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# Ejercicio 9

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### Ejercicio 9

1. 1. TEMA: EJERCICIO 9 INTERPRETACIÓN DE HISTOGRAMAMATERIA: CONTROL ESTÁDISTICO DEL PROCESOGRUPO: 4to. – A NOCTURNOCARRERA: TSU. PROCESOS INDUSTRIALES UNIVERSIDAD AREA DE MANUFACTURA TECNOLÓGICADOCENTE: LIC. EDGAR DE TORREÓN MATA ORTIZFECHA: 10/MARZO/2012LUGAR: TORREÓN, COAH. MX.
2. 2. DATOS (DATA) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 2.728 2.811 2.749 2.813 2.817 2.756 2.776 2.841 2.814 2.781 2.821 2.808 2.791 2.844 2.867 2.774 2.741 2.850 2.762 2.8002 2.787 2.858 2.774 2.772 2.811 2.796 2.838 2.802 2.768 2.786 2.816 2.818 2.874 2.814 2.794 2.827 2.837 2.803 2.852 2.7703 2.820 2.715 2.803 2.795 2.738 2.780 2.798 2.819 2.797 2.774 2.792 2.774 2.799 2.782 2.786 2.826 2.816 2.773 2.852 2.7944 2.883 2.857 2.832 2.830 2.788 2.729 2.828 2.758 2.821 2.724 2.773 2.764 2.831 2.811 2.791 2.824 2.796 2.790 2.817 2.8015 2.830 2.797 2.775 2.852 2.781 2.841 2.810 2.781 2.803 2.833 2.774 2.755 2.694 2.829 2.817 2.793 2.848 2.762 2.837 2.8246 2.803 2.829 2.755 2.885 2.779 2.851 2.727 2.763 2.786 2.804 2.813 2.791 2.726 2.769 2.860 2.755 2.816 2.779 2.792 2.8167 2.764 2.748 2.842 2.791 2.731 2.827 2.788 2.793 2.773 2.778 2.792 2.728 2.740 2.804 2.796 2.830 2.805 2.844 2.836 2.8178 2.820 2.779 2.841 2.813 2.791 2.744 2.808 2.781 2.811 2.797 2.756 2.792 2.811 2.803 2.843 2.847 2.789 2.818 2.809 2.8079 2.841 2.811 2.783 2.782 2.798 2.746 2.797 2.874 2.746 2.760 2.810 2.801 2.809 2.813 2.791 2.773 2.783 2.791 2.821 2.83910 2.865 2.793 2.765 2.820 2.764 2.746 2.832 2.804 2.864 2.753 2.794 2.852 2.802 2.763 2.801 2.749 2.841 2.785 2.836 2.77911 2.830 2.723 2.773 2.798 2.790 2.827 2.771 2.823 2.842 2.758 2.759 2.816 2.768 2.795 2.786 2.791 2.784 2.790 2.873 2.76512 2.726 2.814 2.765 2.845 2.743 2.797 2.829 2.800 2.786 2.787 2.792 2.732 2.847 2.836 2.704 2.794 2.805 2.746 2.769 2.79213 2.767 2.790 2.792 2.878 2.853 2.825 2.828 2.799 2.804 2.771 2.804 2.813 2.771 2.838 2.857 2.788 2.883 2.826 2.837 2.83114 2.783 2.791 2.816 2.838 2.825 2.763 2.811 2.791 2.812 2.747 2.814 2.804 2.814 2.747 2.844 2.791 2.874 2.802 2.751 2.81715 2.815 2.781 2.788 2.802 2.788 2.783 2.734 2.838 2.765 2.835 2.768 2.769 2.808 2.762 2.802 2.831 2.787 2.788 2.812 2.78716 2.794 2.787 2.811 2.817 2.789 2.852 2.792 2.817 2.846 2.755 2.825 2.782 2.838 2.819 2.825 2.830 2.845 2.817 2.754 2.79417 2.789 2.760 2.815 2.779 2.754 2.804 2.811 2.881 2.856 2.789 2.797 2.788 2.797 2.754 2.850 2.804 2.812 2.847 2.768 2.74218 2.794 2.759 2.817 2.830 2.812 2.824 2.832 2.832 2.879 2.799 2.786 2.761 2.778 2.817 2.823 2.749 2.804 2.807 2.856 2.80319 2.812 2.759 2.831 2.843 2.736 2.789 2.773 2.797 2.725 2.797 2.810 2.826 2.790 2.815 2.830 2.806 2.789 2.817 2.864 2.82420 2.838 2.790 2.813 2.783 2.796 2.786 2.733 2.801 2.771 2.785 2.807 2.893 2.814 2.778 2.817 2.858 2.719 2.746 2.771 2.79621 2.846 2.815 2.781 2.719 2.834 2.836 2.785 2.866 2.852 2.752 2.765 2.795 2.810 2.836 2.819 2.786 2.779 2.760 2.836 2.74022 2.781 2.760 2.766 2.807 2.787 2.763 2.772 2.749 2.772 2.759 2.836 2.748 2.795 2.770 2.788 2.833 2.819 2.763 2.839 2.80123 2.829 2.768 2.806 2.780 2.792 2.810 2.827 2.848 2.783 2.768 2.767 2.800 2.788 2.777 2.808 2.847 2.843 2.753 2.822 2.82624 2.824 2.818 2.745 2.797 2.850 2.797 2.752 2.795 2.749 2.845 2.805 2.807 2.824 2.802 2.766 2.848 2.736 2.857 2.837 2.84025 2.805 2.802 2.743 2.766 2.794 2.852 2.817 2.761 2.793 2.823 2.801 2.818 2.760 2.834 2.796 2.796 2.797 2.821 2.827 2.777
