Frec, Interv, graf, Medidas de tendencia central y dispersion.xls

Intervalos: Intervalos:Rango de 810- 888 Rango de 810- 888R= Xn-X1 R= Xn-X1R= 889-810 R= 889-810R= 79 R= 79k=10 k=1010 interva78/10= 7.8= 7 10 intervalos 79/10= 7.9= 7Intervalos: Intervalos:809-816 809-816817-824 817-824825-832 825-832833-840 833-840841-848 841-848849-856 849-856857-864 857-864865-872 865-872873-880 873-880881-888 881-888

889-896

DATO PORCENTAJE

810 2 2 0.0417 0.0417 4%815 2 4 0.0417 0.0833 4%816 1 5 0.0208 0.1042 2%830 3 8 0.0625 0.1667 6%831 1 9 0.0208 0.1875 2%833 2 11 0.0417 0.2292 4%835 3 14 0.0625 0.2917 6%836 2 16 0.0417 0.3333 4%837 2 18 0.0417 0.3750 4%839 1 19 0.0208 0.3958 2%840 3 22 0.0625 0.4583 6%844 3 25 0.0625 0.5208 6%849 2 27 0.0417 0.5625 4%853 2 29 0.0417 0.6042 4%856 2 31 0.0417 0.6458 4%858 2 33 0.0417 0.6875 4%860 1 34 0.0208 0.7083 2%869 1 35 0.0208 0.7292 2%873 2 37 0.0417 0.7708 4%881 2 39 0.0417 0.8125 4%

FRECUENCIA ABSOLUTA

FRECUENCIA ABSOLUTA

ACUMULADA

FRECUENCIA RELATIVA

FRECUANCIA RELATIVA

ACUMULADA

4%; 810 4%; 8152%; 816

6%; 8302%; 831

4%; 833

6%; 835

4%; 836

4%; 837

2%; 8396%; 840

6%; 8444%; 8494%; 8534%; 856

4%; 858

2%; 860

2%; 869

4%; 873

4%; 8812%; 883

4%; 8848%; 888

4%; 889

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

4.5

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

883 1 40 0.0208 0.8333 2%884 2 42 0.0417 0.8750 4%888 4 46 0.0833 0.9583 8%889 2 48 0.0417 1.0000 4%

TOTAL DE DATOS (N) 48

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

4%; 810 4%; 8152%; 816

6%; 8302%; 831

4%; 833

6%; 835

4%; 836

4%; 837

2%; 8396%; 840

6%; 8444%; 8494%; 8534%; 856

4%; 858

2%; 860

2%; 869

4%; 873

4%; 8812%; 883

4%; 8848%; 888

4%; 889

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

4.5

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

4.5

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

810 815 816 830 831 833 835 836 837 839 840 844 849 853 856 858 860 869 873 881 883 884 888 8890

0.5

1

1.5

2

2.5

3

3.5

4

Grupo de Edad Frecuencia

17-26 759 57 o más 27

27-36 1202 47-56 20637-46 654 37-46 65447-56 206 17-26 759

57 o más 27 27-36 12022848

17-2627%

27-3642%

37-4623%

47-567%

57 o más1%

17-26 27-36 37-46 47-56 57 o más

759

1202

654

20627

17-26 27-36 37-46 47-56 57 o más20

220

420

620

820

1020

1220

759

1202

654

206

27

17-2627%

27-3642%

37-4623%

47-567%

57 o más1%

57 o más 47-56 37-46 17-26 27-36

27206

654 759

1202

Carreras FrecuenciaAdministración de empresas turísticas (Adm Emp Tur) 31Biotecnología (Bio) 586Desarrollo comunitario (Des Com) 25Desarrollo de software (Des Soft) 243Energías renovables (Ene Renov) 321Gestión y administración de PYME (Ges y Adm PYME) 66Logística y transporte (Log y Transp) 220Matemáticas (Mate) 44Mercadotecnia internacional (Merc Int) 47Seguridad pública (Seg Pub) 32Técnico Superior Universitario Paramédica (TSU Param) 285Tecnología ambiental (Tec Amb) 528Telemática (Telem) 404

