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D Ea El Et P
100 0.00145444 0.0022 0.00263731 37917.44
150 0.00218166 0.0023 0.00317012 47316.85
200 0.00290888 0.0024 0.00377115 53034.18250 0.0036361 0.0025 0.00441262 56655.64
300 0.00436332 0.0026 0.00507923 59064.06
350 0.00509054 0.0027 0.00576226 60740.06
400 0.00581776 0.0028 0.0064565 61953.08
450 0.00654498 0.0029 0.00715869 62860.67
500 0.00727221 0.003 0.0078667 63559.05
550 0.00799943 0.0031 0.00857909 64109.35
600 0.00872665 0.0032 0.00929486 64551.83
650 0.00945387 0.0033 0.01001327 64913.85
700 0.01018109 0.0034 0.0107338 65214.53750 0.01090831 0.0035 0.01145605 65467.57
800 0.01163553 0.0036 0.01217972 65682.97
850 0.01236275 0.0037 0.01290456 65868.21
900 0.01308997 0.0038 0.01363038 66028.97
950 0.01381719 0.0039 0.01435704 66169.61
1000 0.01454441 0.004 0.01508442 66293.54
100 0.0022
EJERCICIO # 1 ) CALCULO DE DISTANCIA MINIMA DE LINEA BASE PARREQUERIDA CON TS
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ESTACION
3 1.45444E-005
2 mm
12
12
OBTENER LA PRESICION
PRESICION DE LAESTACION PRESICION DE
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 95010000
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
LINEA BASE EN FUNCION DE PRESICION REQUERIDA
Ea El Et
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0.22% 22%
TOTAL
ra
2 !!m
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400.787 400.796 400.792 400.787400.79 400.788 400.797 400.794
400.793 400.791 400.792 400.787
1) "EDIA ARIT"ETICA400.791
2) RESID#ALES
1 -0.004 1.28403E-0052 -0.001 3.40278E-007
3 0.002 5.84028E-006
4 0.005 2.93403E-005
5 -0.003 6.67361E-006
6 0.000 1.73611E-007
7 0.001 2.00694E-006
8 0.006 4.11736E-005
9 0.001 2.00694E-006
10 -0.004 1.28403E-005
11 0.003 1.16736E-00512 -0.004 1.28403E-005
13 -0.004 1.28403E-005
14 -0.002 2.50694E-006
15 -0.003 6.67361E-006
16 -0.005 2.10069E-005
17 -0.006 3.11736E-005
18 -0.001 3.40278E-007
19 0.001 2.00694E-006
20 0.000 1.73611E-007
21 0.007 5.50069E-005
22 0.003 1.16736E-005
23 0.000 1.73611E-007
24 -0.002 2.50694E-006
S#"ATORIA $2 0.0002838333
"EDIA RESID#AL 1.2340580E-005
DES$IACION ESTANDAR 0.004
D&t&rm'(& la )ar'a(*a+ m&'a la &,)'a'( &,ta(ar
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400.787 400.786 400.792 400.794400.789 400.785 400.791 400.791
400.788 400.790 400.798 400.789
0.005 2.93403E-005
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212.22 212.15 212.29212.25 212.23 212.34
212.23 212.11 212.22
1) "EDIA ARIT"ETICA212.229
2) RESID#ALES
1 -0.009 8.71111111105E-0052 0.021 0.0004271111
3 0.001 4.44444444474E-007
4 -0.079 0.0062937778
5 0.001 4.44444444474E-007
6 -0.119 0.0142404444
7 0.061 0.0036804444
8 0.111 0.0122471111
9 -0.009 8.71111111105E-005
10 0.011 0.0001137778
11 -0.039 0.001547111112 0.021 0.0004271111
13 0.041 0.0016537778
14 -0.029 0.0008604444
15 0.021 0.0004271111
S#"ATORIA $2 0.0420933333
$ARIAN/A 0.0030066667
DES$IACION ESTANDAR 0.055
COEICIENTES
E50 73% 0.6745
E95 93% 1.96
E99.7 100% 2.968
DATOS $ALORES EN EL RANO TOTAL PORCENTAE
Calla $"P+ DS+ E50+ E95 RE$SAR SI A AL
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11 15 73%
14 15 93%
15 15 100%
212.22 212.15 212.29 212.24
212.25 212.23 212.34 212.19
212.23 212.11 212.22 212.25
212.22 212.15 212.29 212.24
212.25 212.23 212.34 212.19
212.23 212.11 212.22 212.25
