Estadistica y Probabilidad 2016

7/25/2019 Estadistica y Probabilidad 2016

1/55

ENCUESTA Y DATOS APLICADO POR LA ENCUESTA.

n edad genero es_civ gr_ins n_hijos trabaja ingreso opcion1 47 1 1 1 2 1 2128.0 1

2 34 1 3 1 2 1 1522.9 1

3 30 0 1 1 1 1 1795.0 2

4 48 0 1 1 3 1 1293.6 1

5 59 0 2 1 3 1 1276.9 1

6 30 0 1 1 3 1 1213.5 2

7 41 1 1 2 0 1 1589.3 2

8 44 1 1 3 2 1 1699.2 2

9 43 0 2 1 2 1 2018.2 1

10

45 1 2 1 2 1

1048.1 211 32 1 1 0 1 1 1183.2 1

12 49 1 1 1 2 1 1073.3 2

13 39 1 1 1 2 1 1232.7 2

14 44 1 3 1 1 1 1160.4 2

15 43 1 3 3 3 1 1718.0 2

16 36 1 2 0 1 1 1575.2 1

17 38 1 1 1 2 1 1456.0 3

18 61 1 1 1 2 1 1454.4 1

19 42 0 2 2 1 1 1702.2 1

20 37 1 3 0 1 1 1492.4 1

21 52 1 1 3 1 1 1336.2 2

22 33 1 1 1 2 1 1807.9 4

23 44 0 1 1 1 1 1320.4 1

24 43 1 3 0 2 1 970.3 2

25 23 1 2 1 2 1 1994.1 1

26 37 1 1 3 4 1 1081.4 2

27 51 0 1 1 2 1 1365.3 3

28 25 0 3 1 1 1 1907.2 2

29 28 0 1 1 0 1 1350.0 2

30 29 1 1 0 2 1 2053.1 2

31 50 0 1 1 2 1 1247.5 2

32 41 1 2 1 4 1 1351.0 2

33 38 0 2 1 2 1 1645.7 2

34 40 0 1 1 2 1 1225.3 3

35 52 0 1 1 2 1 877.6 2

36 42 1 2 1 2 1 1610.4 1

37 54 1 1 3 1 1 1832.4 1

38 34 0 1 1 2 1 1249.4 2

a) DATOS APLICADOS A 63 ENCUESTADOS.


2/55

39 30 1 1 3 3 1 1056.5 3

40 50 0 1 1 2 1 1817.1 1

41 32 1 3 1 2 1 1398.9 2

42 39 1 1 1 2 1 1024.2 1

43 52 1 1 1 2 1 1835.2 2

44 36 1 3 2 1 1 1880.5 1

45 42 1 2 1 1 1 1828.8 146 39 0 1 1 3 1 1517.0 1

47 49 1 1 1 2 1 504.6 4

48 41 0 1 1 1 1 1207.3 1

49 42 1 1 0 2 1 1648.7 2

50 35 1 2 0 2 1 1432.6 3

51 33 1 1 1 3 1 1461.7 2

52 34 0 1 1 3 1 934.3 2

53 43 1 1 1 2 1 1220.0 2

54 38 1 1 1 2 1 1525.9 1

55 53 0 1 2 2 1 2064.5 256 47 0 1 1 1 1 1567.5 2

57 41 0 1 1 3 1 1001.4 3

58 35 0 2 1 1 1 1098.8 2

59 40 1 1 1 4 1 1339.8 1

60 43 1 1 0 3 1 1489.4 2

61 46 0 3 2 1 1 1628.5 1

62 37 0 2 2 2 1 1640.8 2

63 46 1 1 0 5 1 1762.4 1


3/55

b) ENCUESTA :


