Detyre-Kursi

Nr Mishi i fresk I shtrenjte

Rendesia Nr i pjestareve

Konsumi mujor(kg)

Te ardhurat mujore (000)lekÇmimi Vendi

1 Jam dakort Shume Mjaft 3 7 900002 S’jam dakort Pak Shume 5 9 700003 Jam dakort Aspak Shume 4 5 1000004 S’jam dakort Pak Aspak 6 10 1100005 Nuk di c’te them Mjaft Mjaft 2 8 900006 Jam dakort Pak Mjaft 5 6 700007 Jam dakort Aspak Pak 4 10 1000008 Nuk di c’te them Shume Shume 7 8 900009 S’jam dakort Shume Pak 2 7 5000010 Jam dakort Pak Mjaft 3 4 2000011 Nuk di c’te them Aspak Mjaft 4 8 6000012 Jam dakort Shume Shume 3 9 9000013 S’jam dakort Pak Shume 5 6 7000014 Nuk di c’te them Aspak Pak 7 8 4000015 Jam dakort Mjaft Mjaft 4 8 10000016 Jam dakort Mjaft Shume 8 5 4000017 S’jam dakort Pak Pak 2 9 3000018 Jam dakort Mjaft Aspak 3 10 10000019 S’jam dakort Mjaft Pak 5 6 8000020 S’jam dakort Aspak Shume 7 3 70000

21 Jam dakort Shume Mjaft 4 5 6000022 Jam dakort Mjaft Pak 4 8 5000023 S’jam dakort Shume Mjaft 3 9 4000024 Jam dakort Shume Aspak 5 9 9000025 Jam dakort Pak Mjaft 6 3 8000026 Nuk di c’te them Aspak Shume 4 10 10000027 S’jam dakort Shume Aspak 6 8 4000028 Nuk di c’te them Mjaft Pak 5 7 7000029 Jam dakort Mjaft Shume 4 5 6000030 Jam dakort Shume Pak 3 10 80000

1) Grupimi sipas 5 kerkesave.

Tab.1

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2) Gjeni: fi ; Wi; Fp ;Fr dhe interpretoni nje vlere per c’do grupim.

Mishi I fresket I shtrenjte

fi Wi Fp Fr

Per pjese

%

Jam dakort 15 0.5 50 15 30

S’jam dakort 9 0.3 30 24 15

Nuk di c’te them 6 0.2 20 30 6

Totali 30 1.0 100

Interpretim: Gjysma(50%) e familjeve jane dakort qe mishi I fresket eshte I shtrenjte.

Fr Fp Wi fi Rendesia fi Wi Fp FrPer pjese

% Çmimi Vendi Per pjese

%

30 9 0.3 30 9 Shume 9 0.3 30 9 3021 17 0.27 27 8 Mjaft 9 0.3 30 18 2113 24 0.23 23 7 Pak 8 0.27 27 24 126 30 0.2 20 6 Aspak 4 0.13 13 30 4

1.0 100 30 Totali 30 1.0 100Interpretim: 30% e familjeve I kushtojne shume rendesi cmimit te mishit te fresket.

27% e familjeve I kushtojne pak rendesi vendit te tregtimit te mishit te fresket.

Nr i pjestareve

fi Wi Fp FrPer pjese

%

0-2 3 0.1 10 3 302-4 14 0.47 47 17 274-6 9 0.3 30 26 136-8 4 0.13 13 30 4



Totali 30 1.0 100

Interpretim: 47% e familjeve perbehen nga 2-4 pjesetare.

Konsumi mujor(kg)


%

2-4 3 0.1 10 3 304-6 7 0.24 24 10 276-8 10 0.33 33 20 208-10 10 0.33 33 30 10Totali 30 1.0 100

Interpretim: 33% e familjeve konsumojne 6-8 kg mish vici ne muaj.

Te ardhurat mujore(000)lek


%

10000-30000 2 0.06 6 2 3030000-50000 6 0.20 20 8 2850000-70000 8 0.27 27 16 2270000-9000 8 0.27 27 24 1490000-110000 6 0.2 20 30 6

fTotali 30 1.0 100 Interpretim: 20% e familjeve kane te ardhura mujore 90000-110000 lek ne muaj.