2832

31

586

25

243321

66

220

44 47 32

285

528

404

Adm Emp Tur Bio Des Com Des Soft Ene Renov Ges y Adm PYME

Log y Transp Mate Merc Int Seg Pub TSU Param Tec Amb

Telem

Adm

Em

p Tu

r

Bio

Des C

om

Des S

oft

Ene

Reno

v

Ges y

Adm

PYM

E

Log

y Tr

ansp

Mat

e

Mer

c Int

Seg

Pub

TSU

Para

m

Tec A

mb

Tele

m

31

586

25

243

321

66

220

44 47 32

285

528

404

Adm

Em

p Tu

r

Bio

Des C

om

Des S

oft

Ene

Reno

v

Ges y

Adm

PYM

E

Log

y Tr

ansp

Mat

e

Mer

c Int

Seg

Pub

TSU

Para

m

Tec A

mb

Tele

m

31

586

25

243

321

66

220

44 47 32

285

528

404

57 o más 47-56 37-46 17-26 27-36

27206

654 759

1202

Adm Emp Tur 31 Des ComBio 586 Adm Emp TurDes Com 25 Seg PubDes Soft 243 MateEne Renov 321 Merc IntGes y Adm PYME 66 Ges y Adm PYMELog y Transp 220 Log y TranspMate 44 Des SoftMerc Int 47 TSU ParamSeg Pub 32 Ene RenovTSU Param 285 TelemTec Amb 528 Tec AmbTelem 404 Bio

Adm Emp Tur1%

Bio21%

Des Com1%

Des Soft9%

Ene Renov11%

Ges y Adm PYME2%

Log y Transp8%

Mate2%

Merc Int2%

Seg Pub1%

TSU Param10%

Tec Amb19%

Telem14%

Adm Emp Tur1%

Bio21%

Des Com1%

Des Soft9%

Ene Renov11%

Ges y Adm PYME2%

Log y Transp8%

Mate2%

Merc Int2%

Seg Pub1%

TSU Param10%

Tec Amb19%

Telem14%

253132444766

220243285321404528586

Adm Emp Tur1%

Bio21%

Des Com1%

Des Soft9%

Ene Renov11%

Ges y Adm PYME2%

Log y Transp8%

Mate2%

Merc Int2%

Seg Pub1%

TSU Param10%

Tec Amb19%

Telem14%

Des C

om

Adm

Em

p Tu

r

Seg

Pub

Mat

e

Mer

c Int

Ges y

Adm

PYM

E

Log

y Tr

ansp

Des S

oft

TSU

Para

m

Ene

Reno

v

Tele

m

Tec A

mb

Bio

25 31 32 44 47 66

220 243285

321

404

528586

Des Com

Adm Emp Tu

r

Seg P

ubMate

Merc In

t

Ges y A

dm PYME

Log y

Tran

sp

Des So

ft

TSU Para

m

Ene R

enov

Telem

Tec A

mb Bio0

100

200

300

400

500

600

Column S

Adm Emp Tur1%

Bio21%

Des Com1%

Des Soft9%

Ene Renov11%

Ges y Adm PYME2%

Log y Transp8%

Mate2%

Merc Int2%

Seg Pub1%

TSU Param10%

Tec Amb19%

Telem14%

DATO PORCENTAJE

810 2 2 0.0417 0.0417 4%815 2 4 0.0417 0.0833 4%

816 1 5 0.0208 0.1042 2%

830 3 8 0.0625 0.1667 6%831 1 9 0.0208 0.1875 2%833 2 11 0.0417 0.2292 4%

835 3 14 0.0625 0.2917 6%

836 2 16 0.0417 0.3333 4%

837 2 18 0.0417 0.3750 4%

839 1 19 0.0208 0.3958 2%

840 3 22 0.0625 0.4583 6%

844 3 25 0.0625 0.5208 6%

849 2 27 0.0417 0.5625 4%

853 2 29 0.0417 0.6042 4%856 2 31 0.0417 0.6458 4%

858 2 33 0.0417 0.6875 4%

860 1 34 0.0208 0.7083 2%869 1 35 0.0208 0.7292 2%873 2 37 0.0417 0.7708 4%

881 2 39 0.0417 0.8125 4%

883 1 40 0.0208 0.8333 2%

884 2 42 0.0417 0.8750 4%

888 4 46 0.0833 0.9583 8%889 2 48 0.0417 1.0000 4%

TOTAL DE DATOS (N) 48

(^)