4/55


5/55


6/55


7/55

PRESENTACION DE DATOS CUALITATIVOS.opcion

a) EN FORMA MATRICIAL X1

1

2

OPINION F.ABSOLUTA F.RELATIVA 1

1 A 24 38.10% 1

2 B 31 49.21% 2

3 BLANCO 6 9.52% 2

4 VICIADO 2 3.17% 2

63 100.00% 1

FUENTE: Encues!a !e"#$a%a &6'&( %e ab!#" &6 2

1

b) EN FORMA RAFICA 22

2

2

1

3

1

1

1

2

4

1

2

1

2

32

2

2

2

2

2

*#

ENCUESTA SO+RE ELECCIONES PARAPRESIDENTE EN A+RIL &6 A NIVEL

NACIONALCUADRO N, &

*&

*-

*3*

*/

*6

*(

*0

*1

*&2

*&&*

&-

*&3

*&

*&/

*&6

*&(

*&0

*&1*

-2

*-&

*--

*-3

*-

*-/

*-6

*-(*

-0

*-1

*32

*3&

*3-

*33

A; 38%

B; 49%

BLANCO; 10%

VICIADO; 3%

PREFERENCIA ELECTORAL DE LAS SE)UNDA VUELTA EN A+RIL DEL -2&6

A B BLANCO VICIADOFUENTE: Cua%! N4 &

50%

60%

A; 38.10%

B; 49.21%

PREFERENCIA ELECTORAL DE LAS SE)UNDA VUELTA EN A+RIL DEL -2&6


8/55

3

2

1

1

2

3

1

2

1

2

1

1

1

4

1

2

3

2

2

2

1

2

2

3

2

1

2

1

2

1

*3

*3/

*36

*3(

*30

*31*

2

*&

*-

*3

*

*/

*6

*(*

0

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*63

A B BLANCO VICIADO

0%

10%

20%

30%

.

.

BLANCO; 9.52%

VICIADO; 3.17%

ppp


9/55

PRESENTACION DE DATOS NUMER

a) EN FORMA MATRICIAL

X

0 2 3.17% 2 3.17% 63

1 16 25.40% 18 28.57% 61

2 31 49.21% 49 77.78% 45

3 10 15.87% 59 93.65% 14

4 3 4.76% 62 98.41% 4

5 1 1.59% 63 100.00% 1

63 100.00%

3& D !"# $'()"# 31 '*$$ 2 +*,"#.

-/.25 E$ ! P-& ! 25.40% ) *&)()($"# '*$$ &$ +*,".

/1

13.6/5

/

16.035

b) EN FORMA RAFIA

X: N&-" ) +*,"# ) !"# $'()"#. /1 /22 /1 /63R

* 0 1 2 3 4 5

DISTRI+UCION DE FRECUENCIA DEL NUMERO DE I7OS DE LA ENCUPREFERENCIA ELECTORAL EN EL PAIS

8#

9#

F#

#

F#

83;

9-;

F;

;

F3;

-;

&25

-25

325

25

/25

625

F!ecuenc#a !e"a#c %e +asnes


10/55

2 & - 3 /25

X

0 1 2 3 4 50.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

C+(-' T*'!

0 1 2 3 4 50.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

C+(-' T*'!


11/55

COS DISCRETOSn_hijos

X

2

2

1

3

3

3

0

100.00% 2

96.83% 2

71.43% 2

22.22% 1

6.35% 2

1.59% 2

1

3

1

2

2

1

1

1

2

1

2

2

4

2

1

0

2

2

4

2

2

2

*#

*&

*-*

3

*

STA SO+RE*

/

*6

#

*(

*0

*1

*&2*

&&

*&-

*&3

*&

*&/

*&6

*&(

*&0*

&1

*-2

*-&

*--

*-3

*-

*-/

*-6*

-(

*-0

*-1

*32

*3&

*3-

*33

*3*

3/


12/55

2

1

2

3

2

2

2

2

1

1

3

2

1

2

2

3

3

2

2

2

1

3

1

4

3

1

2

5

*36

*3(

*30

*31

*2

*&

*-

*3

*

*/

*6

*(

*0

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*/2

*/&

*/-

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*/

*//

*/6

*/(

*/0

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*62

*6&

*6-

*63


13/55

PRESENTACION DE DATOS NUMERICOS CONTINU

&.? CONSTRUCCION DE CLASES EN VARIA+LE CONTINUA

&.? E7EMPLO:

n 1/ INTERVAL

X@

CL

&-/.3- ' &-6.1(B

& &-/.3&

a) I%en#>ca! e" ca! e"


14/55

R ; &6-3./

@ ; (.22 6.1((&

c ; -3&.12 -3&.1-0/(

@CLASE ARCA DE C.