3) Paraqitja grafike e grupimeve.

Grafiku i grupimit “mishi I fresket i shtrenjte”

Grafiku i grupimit “rendesia”.


Jam dakort S'jam dakort Nuk di c'te them02468

10121416

Mishi i fresket i shtrenjte

Mishi i fresket i shtrenjte

Shume

Mjaft

Pak

Aspak 0

5

10

CmimiVendi


Grafikui grupimit “nr i pjesetareve “.

Grafiku i grupimit “konsumi mujor (kg)”


0-2. 2-4. 4-6. 6-8.0

5

10

15

20

25

30

35

FpFr

2-4. 4-6. 6-8. 8-10.0123456789

10

Konsumi mujor(kg)

Konsumi mujor(kg)


Grafiku i grupimit “te ardhurat mujore (000)lek”

4) Grupimi dy permasor per pyetjen 3 dhe 4.

C mujorkonsumi mujor

AT mujoreTe ardhurat mujore

5) Grupimi tre permasor per pyetjen 3,4 dhe 5.


10000-30000

30000-50000

50000-70000

70000-90000

90000-110000

0

1

2

3

4

5

6

7

8

9

Te ardhurat mujore (000)lek

Te ardhurat mujore (000)lek

C mujor

AT mujore 2-4 4-6 6-8 8-10 Totali0-2 0 0 2 1 32-4 1 3 4 6 144-6 1 3 2 3 96-8 1 1 2 0 4

Totali 3 7 10 10 30


C mujor

AT mujore Nr. pjest

2-4

0-2 2-4 4-6 6-8

4-6

0-2 2-4 4-6 6-8

6-8

0-2 2-4 4-6 6-8

8-10

0-2 2-4 4-6 6-8 ∑

10000-30000 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 230000-50000 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 650000-70000 0 0 0 1 0 2 2 0 0 1 1 0 0 0 1 0 870000-90000 0 0 1 0 0 0 1 0 1 1 0 1 0 2 1 0 8

90000-110000 0 0 0 0 0 1 0 0 0 1 0 0 0 3 1 0 6Totali 0 1 1 1 0 3 3 1 2 4 2 2 1 6 3 0 30

3 7 10 10

6) Llogarit: X ; Me ; Q1 ;Mo per te ardhurat mujore.

Te ardhurat mujore

Meset e interval (Xi)

fi Xifi Fp

10000-30000 20 2 40 2

30000-50000 40 6 240 850000-70000 60 8 560 1670000-90000 80 8 640 2490000-110000 100 6 600 30Totali 30 2080

Mesatarja :

x= ΣXifiΣfi ¿ 208030 =69.3

Interpretim: Niveli mesatar I te ardhurave mujore per familje eshte 69300 lek .

Mediana:

Pme=n+12

=312

=15.5

Fme=16

Intervali perkates: 50-70

Me=Xmin+d0.5 xΣfi−(Fme−1)

fme=50+20 0.5 x30−8

8=67.5



Interpretim: Gjysma (50%) e familjeve i kane te ardhurat mujore nen 67500 lek,ndersa gjysma tjeter i kane mbi 67500 lek.

Kuartili:

PQ1=n+14

=314

=7.75

FQ1=8


Q 1=Xmin+d0.25 xΣfi−(FQ1−1 )

fQ1=30+20 0.25 x30−2

6=48.3

Interpretim: 25% e familjeve I kane te ardhurat mujore nen 48300 lek,ndersa 75% e tyre I kane te ardhurat mujore mbi 48300 lek.

Moda:

fmo=8


Mo=Xmin+d fmo−fmo−1(fmo−fmo−1 ) x (fmo−fmo+1)

=50+20 8−6(8−6 ) x (8−8)

=50

Interpretim: Shumica e familjeve kane te ardhura mujore 50000 lek.

7) Llogarit: X ; Me ; Q1 ; Mo per konsumin mujor per familje.



