pb complexa stadiu 1

8/18/2019 Pb Complexa Stadiu 1

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Problemă complexă din capitolele de Seriide distribuţie şi Sondaj

Managerul unui lanţ de magazine intentionează să introducă un nou sistem de facturarcumpără prin credit. Sistemul ar e cient daca rata medie lunară ar mai mare de 17aceasta el a dispus ca departamentul Financiar să-i ofere informaţii pe aza cărora să ia


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pentru clienţii careeuro/client. Pentrucea mai una decizie.


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Accounts (euro) Sum - Accounts (euro) Calcule pentru relatia250 0-60 488.38 xmax-xmin= 366.8

8 .0! 60-"20 3 3 .46 log"0 #in 400= 2.6328.0" "20-"80 "8465.2 "$3.322%log"0(400)= !.6

5. 3 "80-240 2! !3.5 & = 38.02"".82 240-300 " 44.2

244.2" 300-360 5438."8253.46 360-380 34.28"8 Total Result 76401.2

55.4""3!.08200.48

2442"6.26

"62.4240 Accounts (euro)

"6!.65!4.3 'ean "!".003

2!8.33 Stan#ar# rror 3.226!6"5!.2! 'e#ian "8"32.4! 'o#e " 8"38.08 Stan#ar# e*iation 64.53!2"80.8" Sample +ariance 4"65.3""86.3 ,urtosis 0."086"

258 S e ness -0.068"6"2".32 /ange 366. !

35.65 'inimum 3."!"8!.! 'aximum 36!.!80324.8 Sum 640".2

28".53 Count 400

2!3 argest("00) 233. 6"!8.! Smallest("00) "54.33" 6. 2"56.0!2"8.383"2.62

260205.5!

"6""54

3."!"46.!8

233.65"8228.2!"88.6"80.!!"!"."6264.55208.35

235.4"68."

Accounts(euro)


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" 82"0.55" .48" ".5!220.44

34."3"86."5

"80240. 4"43.32"56.63

5!.!!2 0

2"6.5"!.0"

20 .05224.4

"5".452 3.33

364.3208.6"224.!

"86.56255.04"!".!8206.22

2 8"!0.56

".5!"."2

233. 6

"!"68.""4". 3

".3"6".!5

!4.24"3".5"83.42"08.04204.35228.6"2! .42

"4".2458.8!"53.28"8".3!"42."2" 0.!4" 2.53

48.28"28.

" 3.52


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220."4"5!.4624".66

2"42!5.68248.3!"!3.58

2!0248.26"83.!!

45.!362.!3

282"!6

" !.54""!."

2"6.5!2.54"!2

204.5230024!.25

"85"265

"26.!"255

206.2"24 .54232.58"43.05

2!02!56."6

"5 . 42!3.06

63.6"300

""3.200. 420!.!3

"80.2!!.4

230."64.362"5.!"

"83243.53

"!8"60.06234."2"20.36324.44


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225. 88!.0!

20".6525".!6236.0""60."5" ".!!

230."4225.4!23".!!

3"0205.68200.85

" ".8"25.833"4.25

3"0224.4!"!3. 3

" 8. 223".25"!6."8"62.2!

2422 .!3224.!8235.45

6 .82235.4"243.!8"! .0

330"24."4246.04" 4.!""28.43286.5"222.!5"05.2820 ."6

.48""6.2202.5"

"4!.33246.658".54

" 8.38"80. !

!".32" 8

253.642!

"82."2


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""".4"6".658. 4

2"2.06" 4.!5"8!.83235.5

"25."2222. "2! .83"50. 4234.""5 .28"3 .52" 8.8""60.0"2!8.04

2"4" !

203.82238. 4!8. 8

25!"6 .54"68.""220.4!"60.33222.84" ".28

"80"8"

252.02280.552"".85"2!.!5""5."253.45"63.63"03.0!

2"8.6"!5.55

2 !228.84

268.5"40.3!200.38

" !"2 .!!" 4.!!232.2!"62.832"3.46"05.82


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25".84"5".328!.84"82.!3

! ."48. 5

2"0.5

"!8. ""0!. 6"8"

"2 .!"2"2.6""!".53"38."

85.22""5.6258.86"82.4"256."6

"56.45"5".36"!4.43246.5"5!."8"82."42"6."3"4!.0323 .4"323.66

6 .08204.46

"85."6"5 .5""3!."5336.!4

"82"80.82256.44"6"."""66.28235.65"55.34204.54

"2".68203."5"46.6!243.64" 0.3332.66

" 8" 3.86"48.!224!. "


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2 8.88"5".02

"82"!.54"!8.2""54. 3"88.24

"5".6""5.6!250.!"220.!"" 3.2"253.45

"8!" 8" 0

"40.!!2!5. !"43.46

252.08!3.43"0".