X

& /2.62 (36.2 6-2./2 & &./15 &

- (36./2 160.32 0/-.2 - 3.&(5 3

3 160.2 &-22.-2 &20.32 &2 &/.0(5 &3

&-22.32 &3-.&2 &3&6.-2 &6 -/.25 -1

/ &3-.-2 &66.22 &/0.&2 &( -6.105 6

6 &66.&2 &01/.12 &(02.22 && &(.65 /(

( &016.22 -&-(.02 -2&&.12 / (.15 6-

0 -&-(.12 -3/1.(2 --3.02 & &./15 63

63 &22.225

F!ecuenc#a abs"ua.

F!ecuenc#a !e"a#


15/55

3 160.2 &-22.-2 &20.32 &2 &/.0(5 &3 &-22.32 &3-.&2 &3&6.-2 &6 -/.25 -1/ &3-.-2 &66.22 &/0.&2 &( -6.105 66 &66.&2 &01/.12 &(02.22 && &(.65 /(( &016.22 -&-(.02 -2&&.12 / (.15 6-0 -&-(.12 -3/1.(2 --3.02 & &./15 63

1 -3/1.02 -/1&.62 -(/.(2 2 2.225 6363 &22.225

+) PRESENTACION DE D.CONTINUOS EN FORMA RAFICA

300.62 6-2./2 0/-.25

/5

&25

&/5

-25

-/5

325

POLI

25

/5

&25

&/5-25

-/5

325

ISTORAMA

25

/5

&25

&/5

-25

-/5

325

ISTO)RAMA

&225

ISTO)RAMA CRECIENTE R


16/55

&.? E7EMPLO:

n 6 INTERVAL

X@

CL

&-2.3- ' &-&.10B1 120.31

( V @a* ; &-&.1( 2 120.55V @#@ ; &-2.3& 3 120.79

R ; 1.67 4 121.03 @ ; 7 5 121.27) c ; 0.24 6 121.51

7 121.75

D#s!#buc#n %e 8!ecuenc#a %e "s sa"a!#as %e "s encuesa%s:

X: S(!(-*"# ) !"# $'()"#

Se #ene una @ues!a %e 6 e"e@ens c!!esn%#ene a "s ess %e can#ces @#n#@ &-2.3& e" es @a*#@ &-&.1(

Pes %e can#cas en !a@s.

R* LI #

25

&25

-25

325

.25

/25

625

(25

025

125

25

&25

-25

325

25

/25

625

(25

025

125

&225


17/55

/2.6 ' -&-0.2 B

( V @a* ; -&-0.22

V @#@ ; /2.62

R ; 1623.50

@ ; 7

) c ; 231.9

INTERVALO CERRADO

@CLASE

/

1 504.60 736.40 620.50 1 0.01587302 1

2 736.50 968.30 852.40 2 0.03174603 3

3 968.40 1200.20 1084.30 10 0.15873016 13

4 1200.30 1432.10 1316.20 16 0.25396825 29

5 1432.20 1664.00 1548.10 17 0.26984127 46

6 1664.10 1895.90 1780.00 11 0.17460317 57

7 1896.00 2127.80 2011.90 5 0.07936508 62

8 2127.90 2359.70 2243.80 1 0.01587302 63

63 1

R*

8#

9#

F#

LI#

LS#

620.50 852.40 1084.30 1316.20 1548.10 1780.00 2011.90 2243.800

0.05

0.1

0.15

0.2

0.25

0.3

----


18/55

&.? E7EMPLO:

n &2/

X INTERVALO CERRADO

&-&.-2 ' &-3.16B@

CLASE

a) V @a* ; &-3.1/ 1 121.21 121.54

V @#@ ; &-&.-& 2 121.55 121.88

b) R ; -.(/22 3 121.89 122.22

c) @ ; 0.22222 4 122.23 122.56

%) c ; 2.322 5 122.57 122.90

c ; 2.3/ 6 122.91 123.24

7 123.25 123.58

8 123.59 123.92

9 123.93 124.26

PRESENTACION DE DATOS NUMERICOS CONTINUOS.

n 63

X In!ess %e "s encuesa%s.

/2./ ' -&-0.&B

( V @a* ; -&-0.2V @#@ ; /2.6

R ; 1623.50 @ ; 7.00000

) c ; 231.9000c ; 232.0000

@CLASE

/

1 504.6 736.40 620.5 1 0.01587302 1

2 736.50 968.30 852.4 2 0.03174603 3

3 968.40 1200.20 1084.3 10 0.15873016 13

4 1200.30 1432.10 1316.2 16 0.25396825 29

Se #ene una @ues!a %e &2/ e"e@ens c!!esn%#ene a "s ess %e can#ces @#n#@ &-&.-& e" es @a*#@ &-3.1/. Cn esa #n8!@ac#n

#ne!