212.22 212.15 212.29 212.24212.25 212.23 212.34 212.19
212.23 212.11 212.22 212.25
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212.24 212.27212.19 212.2
212.25 212.25
-0.079 0.0062937778
DESARROLLO
LI"ITE IN LI"ITE S#P
212.192 212.266
212.122 212.337
212.067 212.39
#NAS OSER$ACION #ERA DEL NI$EL DE PROAILIDAD DE 99.7
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212.27
212.2
212.25
212.27
212.2
212.25
212.27212.2
212.25
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IAG-201-01 - CÓMPUTOS Y AJUSTES DE MÍNIMOS CUADRADOSMATRICULA 15-2425
17.5 15 13.4 23.9 25.2
39.5 23.5 26.5 21.3 22.3
32.5 32.2 24.2 35.7 28
30.2 33.7 19.7 19.7 25.1
31.2 24.6 30.2 16.8 26.9
POBLACIO13.4 24
15 24.2 $"P 24.902
16.8 24.6
16.8 25.1 R&,'al 132.296004 0.813604
17.5 25.2 98.049604 0.492804
18.8 25.8 65.642404 0.091204
19 26.5 65.642404 0.039204
19.5 26.9 54.789604 0.088804
19.7 27.2 37.234404 0.806404
19.7 27.9 34.833604 2.553604
20.7 28
29.181604 3.99200421.1 28.4 27.060804 5.280804
21.1 28.5 27.060804 8.988004
21.3 30 17.656804 9.597604
21.4 30.2 14.455204 12.236004
21.5 30.2 14.455204 12.945604
21.6 30.7 12.974404 25.989604
22.3 31 12.264004 28.068804
1) Se realizaron 50 observaciones independientes de una misma poligonal de co
a) Determinar media de la población (µ)
b) Determinar la varianza de la población (σ2)
c) Determinar Deviación et!ndar población (σ)
d) Determinar media de la m"etra ( )# Calc"lar para la m"etra $% m"etra 2 & m
e) Determinar la varianza de la m"etra (S 2)# Calc"lar para la m"etra $% m"etra
) Determinar Deviación et!ndar m"etra (S )# Calc"lar para la m"etra $% m"e
) Crear intervalo de conianza del *+, para la media de la m"etra# Calc"lar par
-) Crear intervalo de conianza del *+, para la varianza de la m"etra# Calc"lar p
i) Crear intervalo de conianza del *+, para la comparación de la varianza de l
.) Realizar pr"eba de lo intervalo de conianza para la media% la varianza & la co
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22.5 31.2 11.573604 28.068804
22.7 32.2 10.903204 33.616804
23.3 32.5 6.770404 37.185604
23.5 33.7 5.769604 39.664804
23.5 35.3 4.848804 53.260804
23.9 35.7 2.566404 57.729604
24 39.5 1.965604 77.4048041.965604 108.118404
( 50 1.004004 116.596804
Smatr'a 1245.1 0.813604 213.101604
( 7.07106781
S( 0.79208833
)S2 1568.5098
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19.5 25.8 30 22.5 35.3
21.6 27.2 21.1 24 23.5
24 16.8 21.1 19 30.7
27.9 28.5 22.7 31 28.4
23.3 21.5 18.8 21.4 20.7
MUE13.4 $"P
15 R&,'al
17.5
$ar'a(*a 31.370196 19.5
D&,)'a'( 5.60091028 22.5
23.9
25.2
25.8
30
35.3
( 10
(-1 9
Smatr'a 228.1
( 3.16227766
S( 2.14042831
)S2 412.329
nexión. Para este set de observaciones:
etra '#
2 & m"etra '#
ra 2 & m"etra '#
a la m"etra $% m"etra 2 & m"etra '#
ara la m"etra $% m"etra 2 & m"etra '#
m"etra $ & la m"etra '#
mparación de la varianza de do m"etra#
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I(t&r)al & (:a(*a &l 95% & la m&'a !ara l
$alr ta;la 2.262
E95%!ara m&'a 17.9683511717
27.6516488283
I(t&r)al & (:a(*a &l 95% !ara la )ar'a(*a $alr ta;la !ara 0.025 19.02
$alr ta;la !ara 0.975 2.700
a
t
S&
a
t
S&
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at
S&
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TRA 122.81 16.8
88.5481 $ar'a(*a 45.8143333 19
60.9961 D&,)'a'( 6.76862862 21.1
28.1961 24
10.9561 24.2
