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GEOESTADISTICA INGENIERIA DE MINAS - UNMSM ING.OSCAR BERNUY V.

PRIMER TRABAJO DE GEOESTADISTICA

TOMANDO 300 DATOS DE LA BASE DE DATOS TURMALINA : Au – Ag

Au Ag0.29 9.412.04 9.230.53 2.270.41 4.380.52 11.100.36 12.900.61 6.100.22 32.510.68 2.401.20 2.500.30 1.102.72 3.901.89 23.700.55 1.602.50 20.104.70 9.940.41 2.460.43 2.050.60 15.100.22 1.560.49 2.740.82 2.000.40 7.800.36 2.160.40 2.500.17 47.190.18 19.941.87 7.750.73 3.50

0.47228.0

01.12 9.504.87 14.300.60 99.570.40 35.100.19 0.410.23 0.430.32 0.470.10 0.700.29 1.000.25 0.900.49 1.640.45 1.550.25 1.800.54 3.390.54 1.500.95 6.870.97 13.320.64 6.140.14 4.70

0.26 3.870.29 5.150.25 3.280.28 2.100.38 3.900.31 5.100.79 9.310.63 8.450.18 14.300.27 10.700.22 20.400.55 7.271.17 3.002.20 1.401.04 2.501.17 2.860.89 1.870.71 4.540.43 2.110.22 1.340.16 2.000.16 1.400.38 1.600.10 2.100.04 1.800.69 3.000.29 1.520.28 1.400.19 4.060.11 3.300.80 4.770.15 5.100.25 10.120.33 22.600.09 29.800.55 24.810.26 4.503.05 3.963.23 14.81

4.05163.5

01.25 46.601.45 70.400.12 1.500.98 4.030.80 8.700.08 1.801.14 11.00

0.25171.4

30.16 8.69

0.25 23.760.30 7.600.39 4.000.94 5.390.95 5.990.96 2.96

21.40 13.301.23 1.670.25 1.740.11 2.920.05 2.260.52 2.910.04 2.000.17 2.540.44 2.300.36 1.803.05 83.218.55 18.191.78 17.730.62 1.730.23 6.790.31 3.900.45 5.600.21 5.201.06 17.600.21 2.100.46 13.820.39 2.801.31 24.030.54 21.550.12 3.910.95 12.910.56 14.440.42 4.900.57 3.960.41 2.820.98 41.400.53 28.190.51 36.020.29 12.500.25 5.680.40 40.550.30 3.600.39 16.330.56 15.340.45 5.750.29 1.250.40 1.300.24 1.210.22 1.500.18 1.40

0.22 20.610.15 5.650.15 1.500.32 10.670.41 9.600.52 14.410.15 3.870.56 18.900.21 19.310.94 24.080.43 11.431.01 22.110.32 7.360.16 6.290.28 9.300.27 14.980.27 42.92

1.99120.5

00.42 12.60

6.57138.0

01.17 54.20

1.57102.0

00.22 4.900.88 69.100.19 7.701.63 45.800.27 8.610.87 28.300.47 77.241.75 35.900.37 35.770.44 90.400.31 23.110.15 4.800.17 37.111.00 67.290.29 23.072.84 87.730.75 24.001.27 18.180.53 30.080.57 88.600.28 27.150.25 11.340.41 21.420.22 14.240.33 22.220.12 7.93

1


0.46 4.450.42 1.900.29 3.390.48 3.640.10 2.700.42 34.900.21 3.400.30 3.600.10 20.900.10 39.500.30 5.900.19 37.210.17 21.771.23 22.480.34 36.200.57 82.30

0.34118.3

5

0.70144.9

40.22 10.400.32 17.590.55 27.860.21 40.000.50 14.810.24 8.600.77 15.340.64 17.23

0.50 11.801.45 28.681.65 25.350.46 7.200.73 17.000.62 5.000.40 15.800.76 25.502.09 19.700.52 2.900.68 17.280.91 34.040.45 60.700.52 16.230.15 11.270.39 64.601.67 58.730.34 18.180.43 23.510.14 5.900.26 18.500.09 16.000.31 23.90

3.35196.0

7

9.46279.0

00.65 118.0

00.79 10.30

4.23190.2

20.25 14.600.73 46.881.05 40.511.47 12.600.61 54.500.47 3.90

1.19264.0

00.22 53.360.22 21.700.19 24.240.15 14.30

2.10117.7

91.18 27.260.64 10.900.16 0.900.78 20.580.42 6.350.41 4.490.84 26.701.50 36.461.76 21.921.13 5.68

2.25 12.022.02 5.201.05 19.000.82 16.400.93 5.600.98 7.500.95 11.700.62 12.200.97 6.101.13 2.671.32 3.901.25 3.400.55 2.750.18 4.880.17 7.490.13 8.820.77 8.060.51 15.470.49 10.301.11 18.800.17 23.600.23 5.530.66 5.560.98 3.090.41 1.480.17 1.510.46 1.30

HACIENDO LAS TABLAS ESTADISTICAS

Au AgN° DE DATOS 300 300

X.MAX 21.40 279.00

X.MIN 0.04redondeo 0.41

redondeo

RANGO 21.36 21.00 278.59 279.00N° DE

INTERVALOS 9.228996808 99.22899

7 9

AMPLITUD 2.314444402 2.33333330.1863

8 31suma de datos 248.18 2.3 0.00 31

DONDE:

Rango= Xmax –X min Numero de intervalos(h. sturges) : m=1+3.322*log(n) Amplitud de cada intervalo : Ci = R/m Marca de clase : Yi = (Li+Ls)/2

2


TABLA DE FRECUENCIA (Au)Li Ls marca de clase (Yi) fi hi Fi Hi fi*Yi

0.04 2.34 1.19 285 0.95 285 0.95 339.152.35 4.65 3.50 9 0.03 294 0.98 31.54.66 6.96 5.81 3 0.01 297 0.99 17.436.97 9.27 8.12 1 0.003333 298 0.993333 8.129.28 11.58 10.43 1 0.003333 299 0.996667 10.4311.59 13.89 12.74 0 0 299 0.996667 013.90 16.20 15.05 0 0 299 0.996667 016.21 18.51 17.36 0 0 299 0.996667 018.52 20.82 19.67 0 0 299 0.996667 020.83 23.13 21.98 1 0.003333 300 1 21.98

total 300 1 428.61

TABLA DE FRECUENCIA (Ag)Li Ls marca de clase (Yi) fi hi Fi Hi fi*Yi

0.41 31.41 15.91 249 0.83 249 0.83 3961.5931.42 62.42 46.92 26 0.086667 275 0.916667 1219.9262.43 93.43 77.93 10 0.033333 285 0.95 779.393.44 124.44 108.94 6 0.02 291 0.97 653.64

124.45 155.45 139.95 2 0.006667 293 0.976667 279.9155.46 186.46 170.96 2 0.006667 295 0.983333 341.92186.47 217.47 201.97 2 0.006667 297 0.99 403.94217.48 248.48 232.98 1 0.003333 298 0.993333 232.98248.49 279.49 263.99 2 0.006667 300 1 527.98

total 300 1 8401.17

1 2 3 4 5 6 7 8 90

50

100

150

200

250

300

histograma de la frecuencia relativa

Series1Series2

li-ls

fi

3


1 2 3 4 5 6 7 8 90

50

100

150

200

250

300

HISTOGRAMA DE LA FRECUENCIA ACU-MULADA

Au-Ag

Fi

HISTOGRAMA Au – Ag

1 16 31 46 61 76 91 106 121 136 151 166 181 196 211 226 241 256 271 2860

50

100

150

200

250

300

Series1Series2

Ag

Au

4


CALCULANDO LA MEDIA ARITMETICA

A.-CALCULO DE LA MEDIA DE DATOS NO AGRUPADOS

M(Au) = X = ∑i=1n

Xi

n

= 248.18300

= 0.8272666666666667

M(Ag) = X = ∑i=1n

Xi

n

= 6704.23300

= 22.34743333333333

B.-CALCULO DE LA MEDIA PARA DATOS AGRUPADOS EN TABLA DE FRECUENCIA CON INTERVALOS.

Hallando la Media de la variable ``Y``(Au)

x = ∑i=1

k

Xi∗fi

∑ fi

x = 428.61300

= 1.4287

Hallando la Media de la variable ``X``(Ag)

x = ∑i=1

k

Xi∗fi

∑ fi

x = 8401.17300

= 28.0039

DE LA TABLA OBTENIDA HALLAMOS LA VARIANZA

Hallando la Varianza de la variable ``Y``(Au)

σ 2= ∑i=1k

Au2∗Ag

n - x2= 53450/300-0.83*0.83 =177.477667

Hallando la Varianza de la variable ``X``(Ag)

5


σ 2= ∑i=1k

Ag2∗Au

n - x2= 1619328.627/300-22.35*22.35=4898.23959

COEFICIENTE CORRELATIVO

Coeficiente de correlación

ρ=Cov (xy )σ x∗σy

=Cov (Ag , Au)σAg∗σAu

Entonces hallamos la Cov ( Ag , Au )

Cov ( Ag , Au )=∑ (Ag∗Au )n

−(∑ Ag

n )(∑ Au

n )Cov ( Ag , Au )=10841.61

300−( 248.18

300)(6704.2300

)

Cov ( AuT , Au )=¿17.65149604

HALLANDO LA VARIANZA RELATIVA

Hallamos σAu

σ 2= ∑i=1k

Xi2∗fi

n

- x2

σ 2 ( Au )=√σ2

σ 2 ( Au )=√177.477667

σAu=13.32207443

Hallamos σAg

σ 2= ∑i=1k

Xi2∗fi

n

- x2

6


σ 2 ( Ag )=√σ2

σ 2 ( Ag )=√4898.23959❑

σAg=¿69.98742451

Remplazando los datos hallados podemos hallar Coeficiente de correlación lineal

ρ=Cov (Ag , Au)σAg∗σAu

= 17.6514960413.322∗69.987

ρ=Cov (Ag , Au )σAg∗σAu

=0.0189319226

Como el coeficiente de correlación está cerca a cero hay una relación de independencia

CALCULANDO LA DESVIACION RELATIVA

Para el Au

σ2

x=177.477667 /¿1.4287 =124.2231826135648

Para el Ag

σ2

x=4898.23959 /¿28.0039 =174.9127653648242

Desviación relativa porcentual

σ❑R=¿ √ σ2x *100

Para el Au

σ❑R=¿ √ σ2x *100=√124.2231826135648*100=1114.553722348097%

Para el Ag

σ❑R=¿ √ σ2x *100=√174.9127653648242*100=1322.535443759448

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