"80"6".5

204."5"82."3230.3"23 .!2"2. 6238.52"4".6"

2"5.222"5.6!"6!.23"53.02"43.48253.6!

"80"83" 8

260."!!."3

266.0!

!6.!2302."8"58.6!"0 .!220".3"" 2.3"54.33" 3.!5"02.!5220.62


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2 6. 4"63.42" ".42

" 5"8!.5"23.03250.52

200.222.02"3.65

" . 5"82

"46.3!305.55

5".4"345. !"20.28246.22

! .62

20!.8"" !8".!

"63.2" 8

"!3."636!.!8

"6233 .28230.4523 .32"!.35

76401.15


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lui Sturges

aprox 40


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A. istri1utia clientilor #upa rata lunar a cre#itului

ni xi xi%ni (xi-xme#iu) 2%ni Suma xi (din baza initiala de0-80 22 40 880 5"2308. 2 eroarea A= 0.8363 648 280-"60 !0 "20 "0800 4 4368.4 eroarea = -0.02 48655""60-240 202 200 40400 ""06".52 eroarea C= 0.5222444 32

240-320 5 280 2"000 5 2!0320-400 "" 360 3!60 308250.36otal 400 77040 "8 88!6

76401. istri1utia clientilor #upa rata 6

ni xi xi%ni (xi-xme#iu) 2%ni0-60 "2 30 360 3"0858.8360-"20 40 !0 3600 40 636.""20-"80 ""8 "50 " 00 "! 8 4.4!5"80-240 "44 2"0 30240 5225 .!6240-300 6 2 0 "80!0 4"86 6.46 5300-360 " 330 56"0 3286!3.3425360-420 2 3!0 80 !24".805otal 400 76380 17 523

C. istri1utia clientilor #upa rata lunar a cre#itului

ni xi xi%ni (xi-xme#iu) 2%ni0-40 5 20 "00 "4 !2040-80 " 60 "020 2!6208

80-"20 30 "00 3000 253!20"20-"60 60 "40 8400 "62240"60-200 ""3 "80 20340 "62 2200-240 8! 220 "!580 6! 6240-280 4! 260 "2 40 2265 6280-320 26 300 800 303264320-360 ! 340 3060 "! "36360-400 2 380 60 0688otal 400 76800 1744000

7nter*aleale rateilunare

7nter*aleale rateilunare

7nter*aleale rateilunare 0-!0 !0-1"0 1"0-#$0 #$0

0

&0

100

1&0

#00

#&0

'. (istri utia clientilor dupa ra

0

#0

$0

"0

!0

100

1#0

1$0

1"0

-. (istri utia clientilor dupa rata l

"0

!0

100

1#0

. (istri utia clientilor dupa rata l


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0

#0

$0


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ate) = 76401Cea mai mica eroare este in ca ul #istri1utiei 9 iar cea mai mare la #istri1utia A. inan# cont si #e coe:icient

A.xme#iu= "!2.6*arianta= 46! .24a1.st#.= 68.5C* = 35.6

.xme#iu= "!"*arianta= 4488a1.st#.= 66.!!C* = 35.08

C.xme#iu= "!2*arianta= 4360

a1.st#.= 66.03C* = 34.3!

Se *a calcula eroarea sumei :iecarei #istri1utii;grup ri ast:el


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l #e#e aceea pe aceasta *om lucra mai #eparte ( a se *e#ea celelalte :oi #e calcul #in acest :isier xcel).

1a a #e #ate);suma #in 1a a #e #ate. Se5 9 #ar :iin# ca eroarea cea mai mica


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a a #e #ate :ara *alorile a1erante

250 Accounts (euro) Sum - Accounts (euro)8 .0! "5- 5 !6".!

328.0" 5-"35 52 6.3!5. 3 "35-"!5 24 !0.56

2"".82 "!5-255 28 03.68244.2" 255-3"5 "2 54.34253.46 3"5-3 0 3 " .86

"8 Total Result 76204.855.4"

"3!.08200.48

2442"6.26

"62.4240

"6!.65

!4.32!8.33"5!.2!"32.4!"38.08"80.8""86.3

258"2".32

35.65"8!.!324.8

28".532!3"!8.!" 6. 2"56.0!2"8.383"2.62

260205.5!

"6""54

"46.!8

233.65"8228.2!"88.6"80.!!"!"."6264.55208.35

235.4"68."