0.0961 28
1.1881 30.7
5.7121 32.2
8.9401 32.5
51.6961 35.7
156.0001(
(-1
Smatr'a
(
S(
)S2
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a m&,tra 1 I(t&r)al & (:a(*a
$alr ta;la
=-> E95%
=?>
& la m&,tra 1 I(t&r)al & (:a(*a 21.6787066246 $alr ta;la !ara 0.025
152.7144444444 $alr ta;la !ara 0.975
Inte!"#$ %e &$n'"n(" %e# *+ ,"" #" &$,""&./n %e #" !"."n("
"&,tra 1 "&,tra 3
$ar'a(*a 45.8143333 $ar'a(*a 22.2448888889$alr ta;la => 4.03 $alr ta;la = 4.03
0.51105317 8.2999633873
I(t&r)al, & (:a(*a !ara la m&'a
$"P m&,tra1 22.81
$"P m&,tra2 26.42
$"P m&,tra3 23.54$"P !;la'( 24.902
Para m&,tra 1
22.81 @ 24.902
0.9773744788 S&
2.262
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0.754 B 2.262
Para m&,tra 3
23.54 @ 24.9020.9131917665 S&
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MUESTRA 2$P" 26.42
R&,'al 92.5444 $ar'a(*a 40.444
55.0564D&,)'a'( 6.3595597332
28.3024
5.8564
4.9284
2.4964
18.3184
33.4084
36.9664
86.118410
9
264.2
3.16227766
2.01106937
363.996
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&l 95% & la m&'a !ara la m&,tra 2
2.262
!ara m&'a 21.8709611 =->
30.9690389 =?>
&l 95% !ara la )ar'a(*a & la m&,tra 219.02 19.1375394
2.700 134.813333
%e #" et" 1 et" 3
I(t&r)al, & (:a(*a !ara la )ar'a(*a
$ar'a(*a m& 45.8143333
$ar'a(*a m& 40.444
$ar'a(*a m& 22.2448889$ar'a(*a !;l 31.370196
Para m&,tra 1
6.1625204
19.02 S&
6.16 B 19.02
S&
Para m&,tra 2
6.98080714
19.02
6.98 B 19.02
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S&
Para m&,tra 3
12.691983619.02
12.69 B 19.02
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MUESTRA 316.8 $"P 23.54
18.8 R&,'al 45.4276 $ar'a(*a
20.7 22.4676 D&,)'a'(
21.4 8.0656
21.5 4.5796
23.3 4.1616
24.6 0.0576
26.9 1.1236
30.2 11.2896
31.2 44.3556
58.6756( 10
(-1 9
Smatr'a 235.4
( 3.16227766
S( 1.49147205
)S2 200.204
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I(t&r)al & (:a(*a &l 95% & la m&'a !ara la m&,tra 3
$alr ta;la 2.262
E95%!ara m&'a 20.1662902 =->
26.9137098 =?>
I(t&r)al & (:a(*a &l 95% !ara la )ar'a(*a & la m&,tr$alr ta;la !ara 0.025 19.02 10.5259727
$alr ta;la !ara 0.975 2.700 74.1496296
Cm!ara'( & )ar'a(*a &(tr& , m&,tra,
$ar'a(*a m& 45.8143333
$ar'a(*a m& 40.444
$ar'a(*a m& 22.2448889
Cm!ara'( m&,tra 1 m&,tra 2
1.28320056
3.72
1.28 B 3.72
Cm!ara'( m&,tra 2 m&,tra 33.30558038
3.72
3.30 B 3.72
Cm!ara'( m&,tra 1 m&,tra 3
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0.09258506
3.72
0.09 B 3.72
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22.2448889
4.71644876
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DE AGRIMENSURAIAG-201-01 - CÓMPUTOS Y AJUSTES DE MÍNIMOS CUAMATRICULA 15-2425
468.09 468.13 468.11 468.13 468.1 468.13
468.1 468.1 468.12 468.14 468.16 468.12
468.13 468.12 468.18 468.15 468.08 468.15
4ALORES PARA LA POBLACION
468.08 ( 27 $"P 468.122963
468.09 (-1 26
468.09 ,matr'a12639.32 R&,'al 0.00184582
468.1 ( 5.19615242 0.00108656
468.1 S( 0.00479835 0.00108656468.1 )S2 0.01616296 0.0005273
468.1 0.0005273
468.1 0.0005273
468.11 0.0005273
468.11 0.0005273
468.12 0.00016804
468.12 0.00016804
1) Se realizaron 27 observaciones independientes de una misma poligonal de co
a) Determinar media de la población (µ)
b) Determinar la varianza de la población (σ2)
c) Determinar Deviación et!ndar población (σ)
d) Determinar media de la m"etra ( )# Calc"lar para la m"etra $% m"etra 2 & m
