Mavzu-11: Matematik statistika fanining vazifalari

MAVZU-11: Matematik statistika fanining vazifalari.

Reja 1). Matematik statistika fanining vazifalari 2). Tanlanmaning statistik taqsimoti va uni geometrik izohlash. 3). Intervalli statistik taqsimot, gistogramma

1). Matematik statistika fanining vazifalari

Xi	x1	x2	...	xk
ni	n 1	n2	...	nk
Wi	W1	w2	...	wk

Bosh va tanlanma to’plam, reprezentativ tanlanma to’plam.
Tanlanmaning statistik taqsimotini
geometrik izohlash.
Poligon va gistogrammasini chizish.

Bu erda: xi – variantlar, ni – mos chastotalar, wi- mos nisbiy chastotalar. Koordinatalar tekisligida (x1, n1), (x2, n2), . . . ,(xk, nk) nuqtalarni o’zaro tutashtiruvchi siniq chiziq chastotalar poligoni deyiladi.

Intervalli statistik taqsimot.

Tanlanma-ning hajmin	25-40	40-60	60-100	100-200	p  200
Intervallar soni k	5-6	6-8	7-10	8-12	10-15

,
.

Varianta intervallari [Xi; Xi+1)	Intervalga tegishli variantalar soni ni
[Xmin; Xmin+h)	n1
[Xmin+h; Xmin+2h)	n2
...	...
[Xmin+(k-1)h; Xmin+kh)	nk

2. Taqsimot parametrlarini statistic baholari. Nuqtaviy statistik baho

Xi	x1	x2	...	xk
ni	n 1	n2	...	nk
Wi	W1	w2	...	wk

Misol-3. Paxtazordan tasodifiy ravishda olingan 50 dona g`o`zani har birini paxtasi terib o`lchanganida gramm hisobida quyidagicha bo`ldi:
28, 30, 28, 27, 26, 26, 29, 29, 30, 26, 29, 25, 25, 32, 24, 27, 27, 28, 24, 25, 25, 32, 28, 28, 28, 27, 27, 26, 29, 29, 26, 28, 28, 27, 27, 27, 30, 27, 30, 28, 28, 28, 28, 28, 26, 29, 28, 29, 29.
Statistik taqsimotini tuzib geometric
Izohlang.
Misol-4. Mahalliy sog`iladigan 40 ta sigir sutining o`rtacha yog`lilik darajasi foiz hisobida quyidagicha bo`ldi:
3,45; 3,56; 3,68; 3,66; 3,70; 3,76; 3,75; 3,78; 3,80; 3,94; 3,2; 3,86; 3,88; 3,94; 3,93; 3,90; 3,96; 4,3; 4,03; 3,98; 4,00; 3,95; 4,10; 4,18; 4,30; 3,90; 3,85; 3,94; 3,92; 3,88; 3,98; 4,00; 4,20; 4,35; 4,10; 3,9.
Intervalli statistik taqsimot tuzib gistogrammasini chizing.

Emperik taqsimot funksiya

2). Tanlanmaning statistik taqsimoti va uni geometrik izohlash.

Misol-1.

Xt	0	1	2	3	4	5	6	7	8
ni	2	3	5	8	15	9	5	2	1

2). Intervalli statistik taqsimot , gistogramma

Misol-2.

Intervallar soni	xi;xi+1)	ni	Wi
1	0 - 1,2)	5	0,1
2	1,2 - 2,4)	5	0,1
3	2,4 - 3,6)	8	0,16
4	3,6 - 4,8)	15	0,13
5	4,8 - 6,0)	9	0,18
6	6,0 - 7,2)	7	0,14
7	7,2 - 8,4)	1	0,02
		50	1,00

Shakl -4

Misol-3 n=30 dona pillani og’irligi:

1,55; 1,60; 1,60; 1,65; 1,65; 1,65; 1,70; 1,70; 1,70; 1,75; 1,75; 1,75; 1,75; 1,80; 1,80; 1,80; 1,80; 1,80; 1,85; 1,85; 1,85; 1,80; 1,90; 1,90; 1,90; 1,95; 1,95; 2,00; 2,00; 2,05.

