Statistika 1.(Detyre Kursi)
23
-
Upload
orgest-shehu -
Category
Data & Analytics
-
view
624 -
download
30
Transcript of Statistika 1.(Detyre Kursi)
Intervistoni 30 kryefamiljare ne zonen ku banoni (duke bere nje zgjedhje te rastit) lidhur me kerkesat e pyetesorit te meposhtem:
Shenoni nivelin e pranimit tuaj per pohimin e meposhtem:
1.Mishi i fresket eshte i shtrenjte?
xi fi Fp Fr Wi %=fi/n *100
Jam dakort 12 12 30 40%
S’jam dakort 10 22 18 33.3%
Nuk di c’te them
8 30 8 26.7%
Shuma 30 100%
Cmimi Vleresimi Denuria relative ne %
Vendi ku shitet
Vleresimi Wi% per vendin
xi fi Fp Fr wi % xi fi Fp Fr Wi%
Shume rendesi
7 7 30 23.3% Shume rendesi
20 20 30 66.7%
Mjaft rendesi
5 12 23 16.7% Mjaft rendesi
5 25 10 16.7%
Pak rendesi
10 22 18 33.3% Pak rendesi
3 28 5 10.0%
Aspak rendesi
8 30 8 26.7% Aspak rendesi
2 30 2 6.6%
Shuma 30 100% 100%
2.Vleresoni sa rendesi ka sa me poshte per ju kur blini mish te fresket:
3.Sa eshte numri i pjestareve te familjes tuaj?Numri I pjestareve te familjes:
2,3,4,2,3,4,4,4,4,3,5,5,5,6,6,6,6,5,5,5,5,6,6,5,5,7,7,8,9,10
Bejm Grupimin sipas pjestareve te familjes -Gjejm numrin e grupeve K=(2n)^0.33=(2*30)^0.33=4 grupe-Gjejm amplitudenA=Vlera max-Vleren min=10-2=8-Gjejm gjeresin e grupit dd=A/K=8/4=2 Kufiri Poshtem Kufiri i SipermGrupi 1: Vlera min(2)--------------->Vlera min+d(2+2)=4Grupi 2: (4)-------------------------> (4+2)=6Grupi 3: (6)------------------------->(6+2)=8Grupi 4: (8)------------------------->(8+2)=10
Grupet Fi Fp Fr Wi=fi/n*100
2----->4 10 10 30 10/30*100=33,3%
4------>6 15 25 20 15/30*100=50%
6------>8 3 28 5 3/30*100=10%
8---->10 2 30 2 2/30*100=6.7%
Shuma 30 100%
4. Cili eshte konsumi mujor i mishit te vicit ne (kg)?
Konsumi mujor I familjeve eshte: 2,3,4,2,4,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,8,9,9,9,10,10,10,10,10
Formojm Grupet
-Gjejm numrin e grupeve K
K=(2n)^0.33=(2*30)^0.33=4 grupe
-Gjejm amplituden
A=Vlera max-Vleren min=10-2=8
-Gjejm gjeresin e grupit d
d=A/K=8/4=2
Kufiri Poshtem Kufiri i Siperm
Grupi 1: Vlera min(2)--------------->Vlera min+d(2+2)=4
Grupi 2: (4)-------------------------> (4+2)=6
Grupi 3: (6)------------------------->(6+2)=8
Grupi 4: (8)------------------------->(8+2)=10
Grupet fi Fp Fr wi%=fi/n*100
2------>4 5 5 30 5/30*100=16.7%
4------>6 7 12 25 7/30*100=23.3%
6------>8 10 22 18 10/30*100=33.3%
8--->10 8 30 8 8/30*100=26.7%
Shuma 30 100%
5.Cilat jane te ardhurat mujore te familjeve?
10000,30000,20000,20000,20000,25000,25000,15000,22000,20000,30000,30000,25000,30000,
10000,15000,25000,30000,35000,40000,45000,50000,40000,80000,90000,90000,60000,65000,
70000,55000
Bejm grupimin
-Gjejm numrin e grupeve K
K=(2n)^0.33=(2*30)^0.33=4 grupe
-Gjejm amplituden
A=Vlera max-Vleren min=90000-10000=80000
-Gjejm gjeresin e grupit d
d=A/K=80000/4=20000
Kufiri Poshtem Kufiri i Siperm
Grupi 1: Vlera min(10000)--------------->Vlera min+d(10000+20000)=30000
Grupi 2: 30000------------>50000
Grupi 3: 50000------------->70000
Grupi 4: 70000------------>90000
Grupet fi wi %=fi/n*100 Fp Fr xi
10000--->30000 18 18/30*100=60% 18 30 20000
30000---->50000 5 5/30*100=16% 23 12 40000
50000--->70000 4 4/30*100=14% 27 7 60000
70000---->90000 3 3/30*100=10% 30 3 80000
Shuma 30 100%
Interpretimi i nje vlere: Pershembull: Marim grupimin intervalor te te ardhurave prej 10000-30000.Denduria absolute e saj fi=18 nenkupton se 18 persona marin te ardhura nga 10000-30000.Denduria relative wi=60% tregon se 60% e totalit te familjeve nga 100% marin te ardhura nga 10000-30000.