^2

(^)

FRECUENCIA ABSOLUTA

FRECUENCIA ABSOLUTA

ACUMULADA

FRECUENCIA RELATIVA

FRECUANCIA RELATIVA

ACUMULADA

Re =

Re = 889 - 810

Re = 79

δ

δ =

máx xi - min xi

Datos agrupados en frecuencias

X =810 + 815 + 816 +

n

801*2

X = = (810*2)+(815*2)+(816*1)+(830*3)+(831*1)+(833*2)+(835*3)+(836*2)+(837*2)+(839*1)+(840*3)+(844*3)+(849*2)+(853*2)+(856*2)+(858*2)+(860*1)+(869*1)+(873*2)+(881*2)+(883*1)+(884*2)+(888*4)+(889*2)

n 48

= 1620 + 1630 + 816 +48

= 4084548

= 850.9375

= 48 = 242

µ= = 810+815+816+830+831+833+835+836+837+839+840+844+849+853+856+858+860+869+873+881+883+884+888+889

N 48

= 2040948

µ= = 425.188

= + (815- 425.1875)² + (816- 425.1875)² +

48

(835- 425.1875)² + (836- 425.1875)² + (837- 425.1875)² +48

(849- 425.1875)² + (853- 425.1875)² + (856- 425.1875)² +48

(873- 425.1875)² + (881- 425.1875)² + (883- 425.1875)² +

48

(810- 425.1875)²

∑_(i=1)^n▒xifi

∑_(i=1)^n▒xifi

∑_(i=1)^n▒xifi

= 148080.66015625 + 151953.7851563 + 152734.4101563 +

48

167946.28515625 + 168766.9101563 + 169589.5351563 +

48

179617.03515625 + 183023.5351563 + 185599.4101563 +

48

200536.03515625 + 207765.0351563 + 209592.2851563 +

48

= 4351971.4687548

= 90666.072265625

=

= 301.1080741

√90666.07227

830 + 831 + 833 + 835 + 836 +

(810*2)+(815*2)+(816*1)+(830*3)+(831*1)+(833*2)+(835*3)+(836*2)+(837*2)+(839*1)+(840*3)+(844*3)+(849*2)+(853*2)+(856*2)+(858*2)+(860*1)+(869*1)+(873*2)+(881*2)+(883*1)+(884*2)+(888*4)+(889*2)

48

2490 + 831 + 1666 + 2505 + 1672 +48

810+815+816+830+831+833+835+836+837+839+840+844+849+853+856+858+860+869+873+881+883+884+888+889

48

(830- 425.1875)² + (831- 425.1875)² + (833- 425.1875)² +

48

(839- 425.1875)² + (840- 425.1875)² + (844- 425.1875)² +48

(858- 425.1875)² + (860- 425.1875)² + (869- 425.1875)² +48

(884- 425.1875)² + (888- 425.1875)² + (889- 425.1875)²

48

163873.1601563 + 164683.7851563 + 166311.0351563 + 947636.8359375

48

171240.7851563 + 172069.4101563 + 175403.9101563 + 1025016.835938

48

187326.6601563 + 189061.9101563 + 196969.5351563 + 1121598.085938

48

210508.9101563 + 214195.4101563 + 215122.0351563 1257719.710938

48

4351971.46875

837 + 839 + 840 + 844 + 849 +

(810*2)+(815*2)+(816*1)+(830*3)+(831*1)+(833*2)+(835*3)+(836*2)+(837*2)+(839*1)+(840*3)+(844*3)+(849*2)+(853*2)+(856*2)+(858*2)+(860*1)+(869*1)+(873*2)+(881*2)+(883*1)+(884*2)+(888*4)+(889*2)

48

1674 + 839 + 2520 + 2532 + 1698 +48

853 + 856 + 858 + 860 + 869 +

1706 + 1712 + 1716 + 860 + 869 +48

873 + 881 + 883 + 884 + 888 +

1746 + 1762 + 883 + 1768 + 3552 +48

889

177848

122

172 INTERVALO

182 1 121-131192 2 132-142192 3 143-153

182 4 154-164187 5 165-175142 6 176-186152 7 187-197195 8 198-208227 9 209-219

228 10 220-230

217 TOTAL DE DATOS 20216

225229

221211 122 142203 203 205205

·         Medidas de tendencia central y dispersión por intervalos para el problema 2.