e) Determinar la varianza de la m"etra (S 2)# Calc"lar para la m"etra $% m"etra
) Determinar Deviación et!ndar m"etra (S )# Calc"lar para la m"etra $% m"e
2) Para los resultados obtenidos en el eercicio anterior:
a) Crear intervalo de conianza del *+, para la media de la m"etra# Calc"lar par
b) Crear intervalo de conianza del *+, para la varianza de la m"etra# Calc"lar p
c) Crear intervalo de conianza del *+, para la comparación de la varianza de l
!) "ealizar prueba de los intervalos de con#ianza para la media$ la varianza % la c
&) 'eterminar cu(l de las medias muestrales posee ma%or precisión con relació
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468.12 8.7791E-006
468.12 8.7791E-006
468.12 8.7791E-006
468.13 8.7791E-006
468.13 8.7791E-006
468.13 4.9520E-005
468.13 4.9520E-005468.13 4.9520E-005
468.14 4.9520E-005
468.14 4.9520E-005
468.15 0.00029026
468.15 0.00029026468.16 0.000731468.17 0.000731
468.18 0.001371740.00221248
0.00325322
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468.12 468.09 468.14
468.1 468.1 468.11
468.12 468.13 468.17
468.09 (
468.09 (-1
$ar'a(*a 0.00062165 468.1 ,matr'a
D&,)'a'( 0.02493296 468.11 (
468.12 S(468.13 )S2
468.13
468.13
468.14
nexión. Para este set de observaciones:
etra '#
2 & m"etra '#
ra 2 & m"etra '#
a la m"etra $% m"etra 2 & m"etra '#
ara la m"etra $% m"etra 2 & m"etra '#
a m"etra $ & la m"etra 2#
omparación de la varianza de dos muestras.
a la media poblacional.
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4ALORES PARA LA MUESTRA 1
9 $"P 468.115556 $ar'a(*a 0.0003527778
8 D&,)'a'( 0.0187823794
4213.04 R&,'al 0.00065309
3 0.00065309
0.00626079 0.00024198 Inte!"#$ %e &$n'"n(" %e# *0.00282222 3.0864E-005 $alr ta;la 2.306
1.9753E-005 E95%!ara m&'a0.00020864
0.00020864
0.00020864
0.00059753 nte!"#$ %e &$n'"n(" %e# *$alr ta;la !ara 0.025
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$alr ta;la !ara 0.975
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468.1 (
468.1 (-1
468.1 ,matr'a
468.1 (
+ %e #" e%." ,"" #" et" 1 468.11 S(468.12 )S2
468.101118 =-> 468.12
468.129993 =?> 468.14
468.16
,"" #" !"."n(" %e #" et"17.53 0.00016099
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2.180 0.0012946
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4ALORES PARA LA MUESTRA 2
9 $"P 468.116667 $ar'a(*a 0.00045
8 D&,)'a'( 0.0212132034
4213.05 R&,'al 0.00027778
3 0.00027778
0.00707107 0.00027778 Inte!"#$ %e &$n'"n(" %e# 0.0036 0.00027778 $alr ta;la 2.306
4.4444E-005 E95%!ara m&'a1.1111E-005
1.1111E-005
0.00054444
0.00187778 te!"#$ %e &$n'"n(" %e# *$alr ta;la !ara 0.025
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$alr ta;la !ara 0.975
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468.08 (
468.12 (-1
468.12 ,matr'a
468.13 (
+ %e #" e%." ,"" #" et" 2 468.13 S(468.15 )S2
468.100361 =-> 468.15
468.132973 =?> 468.17
468.18
,"" #" !"."n(" %e #" et"17.53 0.00020536
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2.180 0.00165138
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4ALORES PARA LA MUESTRA 3
9 $"P 468.136667 $ar'a(*a 0.0009
8 D&,)'a'( 0.03
4213.23 R&,'al 0.00321111
3 0.00027778
0.01 0.00027778 Inte!"#$ %e &$n'"n(" %e# *0.0072 4.4444E-005 $alr ta;la 2.306
4.4444E-005 E95%!ara m&'a0.00017778
0.00017778
0.00111111
0.00187778 nte!"#$ %e &$n'"n(" %e# *$alr ta;la !ara 0.025