19/55

5 1432.20 1664.00 1548.1 17 0.26984127 46

6 1664.10 1895.90 1780.0 11 0.17460317 57

7 1896.00 2127.80 2011.9 5 0.07936508 62

8 2127.90 2359.70 2243.8 1 0.01587302 63

63 1

@CLASE

/

1 504.6 736.5 620.550 1

2 736.6 968.5 852.550 2

3 968.6 1200.5 1084.550 10

4 1200.6 1432.5 1316.550 16

5 1432.6 1664.5 1548.550 17

6 1664.6 1896.5 1780.550 11

7 1896.6 2128.5 2012.550 6

63

Ee@"u !cenae %e c#u%a%ans #enen #n!es @W*#@ %e &22 s"es

@CLASE

/

1 504.6 736.40 620.5 1 0.01587302

2 736.50 968.30 852.4 2 0.03174603

3 968.40 1200.20 1084.3 10 0.15873016

4 1200.30 1432.10 1316.2 16 0.25396825

5 1432.20 1664.00 1548.1 17 0.26984127

6 1664.10 1895.90 1780.0 11 0.17460317

7 1896.00 2127.80 2011.9 5 0.07936508

8 2127.90 2359.70 2243.8 1 0.01587302

63 1

& u !cenae %e c#u%a%ans #enen #n!es @W*#@ %e &22 s"es

- u PORCENTA7E DE LOS CIUDADANOS TIENEN COMO ENTRE &016 Y -&-('02

3 u !cenae %e c#u%a%ans #ene c@ #n!es @#n#@ %e &-22 s"es

#

+#

F#LI

#LS

#

#

+#LI

#LS

#

Resuesa: E" -'/&5 %e c#u%a%ans #enen #n!ess @a*#@s %e &322 s"es

Resuesa: E" ('15

Resuesa: E" 13'2( 5 DE CIUDADANO TIENEN INRESOS MINIMOS DE &222 SO


20/55


21/55

Singreso

X

2128.0

1522.9

1795.0

1293.6

CERRADO 1276.9

SE ARCA DE C. 1213.5

X 1589.3

&-/./& &-/.& 1699.2

&-/.(- &-/.6- 2018.2

&-/.13 &-/.03 1048.1

&-6.& &-6.2 1183.2

&-6.3/ &-6.-/ 1073.3

&-6./6 &-6.6 1232.7

&-6.(( &-6.6( 1160.4

&-6.10 &-6.00 1718.0

1575.2

TO POR LA D. 1456.0

SE 1454.4

1702.2

&-/./- 1492.4

&-/.(3 1336.2

&-/.1 1807.9

&-6.&/ 1320.4

&-6.36 970.3

&-6./( 1994.1

&-6.(0 1081.4

&-6.11 1365.3

1907.2

1350.0

2053.1

1247.5

1351.0

1645.7

*#

*&

*-

s s#en% e"*

3

*

*/

*6

LS#

*(

*0

*1

*&2

*&&*

&-

*&3

*&

*&/

*&6

*&(

*&0

LS# *&1

*-2

*-&

*--

*-3

*-

*-/

*-6

*-(*

-0

*-1

*32

*3&

*3-

*33


22/55

1225.3

877.6

1610.4

1832.4

1249.4

1056.5

1817.1

1398.9

1024.2

1835.2

1880.5

1828.8

1517.0

504.6

1207.3

&./15 63 &22.225 1648.7

.(65 6- 10.&5 1432.6

-2.635 62 1/.-5 1461.7

6.235 /2 (1.3(5 934.3

(3.2-5 3 /3.1(5 1220.0

12.05 &( -6.105 1525.9

10.&5 6 1./-5 2064.5

&22.225 & &./15 1567.5

1001.4

1098.8

1339.8

1489.4

1628.5

1640.8

1762.4

2.225 63 &22.225&./15 63 &22.225.(65 6- 10.&5

*3

*3/

*36

*3(

*30

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2

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#

F#

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#

F#

#


23/55

-2.635 62 1/.-56.235 /2 (1.3(5(3.2-5 3 /3.1(512.05 &( -6.10510.&5 6 1./-5

&22.225 & &./15

&22.225 2 2.225

&20.32 &3&6.-2 &/0.&2 &(02.22 -2&&.12 --3.02 -(/.(2

ONO DE FRECUENCIA

FICOS O7IVAS


24/55

CERRADO

SE/

120.54 120.425

120.78 120.665

121.02 120.905

121.26 121.145121.50 121.385

121.74 121.625

121.98 121.865

/ ingreso

2128.0

1522.9

1795.0

s s#en% e"

