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Universidad de Guayaquil

Facultad de Ingeniería Química

Carrera: Ingeniería en Sistemasde

Calidad y Emprendimiento

Deber !

Integrantes:

"ania #rtega $ere%ildo&atricia 'ambrano

$art(a "ola )omara Espino*a

+signatura: Si, Sigma-

&aralelo: .F/ Semestre:

0mo

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Ptos.Frec.Acu

m.

% Frec.Abs.

Acum

Frec.Rela

t.

%Relat.

Acum 80-20Ptos.78 4 4 8% 8% 80%Ptos.42 4 8 8% 16% 80%Ptos.84 3 11 6% 22% 80%Ptos.82 3 14 6% 28% 80%Ptos.43 3 17 6% 34% 80%

Ptos.39 3 20 6% 40% 80%Ptos.34 3 23 6% 46% 80%Ptos.85 2 25 4% 50% 80%Ptos.80 2 27 4% 54% 80%Ptos.76 2 29 4% 58% 80%Ptos.49 2 31 4% 62% 80%Ptos.35 2 33 4% 66% 80%Ptos.91 1 34 2% 68% 80%Ptos.87 1 35 2% 70% 80%Ptos.86 1 36 2% 72% 80%Ptos.81 1 37 2% 74% 80%Ptos.

77 1 38 2% 76% 80%Ptos.75 1 39 2% 78% 80%Ptos.73 1 40 2% 80% 80%Ptos.70 1 41 2% 82% 80%Ptos.68 1 42 2% 84% 80%Ptos.48 1 43 2% 86% 80%

Ptos.45 1 44 2% 88% 80%

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Ptos.44 1 45 2% 90% 80%Ptos.41 1 46 2% 92% 80%Ptos.

38 1 47 2% 94% 80%Ptos.31 1 48 2% 96% 80%Ptos.30 1 49 2% 98% 80%Ptos.29 1 50 2% 100% 80%

"#"+1   50100

%

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0

5

10

15

20

25

30

35

40

45

50

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Chart !tle

Frec. Acum.

% Relat. Acum

80-20

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Tabla de frecuencias

#untos sumados

preguntas

$recuencia

absoluta

$recuencia

absoluta

acumulado

$recuencia

relativa

$recuencia

relativa

acumulado

%& 1 1 %,0 %,0

'0 1 % %,0 (,0

'1 1 ' %,0 ),0

'( ' ) ),0 1%,0

'* % + (,0 1),0

'+ 1 & %,0 1+,0

'& ' 1% ),0 %(,0

(1 1 1' %,0 %),0

(% ( 1 +,0 '(,0

(' ' %0 ),0 (0,0

(( 1 %1 %,0 (%,0

(* 1 %% %,0 ((,0

(+ 1 %' %,0 (),0

(& % %* (,0 *0,0

)+ 1 %) %,0 *%,0

0 1 % %,0 *(,0

' 1 %+ %,0 *),0

* 1 %& %,0 *+,0

) % '1 (,0 )%,0

1 '% %,0 )(,0

+ ( ') +,0 %,0

+0 % '+ (,0 ),0

+1 1 '& %,0 +,0

+% ' (% ),0 +(,0

+( ' (* ),0 &0,0

+* % ( (,0 &(,0

+) 1 (+ %,0 &),0

+ 1 (& %,0 &+,0

&1 1 *0 %,0 100,0

Total *0 100,0

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0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

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Histogramas

Datos

" 50

m!" 29

ma# 91

Ra"$o 62

7

& 8'857

Clase ( !") ( su* m! "! +! , F!1 29 37'86 33   8   8 0'16 0'16

2 37'857 46'71 42   14   22 0'28 0'44

3 46'714 55'57 51   3   25 0'06 0'5

4 55'571 64'43 60   0   25 0 0'5

5 64'429 73'29 69   3   28 0'06 0'56

6 73'286 82'14 78   14   42 0'28 0'84

7 82'143 91'00 87   8   50 0'16 1

0

0.05

0.1

0.15

0.2

0.25

0.3

2istograma

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  iagrama escalonado

numero

Frecuencia

absolutaacum

veces

0 0 0

1 1   1

2 %   1

3 '   1

4 )   1

5 +   16 &   1

7 1%   1

8 1'   1

9 1   1

10 %0   1

11 %1   1

12 %%   1

13 %'   1

14 %*   1

15 %)   116 %   1

17 %+   1

18 %&   1

19 '1   1

20 '%   1

21 ')   1

22 '+   1

23 '&   1

24 (%   1

25 (*   126 (   1

27 (+   1

28 (&   1

29 *0   1

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 290

10

20

30

40

50

60

Diagrama escalonado

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  iagrama de Barras

Puntos sumadospreguntas

Frecuenciaabsoluta

%& 1

'0 1

'1 1

'( '

'* %

'+ 1

'& '

(1 1

(% (

(' '

(( 1

(* 1

(+ 1

(& %

)+ 1

0 1

' 1

* 1

) %

1

+ (

+0 %

+1 1

+% '

+( '

+* %

+) 1

+ 1

&11

Total *0

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29 30 31 34 35 38 39 41 42 43 44 45 48 49 68 70 73 75 76 77 78 80 81 82 84 85 86 87 910

1

1

2

2

3

3

4

4

5

Diagramas de barra

Frecuencia

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  iagrama de Sectores

Puntos sumadospreguntas

Frecuenciaabsoluta

%& 1

'0 1

'1 1

'( '

'* %

'+ 1

'& '

(1 1(% (

(' '

(( 1

(* 1

(+ 1

(& %

)+ 1

0 1

' 1

* 1) %

1

+ (

+0 %

+1 1

+% '

+( '

+* %

+) 1

+ 1

&1 1

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2%2%2%6%

4%2%

6%

2%

8%

6%

2%2%2%4%2%2%2%2%4%

2%

8%

4%

2%

6%

6%

4%  2%2%2%

Diagrama de sectores

29 30 31 34 35 38 39 41 42 43 44 45 48 49 68

70 73 75 76 77 78 80 81 82 84 85 86 87 91

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Media, Mediana y Moda

Datos78 78 82   85 81 86 80 73 84 7868 84 75   78 76 76 82 85 91 8070 87 77   82 84 48 49 39 39 4335 42 34   44 49 34 30 43 31 3441 42 45   42 35 38 39 42 43 29

#untos sumadospreguntas

$recuenciaabsoluta

%& 1

'0 1

'1 1

'( '

'* %

'+ 1

'& '

(1 1

(% (

(' '

(( 1

(* 1

(+ 1

(& %

)+ 1

0 1

' 1

* 1

) %

1

+ (

+0 %

+1 1

+% '

+( '

+* %

+) 1

+ 1

&1 1

Total *0

$edia:   59'80

$ediana:   58'50$oda:   78

$ediana:   "1/2 501/2

"1/2 512

"1/2 25.5

$ediana:4968/

2 58.50