This document contains data from an experiment measuring 25 samples over 20 intervals. It includes the raw data, calculations of statistical measures like the mean, standard deviation, and variance. It also shows how to plot the data as a histogram. The histogram depicts the distribution of the data, with the highest frequencies near the mean of 2.8. It identifies one interval from 2.65 to 2.7 as being outside specifications.

2. TEMA: EJERCICIO 9
INTERPRETACIÓN DE HISTOGRAMA
MATERIA: CONTROL ESTADÍSTICO DEL
PROCESO
GRUPO: 4to. – A NOCTURNO
CARRERA: TSU. PROCESOS INDUSTRIALES UNIVERSIDAD
AREA DE MANUFACTURA
TECNOLÓGICA
DOCENTE: LIC. EDGAR
DE TORREÓN
MATA ORTIZ
FECHA: 10/MARZO/2012
LUGAR: TORREÓN, COAH. MX.

3. DATOS (DATA)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 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 2.800
2 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 2.770
3 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 2.794
4 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 2.801
5 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 2.824
6 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 2.816
7 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 2.817
8 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 2.807
9 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 2.839
10 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 2.779
11 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 2.765
12 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 2.792
13 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 2.831
14 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 2.817
15 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 2.787
16 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 2.794
17 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 2.742
18 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 2.803
19 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 2.824
20 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 2.796
21 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 2.740
22 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 2.801
23 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 2.826
24 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 2.840
25 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

4. 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 0.00144062
inter. 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

5. X Y
2.6935 0
2.6935 3
2.7165 3
Datos para graficar un histograma se necesitan 2.7165 0
2.7165 18
Las desviaciones estándar y medias aritméticas y para tener 2.7395 18
mis X,Y tomo los datos de mis intervalos reales superiores con 2.7395 0
2.7395 52
de esta forma tengo la Y, y con la frecuencia fi tengo mi X. 2.7625 52
To plot a histogram data are needed 2.7625 0
The arithmetic means and standard deviations and have 2.7625 83
my X, and take my data with higher real intervals 2.7855
2.7855
83
0
I 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

6. HISTOGRAMA (HISTOGRAM)
160
140
120
100
80
60
40
20
0
2.65 2.7 2.75 2.8 2.85 2.9 2.95
El histograma indica que nuestra media aritmética se encuentra en el punto medio del mismo, la
media aritmética es de 2.800174 y la desviación estándar es de 0.034599 tenemos dentro de el
histograma una desestabilidad marcada por el intervalo de 2.65 a 2.7. Nos indica un punto fuera de
nuestras 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.

7. 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%
7
El gráfico de pastel nos sirve para saber los porcentajes de nuestro proceso.
En que porcentaje encontramos nuestras frecuencias para mejorar el proceso
o en que intervalo es donde nos encontramos

8. Tenemos nuestra media
(mediana) y nuestra
moda para denotar en
que intervalo se
encuentran nuestras
frecuencias mas inferior superior inferior superior xi fi fia
repetidas 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