xi 3 8 9 12
ni 11 14 14 11
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2
wi 0 ,17
4 ,5
0 ,18
7 ,5
4 ,2
9
0 ,23
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini yasang:
i
|
xi 1 xi
|
ni
|
ni h
|
1
2
3
4
5
6
7
|
5-10
10-15
15-20
20-25
25-30
30-35
35-40
|
5
7
16
26
14
8
6
|
1
1,4
3,2
5,2
2,8
1,6
1,2
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
14 17 18 20
10 12 14 14
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
8, 13,
36 ,
82,
96 ,
40,
23, 10
Nazariy chastotalar:
ni :
9, 14,
38,
94,
96 ,
40,
20, 11
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
2
3
|
6
10
14
|
10
14
18
|
11
19
28
|
4
5
6
7
8
9
|
18
22
26
30
34
38
|
22
26
30
34
38
42
|
24
42
31
22
14
9
|
variant 1.Tanlanma taqsimot berilgan:
xi 7 9 12 15
ni 13 12 15 10
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 5
ni 24
9 14
36 40
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2,5
wi 0 ,32
6
0 ,26
9
1,4
11,5
0 ,28
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini yasang:
Interval nomeri
|
Qismiy interval
|
Intervaldagi va- riantalar chasto- talari yig‗indisi
|
Chastota zichligi
|
i
|
xi1 xi
|
ni
|
ni h
|
1
2
3
4
5
6
7
|
4-8
8-12
12-16
16-20
20-24
24-28
28-32
|
6
10
16
24
18
16
10
|
1,5
2,5
4
6
4,5
4
2,5
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
10 15 18 2
14 11 12 13
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
6 , 14,
38,
86 ,
104,
39,
24, 12
Nazariy chastotalar:
ni :
8, 16 ,
39,
96 ,
98,
38,
14, 6
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
|
7
|
9
|
12
|
2
|
9
|
11
|
19
|
3
|
11
|
13
|
26
|
4
|
13
|
15
|
24
|
5
|
15
|
17
|
42
|
6
|
17
|
19
|
34
|
7
|
19
|
21
|
26
|
8
|
21
|
23
|
8
|
9
|
23
|
25
|
9
|
variant 1.Tanlanma taqsimot berilgan:
xi 1 4
ni 9 16
6 9
14 11
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 2 6 9
ni 16 60 24
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 4
wi 0 ,28
7
0 ,22
9
0 ,18
13
3,2
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
|
6-9
|
9
|
3
|
2
|
9-12
|
15
|
5
|
3
|
12-15
|
18
|
6
|
4
|
15-18
|
24
|
8
|
5
|
18-21
|
15
|
5
|
6
|
21-24
|
12
|
4
|
7
|
24-27
|
3
|
1
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
9 12 16 20
12 13 12 13
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
9, 15,
39,
78,
106 ,
85,
32, 12
Nazariy chastotalar:
ni :
9, 16 ,
42,
94,
98,
50,
18, 11
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
|
7
|
10
|
10
|
2
|
10
|
13
|
23
|
3
|
13
|
16
|
14
|
4
|
16
|
19
|
28
|
5
|
19
|
22
|
39
|
6
|
22
|
25
|
36
|
7
|
25
|
28
|
24
|
8
|
28
|
31
|
14
|
9
|
31
|
34
|
12
|
variant 1.Tanlanma taqsimot berilgan:
xi 8
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