Accounts(euro)


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" 82"0.55" .48" ".5!220.44

34."3"86."5

"80240. 4"43.32"56.63

5!.!!2 0

2"6.5"!.0"

20 .05224.4

"5".452 3.33

364.3208.6"224.!

"86.56255.04"!".!8206.22

2 8"!0.56

".5!"."2

233. 6

"!"68.""4". 3

".3"6".!5

!4.24"3".5"83.42"08.04204.35228.6"2! .42

"4".2458.8!"53.28"8".3!"42."2" 0.!4" 2.53

48.28"28.

" 3.52


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220."4"5!.4624".66

2"42!5.68248.3!"!3.58

2!0248.26"83.!!

45.!362.!3

282"!6

" !.54""!."

2"6.5!2.54"!2

204.5230024!.25

"85"265

"26.!"255

206.2"24 .54232.58"43.05

2!02!56."6

"5 . 42!3.06

63.6"300

""3.200. 420!.!3

"80.2!!.4

230."64.362"5.!"

"83243.53

"!8"60.06234."2"20.36324.44


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225. 88!.0!

20".6525".!6236.0""60."5" ".!!

230."4225.4!23".!!

3"0205.68200.85

" ".8"25.833"4.25

3"0224.4!"!3. 3

" 8. 223".25"!6."8"62.2!

2422 .!3224.!8235.45

6 .82235.4"243.!8"! .0

330"24."4246.04" 4.!""28.43286.5"222.!5"05.2820 ."6

.48""6.2202.5"

"4!.33246.658".54

" 8.38"80. !

!".32" 8

253.642!

"82."2


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""".4"6".658. 4

2"2.06" 4.!5"8!.83235.5

"25."2222. "2! .83"50. 4234.""5 .28"3 .52" 8.8""60.0"2!8.04

2"4" !

203.82238. 4!8. 8

25!"6 .54"68.""220.4!"60.33222.84" ".28

"80"8"

252.02280.552"".85"2!.!5""5."253.45"63.63"03.0!

2"8.6"!5.55

2 !228.84

268.5"40.3!200.38

" !"2 .!!" 4.!!232.2!"62.832"3.46"05.82


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25".84"5".328!.84"82.!3

! ."48. 5

2"0.5

"!8. ""0!. 6"8"

"2 .!"2"2.6""!".53"38."

85.22""5.6258.86"82.4"256."6

"56.45"5".36"!4.43246.5"5!."8"82."42"6."3"4!.0323 .4"323.66

6 .08204.46

"85."6"5 .5""3!."5336.!4

"82"80.82256.44"6"."""66.28235.65"55.34204.54

"2".68203."5"46.6!243.64" 0.3332.66

" 8" 3.86"48.!224!. "


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2 8.88"5".02

"82"!.54"!8.2""54. 3"88.24

"5".6""5.6!250.!"220.!"" 3.2"253.45

"8!" 8" 0

"40.!!2!5. !"43.46

252.08!3.43"0".

"80"6".5

204."5"82."3230.3"23 .!2"2. 6238.52"4".6"

2"5.222"5.6!"6!.23"53.02"43.48253.6!

"80"83" 8

260."!!."3

266.0!

!6.!2302."8"58.6!"0 .!220".3"" 2.3"54.33" 3.!5"02.!5220.62


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2 6. 4"63.42" ".42

" 5"8!.5"23.03250.52

200.222.02"3.65

" . 5"82

"46.3!305.55

5".4"345. !"20.28246.22

! .62

20!.8"" !8".!

"63.2" 8

36!.!8"62

33 .28230.4523 .32"!.35

76204.8


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A. istri1utia clientilor #upa rata lunar a cre#itului7nter*ale alni xi xi%ni nicumulat >xi-xme#iu>%ni (xi-xme#iu) 2%ni0-60 "2 30 360 "2 360.0 "0800.060-"20 40 !0 3600 52 3600.0 324000.0"20-"80 ""8 "50 " 00 " 0 " 00.0 2655000.0"80-240 "44 2"0 30240 3"4 30240.0 6350400.0240-300 6 2 0 "80!0 38" "80!0.0 4884300.0300-360 " 330 56"0 3!8 56"0.0 "85"300.0360-420 2 3!0 80 400 80.0 304200.0

otal 400 76380 76380 16380000

!"#!$%T&R!! T'"#!"T'! $'"TR% '?rima etapa se re:era la #istri1utia A9 #e mai sus.