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$alr ta;la !ara 0.975
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Dete.n"
P;la'(
$"P
0.02627415
+ %e #" e%." ,"" #" et" 3
468.113607 =->
468.159727 =?>
,"" #" !"."n(" %e #" et"17.53 0.00041072
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2.180 0.00330275
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&5# %e #" e%." et"#e ,$ee "$ ,e&../n &$n e#"&.
"&,tra 1 "&,tra 2 "&,tra 3
468.122963 $"P 468.115556 $"P 468.116667 $"P
0.02469145 0.02492885 0.02920235
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n " #" e% Inte!"#$ %e &$n'"n(" %e# *+"&,tra 1
$ar'a(*a 0.00035278
468.136667 $alr ta;la => 4.43
0.17696402
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,"" #" &$,""&./n %e #" !"."n(" %e #" et" 1 et" 2"&,tra 2
$ar'a(*a 0.00045
$alr ta;la => 4.43
3.47290123
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Pe6" %e .nte!"#$ %e$"P m&,tra 468.115556 Para m&,tra
$"P m&,tra 468.116667 a 468.1155 @
$"P m&,tra 468.136667 t 1.18314201
$"P !;la' 468.122963
S&
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&$n'"n(" ,"" #" e%."1 Para m&,tra 2 Para m&,tra 3
a468.1166 @ a468.136 @ 468.122
t 0.89043076 t 1.37037037
S&
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Pe6" %e .nte!"#$ %e &$n'"n(" ,"$ar'a(*a m&,tra1 0.00035278 Para m&,tra 1
$ar'a(*a m&,tra2 0.00045 14.0973
$ar'a(*a m&,tra3 0.0009
$ar'a(*a !;la'( 0.00062165 S&
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#" !"."n("Para m&,tra 2 Para m&,tra 3
11.0515986 5.5257993036
17.53 S&
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Pe6" %e .nte!"#$ %e &$n'"n(" ,"$ar'a(*a m&,tra1 0.00035278 Cm!ara'( m&,tra 1$ar'a(*a m&,tra2 0.00045 1.62713125
$ar'a(*a m&,tra3 0.0009 S&
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#" &$,""&.$n %e #" !"."n(" %e %$ et" m&,tra 2Cm!ara'( m&,tra 2 m&,tra 3 Cm!ara'( m&,tra 1
4.00 6.50852502
S&
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&,tra 3
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*+,- -*/ -+3
-4 2!05&62!66 -1200761066
48 459!961066
8' 82&0065766
', ';5160&66
,< ,1020961;66
DETER"INAR LOS A/I"#TES
-4 120.1186111
1) Se observó una poligonal cerrada % se computaron sus (ngulos$ distancias % un
FS#"ATORIA AN#LOS INTERNOS - = N -2>180
$ALORASOL#TO
AN#LOCORREIDO
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48 59.65194444
8' 248.015
', 86.85027778
,< 102.1536111
Pl'
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5> Call, & r&(aa, '(al&,
J=> 399000DEP
=N> 2000000LAT
EST J
A 399000 2000000
C 398744.0934 1999792.08245878
CD 398941.0401 1999718.21856265
DE 398947.9914 1999438.97651913
E 399230.5105 1999461.59194336
A 399287.6027 1999890.82006274
399000 2000000
A/I"#T INAL DISTANCIAS INALES
230.9070321426 329.7239971106
110.5583078069 210.3423183519
178.5740011165 279.3285514667
85.423277 283.422782436
7.57651617 433.0084280428
290.7878 307.6289223696
ERROR DE CIERRE LINEAL0.0235162
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'*S-+8*- ?m)
!29.722 CON$ERTIR DE RADOS A DECI"ALES
210.!&5
279.!! A 120.119444 A>2!.&2; B 59.6527778 >&!!.007 C 248.015833 C>!07.;25 D 86.8511111 D>
E 102.154444 E>F 103.211389 >
SUMATORIA 720.005
0.0 0.3 18
0.0050
351.025
azimut de partida para la l=nea AB. "ealizar auste de la poligonal por el m>todo de 8ompass ?4r@ula).
