2.805 2.771 2.794 2.825 2.820 2.809 2.768 2.823 2.860 2.781 2.791 2.785 2.801 2.845 2.791 2.833 11 2.815 2.781 2.827 2.755 2.828 2.800 2.817 2.793 2.797 2.766 2.800 2.846 2.820 2.813 2.794 2.802 2.836 2.820 2.796 2.789 12 2.785 2.789 2.785 2.768 2.829 2.750 2.774 2.777 2.795 2.789 2.803 2.803 2.773 2.812 2.792 2.848 2.795 2.786 2.782 2.798 13 2.771 2.807 2.795 2.788 2.774 2.840 2.828 2.806 2.789 2.779 2.830 2.817 2.757 2.771 2.815 2.797 2.817 2.836 2.793 2.788 14 2.755 2.772 2.809 2.790 2.810 2.812 2.802 2.821 2.765 2.818 2.834 2.805 2.825 2.788 2.802 2.807 2.760 2.811 2.821 2.774 15 2.809 2.795 2.773 2.778 2.797 2.757 2.796 2.774 2.803 2.759 2.797 2.767 2.766 2.836 2.790 2.795 2.772 2.808 2.782 2.803 16 2.848 2.780 2.797 2.789 2.830 2.779 2.805 2.811 2.810 2.818 2.751 2.802 2.818 2.747 2.799 2.817 2.809 2.840 2.771 2.798 17 2.782 2.786 2.826 2.830 2.793 2.795 2.807 2.774 2.818 2.795 2.849 2.840 2.808 2.766 2.754 2.757 2.790 2.815 2.787 2.795 18 2.790 2.834 2.808 2.829 2.764 2.852 2.801 2.803 2.808 2.790 2.780 2.821 2.777 2.810 2.819 2.779 2.792 2.814 2.826 2.779 19 2.838 2.788 2.773 2.785 2.781 2.823 2.852 2.787 2.802 2.809 2.795 2.787 2.832 2.768 2.797 2.823 2.801 2.814 2.817 2.777 20 2.849 2.821 2.825 2.793 2.769 2.823 2.816 2.817 2.789 2.836 2.807 2.789 2.792 2.806 2.823 2.790 2.766 2.788 2.783 2.820 21 2.781 2.824 2.785 2.802 2.785 2.802 2.806 2.796 2.774 2.782 2.795 2.774 2.844 2.805 2.771 2.746 2.818 2.804 2.787 2.801 22 2.741 2.808 2.794 2.814 2.813 2.768 2.796 2.756 2.817 2.790 2.795 2.748 2.811 2.795 2.802 2.817 2.780 2.816 2.892 2.791 23 2.832 2.778 2.752 2.771 2.770 2.797 2.807 2.789 2.861 2.814 2.774 2.845 2.804 2.794 2.827 2.774 2.752 2.802 2.789 2.819 24 2.768 2.815 2.821 2.820 2.746 2.809 2.810 2.802 2.806 2.803 2.802 2.782 2.808 2.787 2.793 2.780 2.817 2.811 2.796 2.792 25 2.807 2.811 2.774 2.753 2.788 2.806 2.816 2.769 2.802 2.791 2.782 2.768 2.804 2.835 2.783 2.810 2.774 2.823 2.814 2.792
  • 3.
  • 4.
    Marca de Inferior Superior Inferior Superior Clase fi fia fr fra (fi)(xi) |Xi-Xm|Fi |Xi-Xm|^2Fi 2.741 2.751 2.7405 2.7515 2.746 9 9 0.018 0.018 24.714 0.478170 0.008468 2.752 2.762 2.7515 2.7625 2.757 22 31 0.044 0.062 60.654 0.926860 0.005325 2.763 2.773 2.7625 2.7735 2.768 43 74 0.086 0.148 119.024 1.338590 0.002907 2.774 2.784 2.7735 2.7845 2.779 55 129 0.11 0.258 152.845 1.107150 0.001216 2.785 2.795 2.7845 2.7955 2.79 93 222 0.186 0.444 259.470 0.849090 0.000250 2.796 2.806 2.7955 2.8065 2.801 94 316 0.188 0.632 263.294 0.175780 0.000010 2.807 2.817 2.8065 2.8175 2.812 79 395 0.158 0.790 222.148 1.016730 0.000497 2.818 2.828 2.8175 2.8285 2.823 53 448 0.106 0.896 149.619 1.265110 0.001709 2.829 2.839 2.8285 2.8395 2.834 28 476 0.056 0.952 79.352 0.976360 0.003648 2.840 2.850 2.8395 2.8505 2.845 16 492 0.032 0.984 45.520 0.733920 0.006312 2.851 2.861 2.8505 2.8615 2.856 4 496 0.008 0.992 11.424 0.227480 0.009703 2.862 2.872 2.8615 2.8725 2.867 2 498 0.004 0.996 5.734 0.135740 0.013819 2.873 2.883 2.8725 2.8835 2.878 1 499 0.002 0.998 2.878 0.078870 0.018661 2.884 2.894 2.8835 2.8945 2.889 1 500 0.002 1 2.889 0.089870 0.024230 Suma 1399.565 9.399720 0.096756 Media Aritmética 2.799130 Desviación Mediana Media 0.018799 2.798 Moda Varianza 0.0001935 Desviación 2.795 Std 0.0139108
  • 5.
    Media 2.799 0 2.799 99 Media - Desviación Std 2.785 0 2.785 99 Media + Desviación Std 2.813 0 2.813 99 Media -2 Desviación Std Desviación 2 Desviación 3 Desviación 2.771 0 STD Std Std 2.771 99 0.014 0.028 0.042 Media +2 Desviación Std 2.827 0 2.827 99 Media +3 Desviación Std 2.841 0 2.841 99 Media -3 Desviación Std 2.757 0 2.757 99
  • 6.
    2.7405 0 2.7405 9 2.8285 0 2.7515 9 2.8285 28 2.7515 0 2.8395 28 2.7515 22 2.8395 0 2.7625 22 2.8395 16 2.7625 0 2.8505 16 2.7625 43 2.8505 0 2.7735 43 2.8505 4 2.7735 0 2.8615 4 2.7735 55 2.8615 0 2.7845 55 2.8615 2 2.7845 0 2.7845 93 2.8725 2 2.7955 93 2.8725 0 2.7955 0 2.8725 1 2.7955 94 2.8835 1 2.8065 94 2.8835 0 2.8065 0 2.8835 1 2.8065 79 2.8945 1 2.8175 79 2.8945 0 2.8175 0 2.8175 53 2.8285 53
  • 7.
    Grafica Media 100 93 94 Media +3 Desviacion Std Media -3 Desviacion Std Media - DesviacionMedia + Desviacion Std Std 79 80 Media -2 Desviacion Std Media +2 Desviacion Std 60 55 53 43 40 28 22 20 16 9 4 2 1 1 0 2.73 2.75 2.77 2.79 2.81 2.83 2.85 2.87 2.89