Konsumi mujor(kg)

fi Meset e interval (Xi)

Xifi Fp

2-4 3 3 9 34-6 7 5 35 106-8 10 7 70 208-10 10 9 90 30Totali 30 204

Mesatarja:

x= ΣXifiΣfi

=20430

=6.8

Interpretim: Niveli mesatar I konsumit mujor per familje eshte 6.8 kg.Mediana:

Pme=n+12

=312

=15.5

Fme=20Intervali perkates: 6-8

Me=Xmin+d 0.5 xΣfi−Fme−1fme

=6+2 0.5 x30−107

=7.4

Interpretim: 50% e familjeve konsumojne nen 7.4 kg mish ne muaj dhe 50% e tyre konsumojne mbi 7.4 kg mish ne muaj.

Kuartili:

PQ1=n+14

=314

=7.75

FQ1=10Intervali perkates: 4-6

PQ1=Xmin+d 0.25 xΣfi−FQ−1fQ1

=4+2 0.25 x30−37

=5.3

Interpretim: 25% e familjeve konsumojne nen 5.3 kg mish ne muaj dhe 75% e tyre konsumojne mbi 5.3 kg mish ne muaj.



Moda:

fmo=10Intervali perkates: 6-8

Mo=Xmin+d fmo−fmo−1( fmo−fmo−1) x (fmo−fmo+1)

=6+2 10−7(10−7) x (10−10)

=6

Interpretim: Shumica e familjeve konsumojne 6kg mish ne muaj.

8) Llogarit: σ²; σ; ;Kv dhe beni interpretimet perkatese.

Konsumi mujor(kg)

Meset e interval (Xi)

fi (Xi-X) (Xi-X)fi (Xi-X)² (Xi-X)²fi

2-4 3 3 3.8 11.4 14.44 43.24-6 5 7 1.8 12.6 3.24 22.686-8 7 10 0.2 2 0.04 0.48-10 9 10 2.2 22 4.84 48.4Totali 30 48 114.68

X=6.8

Dispersioni:

σ ²=Σ (Xi−X ) ² fi

Σfi=114.68

30=3.8

Interpretim:

Mesatarja kuadratike:

σ=√σ ²=√3.8=1.9

Interpretim:

Koeficienti I variacionit:

Kv= σX

=1.96.8

=0.3

Interpretim:



9) Ndani familjet ne dy grupe lidhur me konsumin mujor: a)deri ne 4 pjestare b) mbi 4 pjestareLlogarit: dispersionin midis grupeve dhe dispersionet brenda grupeve.Percaktoni dhe interpretoni efektin e ndikimit te numrit te pjestareve te familjes ne variacionin e konsumit mujor.

Konsumi mujor (kg)

fi Deri ne 4 pjestare

Mbi 4 pjestare

2-4 3 1 24-6 7 3 46-8 10 6 48-10 10 7 3Totali 17 13

Dispersioni midis grupeve:

δ ²=Σ (Xi−X )2∋ ¿Σni

= (7.2−6.8 )2 x17+¿¿¿

Dispersioni brenda grupit me deri 4 pjestare:

σ ²=Σ (Xi−X ) ²∋ ¿Σni

=(3−7.2 )2 x 1+ (5−7.2 )2 x 3+(7−7.2 )2 x 6+(9−7.2 )2 x 7

17=55.0817

=3.24¿

Dispersioni brenda grupit me mbi 4 pjestare:

σ ²=Σ(Xi−X) ²∋ ¿Σni

=(3.−7.3 )2 x 2+(5−7.3 )24+(7−7.3 )2 x 4+(9−7.3 )2 x 3

13=67.17

13=5.167¿

Dispersioni mesatar brenda grupeve:


Treguesit fi X σ² σ Kv

Te gjitha familjet 30 6.8 1.6 1.3 0.2Familjet e vogla 17 7.2 3.2 1.8 0.25Familjet e medha 13 7.3 5.2 2.3 0.3


σ ²=Σσi ²∋ ¿Σni

=3.24 x 17+5.167 x1330

=55.08+67.1730

=4.075¿

Dispersioni i pergjithshem:

σ²=δ²+σ²=5.97+4.075=10.045

Koeficienti I percaktueshmerise:

ŋ ²= δ ²σ ²x 100= 5.97

10.045x100=59.4%

10) Ndertoni dendurite teorike dhe vleresoni ndryshimet e dendurive faktike me ato teorike.