1.Mishi i vicit eshte i shtrenjte?
0
2
4
6
8
10
12
Jam dakort
S’jam dakort
Nuk di c’te them
2.a Rendesia e cmimit te blerjes
0123456789
10
Shume rendesi
Mjaft rendesi
Pak rendesi
Aspak rendesi
2.b Rendesia e vendit te blerjes
0
2
46
8
1012
14
1618
20
Shume rendesi
Mjaft rendesi
Pak rendesi
Aspak rendesi
3.Numri i pjestareve te familjes
0
2
4
6
8
10
12
14
16
2----->4
4------>6
6------>8
8---->10
4.Konsumi mujor i mishit te vicit
0
2
4
6
8
10
2------>4
4------>6
6------>8
8--->10
5.Te ardhurat mujore te familjeve
0
2
4
6
8
10
12
14
16
18
10000--->30000
30000-->50000
50000--->70000
70000--->90000
Bejm grupimin 2 permasor sipas konsumit edhe numrit te personave ne familje
Grupet fi wi %=fi/n*100 Fp Fr xiXi*fi
10000--->30000 18 18/30*100=60% 18 30 20000
360000
30000---->50000 5 5/30*100=16% 23 12 40000
200000
50000--->70000 4 4/30*100=14% 27 7 60000
240000
70000---->90000 3 3/30*100=10% 30 3 80000
240000
Shuma 30 100% 1040000
Kerkesa 6. Per familjet e intervistura llogarisni nivelin mesatar te te ardhurave mujore per familje,kuartilin e pare ,moden,medianen edhe beni interpretimet perkatese per cdo rast.-Ndertoj edhe njeher tabelen,duke shtuar prodhimin Xi*fi
x mesatar=∑xi*fi/∑fi=1040000/30≈34666.6
x mesatar=34666.6 jane te ardhurat mesatarisht qe marin familjet.
-Gjej Q1=X0+d[(n/4-Fq-1)]/fq1
-Rendisim te dhenat .
-Gjej Fp ok
-Pozicioni=(n+1)/4=(30+1)/4=31/4=7.75
Pozicioni kuartilit 1 eshte 7.75 edhe Q1 eshte ne intervalin 10000-30000
Te dhenat jane : X0=10000,d=20000,n=30,Fq-1=0,fq1=18
Gjej Q1 =X0+d[(n/4-Fq-1)]/fq1=10000+20000[(30/4-0)]/18=10000+20000(7.5/18)
Q1=10000+20000*0.416=10000+8611=18611
Q1=18611 dmth25% e familjeve kane mare deri 18611 te ardhura
Mediana= X0+d[(n/2-Fme-1)]/fme
Pozicioni medianes=(n+1)/2=(30+1)/2=15.5
Renditja Ok
Fp ok
Intervali Median 10000-30000
Me=10000+20000[(30/2-0)]/18
Me=10000+20000*15/18=10000+16666.6
Mediana=26666.6
Nenkupton se 50% e familjeve marin te ardhura deri 26666.6
-Gjej Mo=X0+d[(fmo-fmo-1)/(2fmo-fmo-1-fmo+1)]
Intervali mode eshte 10000-30000 sepse ka dendurin absolute me te madhe te shperndarjes.
Moden e gjejm me 3 menyra: a) Me mesataren e dy skajeve te intervalit mode 10000-30000
=(10000+30000)/2=40000/2=20000
Mo=20000
B) Me menyren e grafikut
0
5
10
15
20
10000--->30000
30000---->50000
50000--->70000
70000---->90000
X0
Ne mesin e kollones se pare ku bie pike prerja e X0 eshte eshte edhe moda.
Menyra C) Mo=X0+d[(fmo-fmo-1)/(2fmo-fmo-1-fmo+1)]=10000+20000[(18-0)/(2*18-0-
5)]=10000+20000*18/31=10000+20000*18/31=10000+20000*0.58064516=10000+
11612.9032≈2161
Grupet fi Fp Frwi%=fi/n*100
Xi*fi
xi
│xi-x mesatar│
│xi-x mesatar│*fi
│xi-x mesatar│^2*fi
2------>4 5 5 305/30*100=16.7%
15 3 3.4 3.4*5=17
(3.4)^2*5=57.8
4------>6 7 12 257/30*100=23.3%
35 5 1.4 1.4*7=9.8
(1.4)^2*7=13.72
6------>8 10 22 1810/30*100=33.3%
70 7 0.6 0.6*10=6
(0.6)^2*10=3.6
8--->10 8 30 88/30*100=26.7%
72 9 2.6 2.6*8=20.8
(2.6)^2*8=54.08
Shuma 30 100%192 8 53.6 129.2
Kerkesa 8. Llogaritia e dispresionit,shmangies mesatare katrore,dhe koeficientin e variacionit duke i shoqeruar me interpreimet perkatese.(Lidhur me konsumin)
Devijimi mesatar (d mes)=∑│xi-x mesatar│*fi/∑fi=53.6/30=1.786 eshte shmangia e vlerave nga mesataria.