3. 3. intervalos aparentes intervalos reales clase frecuencias tendencia central y disperción maximo 2.893 inferior superior inferior superior xi fi fia fr fra (fi)(xi) (xi-x)* fi (xi-x)^2*fi minimo 2.694 1 2.694 2.716 2.6935 2.7165 2.7050 3 3 0.006 0.006 8.1150 0.285522 0.02717427 2 2.717 2.739 2.7165 2.7395 2.7280 18 21 0.036 0.042 49.1040 1.299132 0.09376355 rango 0.199 3 2.740 2.762 2.7395 2.7625 2.7510 52 73 0.104 0.146 143.0520 2.557048 0.12574028 intervalos 9 4 2.763 2.785 2.7625 2.7855 2.7740 83 156 0.166 0.312 230.2420 2.172442 0.0568615 tam. de 0.0221111 inter 1 5 2.786 2.808 2.7855 2.8085 2.7970 143 299 0.286 0.598 399.9710 0.453882 0.00144062inter. Ajus. 0.023 6 2.809 2.831 2.8085 2.8315 2.8200 111 410 0.222 0.82 313.0200 2.200686 0.0436308 7 2.832 2.854 2.8315 2.8545 2.8430 66 476 0.132 0.952 187.6380 2.826516 0.12104837 8 2.855 2.877 2.8545 2.8775 2.8660 17 493 0.034 0.986 48.7220 1.119042 0.07366206 9 2.878 2.900 2.8775 2.9005 2.8890 7 500 0.014 1 20.2230 0.621782 0.05523041 143 totales 1400.0870 13.536052 0.59855186 media aritmética 2.8001 desviación media 0.0270721 varianza 0.0011971 desviación estándar 0.03459919
4. 4. X Y 2.6935 0 2.6935 3 2.7165 3Datos para graficar un histograma se necesitan 2.7165 0 2.7165 18Las desviaciones estándar y medias aritméticas y para tener 2.7395 18mis X,Y tomo los datos de mis intervalos reales superiores con 2.7395 0 2.7395 52de esta forma tengo la Y, y con la frecuencia fi tengo mi X. 2.7625 52To plot a histogram data are needed 2.7625 0The arithmetic means and standard deviations and have 2.7625 83my X, and take my data with higher real intervals 2.7855 2.7855 83 0I have thus the Y and with frequency fi I have my X. 2.7855 143 2.8085 143 media aritmética 2.8085 0 2.800174 0 2.8085 111 2.800174 148 2.8315 111 2.8315 0 media aritmética + 1 s media aritmética - 1 s 2.8315 66 2.7655748 2.8545 66 2.834773187 0 1 0 2.8545 0 2.7655748 2.834773187 148 1 148 2.8545 17 2.8775 17 media aritmética + 2 s media aritmética - 2 s 2.8775 0 2.7309756 2.8775 7 2.869372374 0 3 0 2.9005 7 2.7309756 2.9005 0 2.869372374 148 3 148 media aritmética + 3 s media aritmética - 3 s 2.6963764
5. 5. HISTOGRAMA (HISTOGRAM) 160 140 120 100 80 60 40 20 0 2.65 2.7 2.75 2.8 2.85 2.9 2.95El histograma indica que nuestra media aritmética se encuentra en el punto medio del mismo, lamedia aritmética es de 2.800174 y la desviación estándar es de 0.034599 tenemos dentro de elhistograma una desestabilidad marcada por el intervalo de 2.65 a 2.7. Nos indica un punto fuera denuestras especificaciones. The histogram indicates that our arithmetic mean is at the point half of it, the arithmetic mean is 2.800174 and the standard deviation is of 0.034599 we have within the histogram marked by a destabilization range of 2.65 to 2.7. It indicates a point outside of our specifications.
6. 6. Gráfico de pastel (pie chart) gráfico de pastel fi 3% 1% 1% 4% 3 18 13% 10% 52 83 17% 143 22% 111 66 17 29% 7El gráfico de pastel nos sirve para saber los porcentajes de nuestro proceso.En que porcentaje encontramos nuestras frecuencias para mejorar el procesoo en que intervalo es donde nos encontramos
7. 7. Tenemos nuestra media(mediana) y nuestramoda para denotar enque intervalo seencuentran nuestrasfrecuencias mas inferior superior inferior superior xi fi fiarepetidas 1 2 2.694 2.717 2.716 2.739 2.6935 2.7165 2.7165 2.7395 2.7050 2.7280 3 18 21 3 3 2.740 2.762 2.7395 2.7625 2.7510 52 73 4 2.763 2.785 2.7625 2.7855 2.7740 83 156 5 2.786 2.808 2.7855 2.8085 2.7970 143 299 6 2.809 2.831 2.8085 2.8315 2.8200 111 410 7 2.832 2.854 2.8315 2.8545 2.8430 66 476 8 2.855 2.877 2.8545 2.8775 2.8660 17 493 9 2.878 2.900 2.8775 2.9005 2.8890 7 500 (2.8315- ME= 2.7855 + 250 - 156 2.8200) 143 ME= 2.7855 94 0.0115 143 ME= 2.7855 + 0.65734266 * 0.0115 ME= 2.7855 + 0.00755944 ME= 2.7931 MODA= 2.7855