NUMERO DE INTERVALO Ni

LI LS MC Mc- x

121 131 1 1 126 -68.2 4651.24 4651.24132 142 1 2 137 -57.2 3271.84 3271.84143 153 1 3 148 -46.2 2134.44 2134.44

154 164 0 3 159 -35.2 1239.04 0165 175 1 4 170 -24.2 585.64 585.64176 186 2 6 181 -13.2 174.24 348.48187 197 4 10 192 -2.2 4.84 19.36198 208 2 12 203 8.8 77.44 154.88209 219 3 15 214 19.8 392.04 1176.12

220 230 5 20 225 30.8 948.64 4743.2

TOTAL DE DATOS 20 17085.2

152 172 182 182 187 192 192 195211 216 217 221 225 227 228 229

FRECUENCIA ABSOLUTA fi

FRECUENCIA Acumulada Fi (Mc- x)² (Mc- x)² * fi

intervalo

229 - 122 = 107107/10 = 10.7

intervalo = 10MEDIA

X = = (126X1) + (137X1) + (148X + (159X+ (170X1)

n 20

= 126 + 137 + 148 + 0 + 17020

= 388420

X = 194.2

MEDIANA

N = 20 = 102 2

Ni = 7Li = 187Fi = 6fi = 4ai = 10

Me = 187 + 10 - 6 (10)4

Me = 187 + 4 (10)4

Me = 187 + 1 (10)

Me = 187 + 10

∑_(i=1)^n▒Mcifi

Me = 197

MODA

Ni = 10Li = 220fi = 5

fi-1 = 3fi+1 = 0

ai = 10

Mo = 220 + 5 - 3 (10)(5-3) + (5-0)

Mo = 220 + 2 (10)

2 + 5

Mo = 220 + 2 (10)7

Mo = 220 + 0.285714 (10)

Mo = 220 + 2.8571

Mo = 222.8571

RECORRIDO

Re =

Re = 229 - 122

Re = 107

VARIANZA

µ= = (126X1) + (137X1) + (148X + (159X+ (170X1)20

N = 126 + 137 + 148 + 0 + 170

máx xi - min xi

∑_(i=1)^n▒xifi

20

= 388420

µ = 194.2

δ² = = 17085.2

N 20

854.26

DESVIACION

δ == 854.26

N

δ = = 29.228

∑_(i=1)^n▒〖 fi(Mc -x)²〗

∑_(i=1)^n▒〖 fi(Mc -x)²〗

+ (181X2) + (192X4) + (203X2) + (214X3) + (225X5)

20

+ 362 + 768 + 406 + 642 + 112520

+ (181X2) + (192X4) + (203X2) + (214X3) + (225X5)20

+ 362 + 768 + 406 + 642 + 1125

20

Medias de tendencia central y dispersión por frecuencias simples, para el problema 1.

DATOS FRECUENCIAS18.04 118.71 1

X =18.92 1 = 18.04 +

19.25 1 n-1 20-1

19.29 1 = 421.6919.44 1 20-119.77 1

20.17 1 = 22.19420.33 120.55 1

20.72 1 Me = 20.55 +21.12 1 221.41 1

21.77 1 Me = 41.2722.11 1 222.43 1

22.85 1 Me = 20.63523.00 123.71 1

28.1 1 MO = NO EXISTE MODA

TOTAL DE DATOS 20

Re =

Re = 28.1-18.04

Re = 10.1

δ² =n-1

X =

máx xi -

∑_(i=1)^n▒xifi

∑_(i=1)^n▒〖 fi(Xi-µ)²〗

∑_(i=1)^n▒xifi

X = =n-1

=

=

δ = =

=

∑_(i=1)^n▒xifi

Medias de tendencia central y dispersión por frecuencias simples, para el problema 1.