LS#

*&

*-

*3


25/55

1293.6

1276.9

1213.5

1589.3

1699.2

2018.2

1048.1

1183.2

1073.3

1232.7

0.01587302 63 1.00000000 1160.4

0.04761905 62 0.98412698 1718.0

0.20634921 60 0.95238095 1575.2

0.46031746 50 0.79365079 1456.0

0.73015873 34 0.53968254 1454.4

0.90476190 17 0.26984127 1702.2

0.98412698 6 0.09523810 1492.4

1.00000000 1 0.01587302 1336.2

1807.9

1320.4

970.3

1994.1

1081.4

1365.3

1907.2

1350.0

2053.1

1247.5

1351.0

1645.7

1225.3

877.6

1610.4

1832.4

1249.4

1056.5

*

*/

*6

*(

*0

*1*

&2

*&&

#

F#

#

*&-

*&3

*&

*&/

*&6

*&(*

&0

*&1

*-2

*-&

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*-

*-/*

-6

*-(

*-0

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*3&

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*33*

3

*3/

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*30

*31


26/55

1817.1

1398.9

1024.2

1835.2

1880.5

1828.8

1517.0

504.6

@CLASE 1207.3

1648.7

1 121.21 121.55 1432.6

2 121.56 121.90 1461.7

3 121.91 122.25 934.3

4 122.26 122.60 1220.0

5 122.61 122.95 1525.9

6 122.96 123.30 2064.5

7 123.31 123.65 1567.5

8 123.66 124.00 1001.4

1098.8

1339.8

1489.4

1628.5

1640.8

1762.4

0.0158730 63 1.0000000

0.0476190 62 0.9841270

0.2063492 60 0.9523810

0.4603175 50 0.7936508

*2

*&

*-

s s#en% e"ea!a! "s

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#

F#

#


27/55

0.7301587 34 0.5396825

0.9047619 17 0.2698413

0.9841270 6 0.0952381

1.0000000 1 0.0158730

PREUNTA 1

0.25396825

231.80 199.70

0.20634921

0.21879836

0.20634921

0.42514757

0.07936508

231.80 696.00

0.23830067

#

F#

#

25

/5

&25

&/5

-25

-/5

325

ISTO)R

-/5

325

POLIONO DE FRE

-'/& 5


28/55

PREUNTA 3

0.15873016

231.80 200.20

0.79365079

0.13709136

0.93074216

300.62 6-2./2 0/-.2 &20.32 &3&6.-2 &/0.&225

/5

&25

&/5

-25

13'2(5


29/55

ingreso ingreso ingreso ingreso ingreso ingreso

X X X X X X

-&-0.2 &&03.- &336.- &-(./ &310.1 &6&.(

&/--.1 &2(3.3 &02(.1 &3/&.2 &2-.- 13.3

&(1/.2 &-3-.( &3-2. &6/.( &03/.- &--2.2

&-13.6 &&62. 1(2.3 &--/.3 &002./ &/-/.1

&-(6.1 &(&0.2 &11.& 0((.6 &0-0.0 -26./

&-&3./ &/(/.- &20&. &6&2. &/&(.2 &/6(./

&/01.3 &/6.2 &36/.3 &03-. /2.6 &22&.

&611.- &/. &12(.- &-1. &-2(.3 &210.0

-2&0.- &(2-.- &3/2.2 &2/6./ &60.( &331.0

&20.& &1-. -2/3.& &0&(.& &3-.6 &01.

V@a* ; -&-0.22 V@#n ; /2.62


30/55


31/55


32/55


33/55


34/55


35/55

MA

UENCIA


36/55

&(02.22 -2&&.12 --3.02 -(/.(2


37/55

MEDIDAS DE TENDENCIA CENTRAL

A.? DATOS NO ARUPADOSE e@ :

XX -&-0.2 &/--.1 &(1/.2 &-13.6 &-(6.1 &-&3./

Y

a MEDIA ARITMETICA

POR FORMULA:&/6.02

CON FUNCION DEL EXCEL:&/6.02

PROPIEDADES::DIV;0

/.22

%) OTROS PROMEDIOS:

#) MEDIA CUADRATICA.

MEDIA CU+ICA.

###) MEDIA +ICUADRATICA.

*&

*-

*3

*

*/

*6

;Z_)/

;

;

;

_;

_;

_;

=?@

=?@

_;QZ

) )^ /

_;

_;

(_\)

_;Q ]( Z

^ )

_;


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#


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@CLASE

/ 8 # 8 #X#LI # LS #

& /2.6 (36.2 6-2./ & 6-2./

- (36./2 160.32 0/-. - &(2.0

3 160.2 &-22.-2 &20.3 &2 &203.2

&-22.32 &3-.&2 &3&6.- &6 -&2/1.-

/ &3-.-2 &66.22 &/0.& &( -63&(.(

6 &66.&2 &01/.12 &(02.2 && &1/02.2

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63 1--0./

&6(.&- Me%#a a!#@e#ca %e %as a!ua%

&/6.-6 Me%#a a!#@e#ca %e %as n a!u

##) MEDIANA EN DATOS ARUPADOS.

@CLASE

/ 8 #LI # LS #

& /2.6 (36.2 6-2./ & &- (36./2 160.32 0/-. - 33 160.2 &-22.-2 &20.3 &2 &3 &-22.32 &3-.&2 &3&6.- &6 -1/ &3-.-2 &66.22 &/0.& &( 6

F#

;;

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25

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25

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125

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6 &66.&2 &01/.12 &(02.2 && /(( &016.22 -&-(.02 -2&&.1 / 6-

0 -&-(.12 -3/1.(2 --3.0 & 63

63

&66.-/

###) MODA EN DATOS ARUPADOS.

