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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.
Máximo 2.892 Mínimo 2.741 Rango 0.151 Numero de intervalos 0.010
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
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