18.71 + 18.92 + 19.25 + 19.29 + 19.44 + 19.77

20-1

20.722

NO EXISTE MODA

28.1-18.04

máx xi - min xi

18.04 + 18.71 + 18.92 + 19.25 + 19.29 + 19.44

20-1

421.6920-1

22.19

+ + + + +20-1

+ + + + +20-1

17.2225 + 12.1104 + 10.6929 + 8.6436 + 8.41 + 7.562520-1

2.1609 + 1.1449 + 0.6084 + 0.1764 + 0.0064 + 0.057620-1

123.2120-1

6.48

6.48

2.55

(18.04-22.19)² (18.71-22.19)² (18.92-22.19)² (19.25-22.19)² (19.29-22.19)² (19.44-22.19)²

(20.72-22.19)² (21.12-22.19)² (21.41-22.19)² (21.77-22.19)² (22.11-22.19)² (22.43-22.19)²

+ 20.17 + 20.33 + 20.55 + 20.72 + 21.12 +

20-1

+ 19.77 + 20.17 + 20.33 + 20.55 + 20.72 +

20-1

+ + + + +20-1

+ + + +20-1

+ 5.8564 + 4.0804 + 3.4596 + 2.6896 +20-1

+ 0.4356 + 0.66 + 2.3104 + 34.928120-1

(19.77-22.19)² (20.17-22.19)² (20.33-22.19)² (20.55-22.19)²

(22.85-22.19)² (23.00-22.19)² (23.71-22.19)² (28.1-22.19)²

21.41 + 21.77 + 22.11 + 22.43 + 22.85 + 23.00

20-1

21.12 + 21.41 + 21.77 + 22.11 + 22.43 + 22.85

20-1

+ 23.71 + 28.1

20-1

+ 23.00 + 23.71 + 28.1

20-1

Grupo de Edad Frecuencia17-26 75927-36 120237-46 65447-56 206

57 o más 2757-66

Carreras FrecuenciaAdministración de empresas turísticas (Adm Emp Tur) 31Biotecnología (Bio) 586Desarrollo comunitario (Des Com) 25Desarrollo de software (Des Soft) 243Energías renovables (Ene Renov) 321Gestión y administración de PYME (Ges y Adm PYME) 66Logística y transporte (Log y Transp) 220Matemáticas (Mate) 44Mercadotecnia internacional (Merc Int) 47Seguridad pública (Seg Pub) 32Técnico Superior Universitario Paramédica (TSU Param) 285Tecnología ambiental (Tec Amb) 528Telemática (Telem) 404

20 30 39 45 55 21 31 40 46 65 74 68 82 108 123 154 167 193141 152 157 173 194 204 208 73 97 94 87 120 151 140 21 64 52 3983 24 193 119

N Inter LI LS FREC fi FREC Fi MC20 1 rango = 188 1 19 - 38 8 8 28.521 2 2 39 - 58 8 16 48.524 1 intervalo = 18.8 3 59 - 78 6 22 68.525 1 4 79 - 98 8 30 88.530 1 Amp inter = 10 5 99 - 118 1 31 108.531 1 6 119 - 138 3 34 128.532 1 7 139 - 158 6 40 148.539 2 8 159 - 178 4 44 168.540 1 9 179 - 198 4 48 188.545 1 10 199 - 218 2 50 208.546 152 255 1 MEDIA Re = 208 -64 2 22865 1 388 18868 1 41173 1 70874 1 108.581 1 385.582 1 89183 1 67487 1 75494 2 41795 197 1 4965

108 1119 1 99.3120 1123 1140 1 Varianza = 3252.40816327141 1151 1 DESVIACION = 57.0298883329152 1154 1157 1165 1167 1172 1173 1

181 1193 2194 1204 1208 1

50

181 95 81 64 25 3252 165 172 94

MC Mc- x (Mc- x)² (Mc- x)² * fi N/2 = 25 ME = 99 + 2528.5 -70.8 5012.64 40101.12 Ni = 5 3148.5 -50.8 2580.64 20645.12 Li = 9968.5 -30.8 948.64 5691.84 Fi = 30 = 97.38709788.5 -10.8 116.64 933.12 fi = 31