@CLASE

/ 8 #LI # LS #

& /2.6 (36.2 6-2./ &- (36./2 160.32 0/-. -3 160.2 &-22.-2 &20.3 &2

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0 -&-(.12 -3/1.(2 --3.0 &

63

&6/.-0

CUARTIL DE DATOS NO ARUPADOS

C(!&!(- !"# &(-'*!# ) !"# *$-#"# ) !"# *&)()($"# $'()"#

1222.65

1456.00

1700.70

2128.00

C(!&!(- !"# p-$'*!# 33 45 78 95 ) !"# *$-#"# ) !"# *&)()($"# $'()"#

1284.58

1395.54

1733.982015.79

CUARTIL DE DATOS ARUPADOS

@CLASE

X 8 # 9 # F #LI # LS #

1 504.6 736.40 620.5 1 0.01587302 1

2 736.50 968.30 852.4 2 0.03174603 3

3 968.40 1200.20 1084.3 10 0.15873016 13

_

;

25

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K _;K _;K _;K _;

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4 1200.30 1432.10 1316.2 16 0.25396825 29

5 1432.20 1664.00 1548.1 17 0.26984127 46

6 1664.10 1895.90 1780.0 11 0.17460317 57

7 1896.00 2127.80 2011.9 5 0.07936508 62

8 2127.90 2359.70 2243.8 1 0.01587302 63

63 &

K___________ ;K___________ ;K___________ ;K___________ ;


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&/01.3 &611.- 12518.4

0.0

X&-&3./&-(6.1&-13.6&/--.1&/01.3&611.-&(1/.2-&-0.2

X Y&2(3.3 /&&62. 3

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ingreso

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2128.01522.9

1795.0

&/2.263 1293.6&2.0/0 1276.9

1-.3/- 1213.56&.66 1589.3

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1832.4

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NO DE FRECUENCIA

GRAFICOS OJIVAS


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# F # #

0.0158730 63 1.0000000

0.0476190 62 0.9841270

0.2063492 60 0.9523810

=)*)(# )p*"$ )

+=

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0.4603175 50 0.7936508

0.7301587 34 0.5396825

0.9047619 17 0.2698413

0.9841270 6 0.0952381

1.0000000 1 0.0158730


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'$)$*( $'-!( #"!" # &*($ (!( )*( (-*''*( & # (!&!(


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MEDIDAS DE DISPERSION

&.? DATOS NO ARUPADOS.

A.? VARIANA

Ee@". &

X -&-0.2 &/--.1 &(1/.2 &-13.6 &-(6.1

317194.24 1755.61 52992.04 73549.44 82886.41

Y 2328.0 1722.9 1995.0 1493.6 1476.9 4256.0 3045.8 3590.0 2587.2 2553.8

n ; 8

03026.63 POR DEFINICION03026.63 FUNCION DEL EXCEL1/((1.2&1/((1.2&

+.? DESVIACION ESTANDAR.

-01.1 POR DEFINICION-01.1321.0 FUNCION DEL EXCEL321.0

Ee@". 3

C@!ba! "as !#e%a%es %e" "a


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DATOS ARUPADOS.

A.? VARIANA

@CLASE

X# > X#>LI# LS#

340 0.00

2.22

2.22

+.? DESVIACION ESTANDAR.

2.22

2.222.22

C.? DESVIACION ESTANDAR APROXIMADO.

2.22

ue !cenae %e c#u%a%ans #enen c@ #n!es @a*#@ #ua" a "a

p @ 50.95

;

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S ;

H3S ; ?3S ;

S ;

;

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n

XXf

S

m

1k

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kk

2

=

=


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&-&3./ &/01.3 &611.-

123411.69 600.25 18063.36 6(2/3.2

1413.5 1789.3 1899.2

2427.0 3178.6 3398.4

;VAR.PN-:N3&)

;VARPN-:N3&)

;DESVEST.PN-:N3&)

&-&3./ &/01.3 &611.-

&/&3./ &001.3 &111.---(.2 3&(0.6 3310.

*6

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)^

^


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0.00

2.222.22

* J(d)d ^

Estadistica y Probabilidad 2016

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