Devijimi linear=(d mesatar/x mesatar )*100=(1.786/6.4)*100=27.90625%≈28%
Dispresioni=∑(xi-x mesatar)^2*fi/∑fi=129.2/30=4.306≈4.3
Devijimi standart=√dispresionit=√4.3≈2.07
Koeficienti variacionit (Kv)=(Devijimi standart/ x mesatar)*100=(2.07/6.4)*100≈32.34%
Domethene :Devijimi standart ne lidhje me konsumin e mishit ndaj mesatares perben nje shifer te konsiderueshme.
Kerkesa 11 :Llogaritni edhe interpretoni Koeficientin e asimetris Ka edhe Koeficientin e eksesit Ke .(mbi konsumin)
Ka=3(X mesatar-Me)/devijimi standart=3*(6.4-6.6)/2.07=3*(-0.2)/2.07≈-0.29
Kemi nje asimetri te paperfillshme negative.
Koeficienti eksesit=(Mjy/devijimin standart^4)-3
Mjy greke=∑[(xi-x mesatar)^4]/fi
Grupet fi
Fp Fr
wi%=fi/n*100
Xi*fi
xi │xi-x mesatar│
│xi-x mesatar│*fi
│xi-x mesatar│^2*fi
(Xi-x mes)^4*fi
2------>4 5 5 30
5/30*100=16.7%
15 3 3.4 3.4*5=17 (3.4)^2*5=57.8
[(3.4)^4]*5=668.168
4------>6 7
12 25
7/30*100=23.3%
35 5 1.4 1.4*7=9.8
(1.4)^2*7=13.72
[(1.4)^4]*7=26.8912
6------>8
10
22 18
10/30*100=33.3%
70 7 0.6 0.6*10=6 (0.6)^2*10=3.6
[(0.6)^4]*10=1.296
8--->10 8
30 8
8/30*100=26.7%
72 9 2.6 2.6*8=20.8
(2.6)^2*8=54.08
[(2.6)^4]*8=365.5808
Shuma
30
100%
192
8 53.6 129.2 1061.936
Mjy greke=∑[(xi-x mesatar)^4]/ ∑ fi =1061.936/30=35.3978667Devijimi standart eshte = 2.07Koeficienti eksesit=(Mjy/devijimin standart^4)-3=[35.3978667/(2.07^4)]-
3=(35.3978667/18.360368)-3=1.92794974-3=-1.0720503= -107,20503%Kemi te bejm me nje Ekses Negativ.
12.Percaktimi i intervalit te besimit lidhur me konsumin mesatar mujor per te gjitha familjet e zones ku banoj per α=0.05.
IB=X mesatar ± Konstante(t α/2;n-1) *Gabimin Standart te x mesatar(S x mesatar)
Te dhenat:
X mesatar eshte 6.4
Nga tabela ne liber shperndarja e studentit (t) per vleren 29 sepse n-1 nga 30 te dhena qe kemi eshte numri 29 dhe i perkon
vlera 2.36. Devijimi standart eshte 2.07,n=30 .
Gjejm Gabimin standart i x mesatar (S x mesatar) fillimisht per ta zevendesuar me pas tek formula e intervalit besimit, kur kemi te
dhene: Devijimin standart edhe numrin e te dhenave (n)=30 .
S x mesatar=Devijim standart/√n=2.07/5.5=0.38
Gjem Intervalin e besimit tani, IB=X mesatar ± Konstante(t α/2;n-1) *Gabimin Standart te x mesatar(S x mesatar)
IB=6.4±2.36*0.38=6.4±0.897
IB= (5.503;7.297)
Interpretimi: Me siguri prej 95% mund te themi se konsumi mesatar per familjet e intervistuara nuk do jete me pak se 5.503 kg edhe
nuk do jete me shume se 7.297 kg.
13.Percaktoni intervalin e besimit lidhur me perpjesen e familjeve qe konsumojne 8 kg e lart, per te gjitha familjet e zones ku banoni per α=0.05.
IB=w±Zα/2*Sp
Dim qe : Zα/2=1.96
W=fi/n=8/30=0.27
Sp=[√w(1-w)/n]=[√0.27(1-0.27)/30]=[√(0.27*0.73)/30]=√0.1971/30=√0.00657=0.08105554
I zevendesojm tek formula e intervalit te besimit:
IB=w±1.96*Sp=0.27±1.96*0.08105554=0.27±0.159
IB=(0.111;0.429)=(11.1%;42.9%)
FUND