Statistik taqsimotini tuzamiz:

Xi	1,55	1,60	1,65	1,70	1,75	1,80	1,85	1,90	1,95	2,00	2,05
ni	1	3	3	3	4	5	3	3	2	2	1

Tanlanma o’rtacha qiymati
1,69 gramm

MODA Eng katta chastotaga ega bo’lgan variantaning qiymatiga moda deyiladi va uni M0 bilan belgilanadi. MEDIANA  Statistik taqsimotni teng ikki qismga bo’ladigan variantaning qiymatiga mediana deyiladi va uni Me bilan belgilanadi.

Mustaqil yechish uchun misol.
Kartoshka kovlanganida, har bir tupidan
kovlab olingan kartoshkalar soni X
quyidagicha bo’ldi:
6, 7, 5, 8, 3, 7, 9, 5, 8, 7, 4, 6, 8, 7, 5, 8, 10, 6, 7, 8, 9, 7, 8, 6, 9, 6, 7, 5, 10, 9, 7, 8, 6, 11, 7, 5, 4, 6, 7, 8, 10, 6, 7, 8, 11, 9, 7, 8, 10, 12.

Yechish

,
t(50;0,05) = 2,009
1ga maydonda o`rtacha 47620 tup kartoshka bo`lishini e’tiborga olsak
(298053; 374341)

Xi	1,55	1,60	1,65	1,70	1,75	1,80	1,85	1,90	1,95	2,00	2,05
ni	1	3	3	3	4	5	3	3	2	2	1

Misol-2
1,55; 1,60; 1,60; 1,65; 1,65; 1,65; 1,70; 1,70; 1,70; 1,75; 1,75; 1,75; 1,75; 1,80; 1,80; 1,80; 1,80; 1,80; 1,85; 1,85; 1,85; 1,80; 1,90; 1,90; 1,90; 1,95; 1,95; 2,00; 2,00; 2,05.
Natijada bu misol uchun statistik taqsimot quyidagicha bo`ladi:
1,76 < a < 1,82
70,4 kg < a < 72,6 kg

Intervalli statistik baho pilla uchun

t(50;0,05) = 2,009
1,76 < a < 1,82
70,4 kg < a < 72,6 kg

Intervallistatistikbaho. X-tasodifiymiqdor N(a; ) parametrli normal taqsimotgaegabo’lsan.

Normal taqsimotning noma’lum o’rtachakvadratikchetlanishi-ga intervalli statistic bahoqurish

a). Tanlanma o’rtacha qiymat

b). O’rtacha qiymatlar

O’rtacha garmonik va geometrik qiymatlar

xgar.<xgeom<xarif <xkvad

Misol-3 n=30 dona pillani og’irligi:

1,55; 1,60; 1,60; 1,65; 1,65; 1,65; 1,70; 1,70; 1,70; 1,75; 1,75; 1,75; 1,75; 1,80; 1,80; 1,80; 1,80; 1,80; 1,85; 1,85; 1,85; 1,80; 1,90; 1,90; 1,90; 1,95; 1,95; 2,00; 2,00; 2,05.

Statistik taqsimotini tuzamiz:

Xi	1,55	1,60	1,65	1,70	1,75	1,80	1,85	1,90	1,95	2,00	2,05
ni	1	3	3	3	4	5	3	3	2	2	1

Tanlanma o’rtacha qiymati
1,69 gramm

• B.Abdalimov “Oliy matematika” “O’qituvchi”, T. 1994.( darslik )

2. Fayziyev A.A., Rajabov B., Rajabova .L.“Oliy matematika, ehtimollar nazariyasi va matematik statistika” T.“TashDAU”, 2014(qo’llanma)
3. B.Sulaymonov, A.A.Fayziyev, J.N.Fayziyev “ Tajriba ma’lumotlarining statistik tahlili”, ToshDAU, 2016 y. (qo’llanma)
4. Zaysev “Vыsshaya matematika” Vыsshaya shkola M., 1991. (qo’llanma)

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