Konsumi mujor(kg)

fi Xi Xifi

2-4 3 3 94-6 7 5 356-8 10 7 70

8-10 10 9 90

Totali 30 204

X=6.8σ=1.9

X=2 Z=2−6.81.9

=−2.53 X=4Z=4−6.81.9

=−1.47

X=6Z=6−6.81.9

=−0.42 X=8Z=8−6.81.9

=0.63

X=10Z=10−6.81.9

=1.68

P1(X<2)=P(Z<-2.053)=0.5-P(-2.53<Z<0)=0.5-P(0<Z<2.53)=0.5-0.4943=0.0057P2(2<X<4)=P(-2.53<Z<-1.47)=P(-2.53<Z<0)-P(-1.47<Z<0)=P(0<Z<2.53)-P(0<Z<1.47)=0.4943-0.4192=0.0751P3(4<X<6)=P(-1.47<Z<-0.42)=P(-1.47<Z<0)-P(-0.42<Z<0)=P(0<Z<1.47)-P(0<Z<0.42)=0.44192-0.1628=0.2564P4(6<X<8)=P(-0.42<Z<0.63) =P(-0.42<Z<0)+P(0<Z<0.63) =P(0<Z<0.42)+P(0<Z<0.63 =0.1628+0.2357=0.3985P5(8<X<10)=P(0<Z<1.68)-P(0<Z<0.63)=0.4535-0.2357=0.2178P6(X>10)=P(Z>1.86)=0.5-P(0<Z<1.86)=0.5-0.4535=0.0465

Dendurite teorike:



ft1=n x P1=30 x 0.0057=0.171ft2=n x P2=30 x 0.0751=2.253ft3=n x P3=30 x 0.2564=7.692ft4=n x P4=30 x 0.3985=11.955ft5=n x P5=30 x 0.2178=6.534ft6=n x P6=30 x 0.0465=1.395

Konsumi mujor(kg)

Dendurite faktike(fi)

Dendurite teorike(fti)

2-4 3 24-6 7 86-8 10 12

8-10 10 8

Totali 30

Inretpretim: Shikojme qe nuk ka ndryshime thelbesore midis dendurive faktike dhe atyre teorike.Kjo do te thote se shperndarja faktike eshte afersisht normale.

11) Llogarit: koeficientin e asimetrise dhe te ekcesit.

Koeficienti I asimetrise:

Ka=3(X−Me)

σ

X=6.8

σ=1.9

Pme=15.5

Me=7.4

Koeficienti I asimetrise:

Ka=3(X−Me)

σ=3(6.8−7.4)

1.9=−0.9

Interpretim: Kemi te bejme me asimetri te majte te moderuar.

Konsumi fi X (Xi-X)⁴ fi



mujor(kg) i2-4 3 3 625.54-6 7 5 73.56-8 10 7 0.0168-10 10 9 234.3Totali 30 933.3

12) Percakto intervalin e besimit lidhur me konsumin.

α=0.05

X=6.8

σ=1.9

δx= σ

√n= 1.9

√30=0.347

tα/2=t0.025:29=2.36

IB: X ± tα/2:n-1 δx∙

IB: 6.8 ± 2.36 0.347 ∙ 6.8 ± 0.819

IB: {X - tα/2:n-1δx

√n}

IB={5.981;7.619}

Me siguri 95% mund t themi se konsumi mujor i mishit per familje nuk eshte me poshte se 5.981 kg dhe nuk eshte me lart se 7.619 kg.

13) Percaktoni intervalin e besimit lidhur me perpjesen e familjeve qe konsumojne 8 kg e lart.



α=0.05

Dispersioni ne lidhje me perpjesen:

ω= 130

=0.033

δω=√ω (1−ω)n

=√ 0.033(1−0.033)30=√ 0.03230 =0.0326

IB: ω ± Zα/2 δω∙

IB: 0.033 ± 1.96 0.0326∙

IB: 0.033 ± 0.064

IB={0.031 100;0.097 100} ∙ ∙ IB={3.0%;9.7%}

Interpretim: Me siguri 95% mund te themi se jo me pak se 3.1% e familjeve dhe jo me shume se 9.7% e tyre konsumojne 8 kg mish ne muaj.



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