108.5 9.2 84.64 84.64 ai = 10128.5 29.2 852.64 2557.92 MO = 19 +148.5 49.2 2420.64 14523.84168.5 69.2 4788.64 19154.56188.5 89.2 7956.64 31826.56 Li = 19 39 79 = 29208.5 109.2 11924.64 23849.28 fi = 8 8 8

fi-1 = 0 8 6159368 fi+1 = 8 6 1 MO = 39 +

20 ai = 10 10 10

= 39

MO = 79 +

= 81.222222

- 30 * 1031

8 - 0 * 108 - 0 + 8 - 8

8 - 8 * 108 - 8 + 8 - 6

8 - 6 * 108 - 6 + 8 - 1

20 30 39 45 55 21 31 40 46 65 74 68 82 108 123 154 167 193 181 95 81 64 25 32141 152 157 173 194 204 208 73 97 94 87 120 151 140 21 64 52 39 52 165 172 9483 24 193 119

MedianaMayor = 208 N Inter LI LS FREC fi FREC Fi MC Mc- x (Mc- x)² (Mc- x)² * fi N/2 = 25 ME = 85 + 25 - 24 * 18

20 20 1 Menor = 20 1 19 - 29 5 5 24 -75.02 5628.0004 28140.002 521 21 2 Rango = 188 2 30 - 40 6 11 35 -64.02 4098.5604 24591.362 Li = 8521 24 1 Int Calculado = 10 3 41 - 51 2 13 46 -53.02 2811.1204 5622.2408 Fi = 24 = 88.624 25 1 Int Sug = 10 4 52 - 62 3 16 57 -42.02 1765.6804 5297.0412 fi = 525 30 1 Amp inter = 18 5 63 - 73 5 21 68 -31.02 962.2404 4811.202 ai = 18 Moda30 31 1 Dato mayor = 208 6 74 - 84 3 24 79 -20.02 400.8004 1202.4012 MO = 118 + 3 - 1 * 1831 32 1 Total Datos = 50 7 85 - 95 5 29 90 -9.02 81.3604 406.802 3 - 1 + 3 - 032 39 2 8 96 - 106 1 30 101 1.98 3.9204 3.920439 40 1 MEDIA 9 107 - 117 1 31 112 12.98 168.4804 168.4804 Li = 118 30 52 = 125.239 45 1 120 10 118 - 128 3 34 123 23.98 575.0404 1725.1212 fi = 3 6 340 46 1 210 11 129 - 139 0 34 134 34.98 1223.6004 0 fi-1 = 1 5 245 52 2 92 12 140 - 150 2 36 145 45.98 2114.1604 4228.3208 fi+1 = 0 2 5 MO = 30 + 6 - 5 * 1846 55 1 171 13 151 - 161 4 40 156 56.98 3246.7204 12986.882 ai = 18 18 18 6 - 5 + 6 - 252 64 2 340 14 162 - 172 3 43 167 67.98 4621.2804 13863.84152 65 1 237 15 173 - 183 2 45 178 78.98 6237.8404 12475.681 = 33.655 68 1 450 16 184 - 194 3 48 189 89.98 8096.4004 24289.20164 73 1 101 17 195 - 205 1 49 200 100.98 10196.96 10196.9664 74 1 112 18 206 - 216 1 50 211 111.98 12539.52 12539.52 Ni = 7 MO = 52 + 3 - 2 * 1865 81 1 369 19 - 0 0 0 Li = 187 3 - 2 + 3 - 568 82 1 0 20 - 0 0 0 0 Fi = 673 83 1 290 21 - 0 0 0 0 fi = 4 = 3474 87 1 624 22 - 0 0 0 0 ai = 1081 94 2 501 23 - 0 0 0 0 1082 95 1 356 24 - 0 0 0 083 97 1 567 25 - 0 0 0 087 108 1 200 26 - 0 0 0 094 119 1 211 27 - 0 0 0 094 120 1 0 28 - 0 0 0 0 83 8795 123 1 0 29 - 0 0 0 097 140 1 0 30 - 0 0 0 0

108 141 1 0 50 170119 151 1 0 Recorrido 162548.98120 152 1 0 Re = 208 - 20 85123 154 1 0 = 6 6 6140 157 1 0 188 18.8141 165 1 0151 167 1 0 Varianza = 3317.32612245152 172 1 0154 173 1 0 DESVIACION = 57.5962335787157 181 1165 193 2 4951167 194 1172 204 1 99.02173 208 1181193 50193194204208

