ni 10
7 8 10
15 13 12
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 2 5 8
ni 18 30 12
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 1,8
wi 0 ,14
2,7
0 ,2
3,1
0 ,4
4 ,5
0 ,26
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini yasang:
Interval nomeri
|
Qismiy interval
|
Intervaldagi va- riantalar chasto- talari yig‗indisi
|
Chastota zichligi
|
i
|
xi 1 xi
|
ni
|
ni h
|
1
2
3
|
5-10
10-15
15-20
|
5
10
20
|
1
2
4
|
4
5
6
7
|
20-25
25-30
30-35
35-40
|
25
20
15
5
|
5
4
3
1
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
5 9 13 17
16 12 10 12
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
10,
16 ,
28,
92,
98,
43,
30, 12
Nazariy chastotalar:
ni :
11,
18,
34,
98,
98,
40,
17 , 10
H0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plamni normal taqsimlangan deb faraz qilib, n=200 haj- mli tanlanmaning bir xil uzunlikdagi intervallar ketma-ketligi va ular- ga mos chastotalar ko‗rinishida berilgan еmpirik taqsimoti bo‗yicha nazariy chastotalarini toping.
Interval nomeri
|
Interval uchlari
|
Chastotalar
|
i
|
xi
|
xi 1
|
hi
|
1
|
6
|
8
|
15
|
2
|
8
|
10
|
25
|
3
|
10
|
12
|
23
|
4
|
12
|
14
|
34
|
5
|
14
|
16
|
36
|
6
|
16
|
18
|
22
|
7
|
18
|
20
|
19
|
8
|
20
|
22
|
16
|
9
|
22
|
24
|
10
|
variant 1.Tanlanma taqsimot berilgan:
xi 2 5 7 10
ni 11 14 14 11
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 6
ni 14
9 14
20 16
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2,3
wi 0 ,2
4
0 ,32
6 ,2
0 ,3
8
0 ,18
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini yasang:
Interval nomeri
|
Qismiy interval
|
Intervaldagi va- riantalar chasto- talari yig‗indisi
|
Chastota zichligi
|
i
|
xi 1 xi
|
ni
|
ni h
|
1
2
3
4
5
6
7
|
2-6
6-10
10-14
14-18
18-22
22-26
26-30
|
4
10
16
20
18
12
10
|
1
2,5
4
5
4,5
3
2,5
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
3 5
8 11
10 17
16 15
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
6 , 12,
24,
81,
110,
82,
30, 14
Nazariy chastotalar:
ni :
6 , 14,
40,
96 ,
99,
68,
20, 12
H0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plam normal taqsimlangan deb faraz qilib, n=200 hajmli tanlanmaning, bir xil uzunlikdagi intervallar ketma-ketligi va ularga mos chastotalar ko‗rinishida berilgan еmpirik taqsimoti bo‗yicha na- zariy chastotalarini toping.
Interval nomeri
|
Interval uchlari
|
Chastotalar
|
i
|
xi
|
xi1
|
h i
|
1
|
3
|
6
|
12
|
2
|
6
|
9
|
26
|
3
|
9
|
12
|
24
|
4
|
12
|
15
|
35
|
5
|
15
|
18
|
33
|
6
|
18
|
21
|
26
|
7
|
21
|
24
|
22
|
8
|
24
|
27
|
16
|
9
|
27
|
30
|
6
|
variant 1.Tanlanma taqsimot berilgan:
xi 3 6
ni 12 14
7 9
13 11
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 5
ni 15
8 12
20 15
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chastota- lar poligonini yasang:
xi 3
wi 0 ,1
5
0 ,4
8
0 ,3
11
0 ,2
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gis- togrammasini yasang:
Interval nomeri
|
Qismiy interval
|
Intervaldagi variantalar chastotalari yig‗indisi
|
Chastota zichligi
|
i
|
xi 1 xi
|
ni
|
ni h
|
1
2
3
4
5
6
7
|
2-5
5-8
8-11
11-14
14-17
17-20
20-23
|
3
6
12
18
12
6
3
|
1
2
4
6
4
2
1
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
11 13 7 18
11 12 17 13
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
4, 12,
38,
76 ,
108,
84,
32, 13
Nazariy chastotalar:
ni :
6 , 14,
42,
86 ,
98,
67 ,
35, 12
H0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plam normal taqsimlangan deb faraz qilib, n=200 hajmli tanlanmaning, bir xil uzunlikdagi intervallar ketma-ketligi va ularga mos chastotalar ko‗rinishida berilgan еmpirik taqsimoti bo‗yicha na- zariy chastotalarini toping.
Interval nomeri
|
Interval uchlari
|
Chastotalar
|
i
|
xi
|
xi 1
|
hi
|
1
|
1
|
3
|
14
|
2
|
3
|
6
|
28
|
3
|
6
|
9
|
21
|
4
|
9
|
12
|
34
|
5
|
12
|
15
|
34
|
6
|
15
|
16
|
24
|
7
|
16
|
19
|
23
|
8
|
19
|
22
|
14
|
9
|
22
|
25
|
8
|
variant 1.Tanlanma taqsimot berilgan:
xi 4
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