PR#EALOICA
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ra "'(t S&
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AN#LOS INALES AN#LOS INALES
325.483755 325.483755143 325.483755
59.6512757 59.6512756644 59.6512757
248.015693 248.01569331 248.015693
86.8492759 86.8492758835 86.8492759
398700 398800 398900 399000 399101999100
1999200
1999300
1999400
1999500
1999600
1999700
1999800
1999900
2000000
2000100
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2.0964798 RADIANES SOLO PARA ENCONTRAR LOS SENOS COSENOS
1.04113738
4.32869289
1.51583785
1.78293141.80137856
531.025
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0 399200 399300 399400
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120.1194444444 0
59.6527777778 0
248.0158333333 0
86.8511111111 0
102.1544444444
103.2113888889720.005
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DE AGRIMENSURA
IAG-201-01 - CÓMPUTOS Y AJUSTES DE MÍNIMOS CUADRADOSMATRICULA 15-2425
8oordenadas:
=nea -4 48 8' '-
-zimut $2345*6'+66 7$4+863966 2*94$'6+266 2'94256+366
'istancia +3$#$8 M 7$2#3$ M 7$+#'+ M +23#$9 M
'eterminar:
*+,- GRADO MINUTO SEGUNDO DISTANCIADECIMALESAB 124 9 35 541.17 124.159722BC 61 57 48 612.41 61.9633333CD 298 13 52 615.35 298.231111DA 238 20 54 524.18 238.348333
S#" 2293.11
*+,- A*'mt C, S&( LAT DEPAB 124.1597222222 -0.56150182 0.8274755 -303.867939 447.804918BC 61.9633333333 0.47003651 0.88264697 287.855061 540.541832CD 298.2311111111 0.47302924 -0.88104673 291.07854 -542.152106DA 238.3483333333 -0.52475374 -0.85125408 -275.065416 -446.210365
0.00024599 -0.01572057
1) Para la siguiente poligonal cerrada realizar el auste el m>todo de la br@ula$ partiendo de l
: A
0$5%555#55
; A
0+%555#55
a) AB % AC corregidas.
b) ,rror de cierre lineal.
c) 8oordenadas B$C.
d) 'eterminar -zimutes % 'istancias
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J=> 10000 DEP
=N> 5000 LAT
*+,- J A:IMU
AB 5000 10000 124.159507BC 4696.1320030734 10447.8086 61.9635234CD 4983.9869980029 10988.3547 298.231292DA 5275.0654719387 10446.2068 238.348122
5000 10000
ERROR DE CIERRE LINEAL0.0157225
4600 4700 4800 4900 5000 5100 5200 5300 5400
9400
9600
9800
10000
10200
10400
10600
10800
11000
11200
10000
10447.8086280729
10988.3546585191
10446.2067710544
10000
Cl
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ACT. LAT ACT. DEP LAT Crr&
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FINAL DISTANCIAS FINALES ANGULOS FINALES
541.173103 65.8113847751 65.8113848612.413675 117.8040166311 117.804017
615.346252 416.2677681151 56.2677681
524.17697 120.1168304787 120.11683
( C
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ANGULOS FINALES
65.8113848117.804017
56.2677681
120.11683