20 30 39 45 55 21 31 40 46 65 74 68 82 108 123 154 167 193141 152 157 173 194 204 208 73 97 94 87 120 151 140 21 64 52 3983 24 193 119

Mayor = 66 N Inter LI LS FREC fi FREC Fi MC20 20 1 Menor = 17 1 17 - 26 759 759 21.521 21 2 Rango = 49 2 27 - 36 1202 1961 31.521 24 1 Int Calculado = 9.8 3 37 - 46 654 2615 41.524 25 1 Int Sug = 9 4 47 - 56 206 2821 51.525 30 1 Amp inter = 5 5 57 - 66 27 2848 61.530 31 1 Dato mayor = 6631 32 1 Total Datos = 2848 7 - 9 0 4.532 39 2 8 - 9 0 4.539 40 1 MEDIA 9 - 9 0 4.539 45 1 16318.5 10 - 9 0 4.540 46 1 37863 11 - 9 0 4.545 52 2 27141 12 - 9 0 4.546 55 1 10609 13 - 9 0 4.552 64 2 1660.5 14 - 9 0 4.552 65 1 0 15 - 9 0 4.555 68 1 0 16 - 9 0 4.564 73 1 0 17 - 9 0 4.564 74 1 0 18 - 9 0 4.565 81 1 0 19 - 068 82 1 0 20 - 0 073 83 1 0 21 - 0 074 87 1 0 22 - 0 081 94 2 0 23 - 0 082 95 1 0 24 - 0 083 97 1 0 25 - 0 087 108 1 0 26 - 0 094 119 1 0 27 - 0 094 120 1 0 28 - 0 095 123 1 0 29 - 0 097 140 1 0 30 - 0 0

108 141 1 0 2848119 151 1 0 Recorrido120 152 1 0 Re = 66 - 17123 154 1 0140 157 1 0 49 4.9141 165 1 0151 167 1 0 Varianza = 85.2525623266152 172 1 0154 173 1 0 DESVIACION = 9.23323141303

157 181 1165 193 2 93592167 194 1172 204 1 32.86236173 208 1181193 50193194204208

181 95 81 64 25 3252 165 172 94

MedianaMC Mc- x (Mc- x)² (Mc- x)² * fi N/2 = 1424 ME = 1721.5 -11.3623596 129.103214556 97989.3431.5 -1.36235955 1.85602354501 2230.9403 Li = 1741.5 8.637640449 74.6088325338 48794.176 Fi = 759 = 19.76622351.5 18.63764045 347.361641523 71556.498 fi = 120261.5 28.63764045 820.114450511 22143.09 ai = 5 Moda

MO =4.5 -28.3623596 804.423439275 04.5 -28.3623596 804.423439275 04.5 -28.3623596 804.423439275 0 Li = 27 27 47 =4.5 -28.3623596 804.423439275 0 fi = 1202 1202 2064.5 -28.3623596 804.423439275 0 fi-1 = 759 759 6544.5 -28.3623596 804.423439275 0 fi+1 = 654 654 27 MO =4.5 -28.3623596 804.423439275 0 ai = 5 5 54.5 -28.3623596 804.423439275 04.5 -28.3623596 804.423439275 0 =4.5 -28.3623596 804.423439275 04.5 -28.3623596 804.423439275 04.5 -28.3623596 804.423439275 0 Ni = 7 MO =0 0 0 Li = 1870 0 0 Fi = 60 0 0 fi = 4 =0 0 0 ai = 100 0 0 100 0 00 0 00 0 00 0 00 0 0 83 870 0 00 0 0

170242714.04

85= 1202 1202 1202

+ 1424 - 759 * 51202

19.766223

27 + 1202 - 759 * 51202 - 759 + 1202 - 654

29.23511604

Grupo de Edad27 + 1202 - 759 * 5

1202 - 759 + 1202 - 654

29.2351160443996

47 + 206 - 654 * 5206 - 654 + 206 - 27

55.32713755

Grupo de Edad Frecuencia17-26 75927-36 120237-46 65447-56 206

57 o más 2757-66