xmin= 3.1 euro cea mai mic rat lunar este 39"! exmax= 36 . 8 euro cea mai mare rat lunar este 36!9!'o#ul= 1 5.1 euro cei mai multi #intre clien@i au rate #e

loc 'e#= 200.5 'e#iana= 1 2.7 euro um tate #intre clien@i au rate mai miloc D"= "00.25 D"= 144.5 euro un s:ert #intre clien@i au rate mai miciloc D3= 300. 5 D3= 234.5 euro 25 #intre clien@i au rate mai mari #

AiE= 8!.! euro a1aterea intercuartilica"95%AiE= "34.! euro

.6 euro limita minima a inter*alului pentru *a36 .4 euro limita maxima *ariantele nea1erante

"oua dist ibutie*7nter*ale alni xi xi%ni nicumulat >xi-xme#iu>%ni (xi-xme#iu) 2%ni"5- 5 "8 45 8"0 "8 26"0.5 3 858".2

5-"35 4! "05 5"45 6 4"66.2 354234.3"35-"!5 "4 "65 24255 2"4 36 8. !205!.8"!5-255 "28 225 28800 342 44 6.8 "565 5.0255-3"5 45 285 "2825 38 42 3.! 405!"0.23"5-3 5 "" 345 3 !5 3!8 " 04. 264"8!.3

otal 3 8 75630 20 10.8 165154 .7

+edia= 1 0.0

!"#!$%T&R!! ,%R!%T!'!a1aterea me#ie liniar = 52.5 euro se *eri:ica ca a1 me#ie liniara este aproximati* = 09

*arian@a (#ispersia)= 414 .6 6494%(4;5)= 5".534050 8 aproximati* apropiata1aterea stan#ar# (a1.me#. patr.)= 64.4 euro

-oe i-ientul de /a ia ie $/ = 33. 0 ?entru ca C* 35 9colecti*itatea celor 400 #e clienti repre i

Se obse / - inte /alul ( 6 36 4) " -u inde toate /a iantele -#e-i baza de date -on ine /a iantele ex-e ionale sau abe ante* 3 1se ie. Se e-omanda sa e a-em se ia ent u a utea dete mina me

ac seria se apropie #e #istri1u@ia normal 9 atunci aplic m regula empiric < 68926 #in totalul clien@ilor #ineuro (a#ic "2596G25494)9 !5945 #intre clien@i au rate lunare in inter*alul "!0F2%6494 euro (a#ica 6"92G3"89!)(0G38393). ?reci are< la ultimul inter*al limita in:erioara a :ost -392euro9 #ar nu are sens in contextul #at9 in coninseamna lipsa #atoriei lunare.

n e antionul celor $00 de clienţmedie este de 1 0 euro2 cu o ade 3 "$2$ euro )sau cu o a aterde 3 & euro*


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!"#!$%T&R!! %S!+'TR!'!Coe:icientul #e asimetrie ?earson,as= :0.07 sla1a asimetrie negati*a sau #e #reapta

ac seria HI se apropie #e #istri1u@ia normal 9 atunci aplic m regula lui Ce1JBe*< 5 #intre clien@i au rate6"92G3"89!) sau 889! au ratele in inter*alul "!0F3%6494 (a#ica (0G38393). ?reci are< la ultimul inter*al limita icontextul #at9 in consecinta am consi#erat limita in:erioar 09 care inseamna lipsa #atoriei lunare.

1&-7& 7&-1%& 1%&-1 & 1 &-#&& #&&-%1& %1&-%7&0

#0

$0

"0

!0

100

1#0

1$0

1"0

(istri utia clientilor cu rate de credit dupa cuantumul acesteia

euro


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uro8 euro"!59" euro.ci #e "!29 euro Bi um tate mai mari #e at t .i #e "4495 euro si 5 au rate mai mari #e at t

23495 euro Bi trei s:erturi mai mici.

riantele nea1erante

98%a1 stan#ar##e 5295 euro

t o colecti*itate omogen #in punctul #e *e#ere al ratei lunare #e cre#it9me#ia este repre entati*a si #e incr

!nte /ale ent u dist ibutia no mala/egula empiric si /egula lui Ce1JBe*

"25.6 254.4

a-te isti-ii studiate ( i e xmin i e xmaxim).si 36 8 eu o e -a e t ebuie s le elimin m dinia indi-ato ii /a iatiei si ai asimet iei.

Bantion au rate lunare cuprinse in inter*alul "!0F6494sau !!9 5 au ratele in inter*alul 1 0 3964 4 (a#ica

secinta am consi#erat inter*alul #e la 09 care

i rata lunarăatere standarde medie liniară


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6".2 3"8.!-3.2 383.3

lunare in inter*alul "!0F2%6494 euro (a#ican:erioara a :ost -3896 euro9 #ar nu are sens in


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e#ere in in:erenta statistica..


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pb complexa stadiu 1

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