xi 1 4
ni 9 16
6 9
15 10
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 6
ni 16
9 14
40 24
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 3
wi 0 ,19
6
0 ,27
10
0 ,33
14
0 ,21
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
|
4-7
7-10
10-13
13-16
16-19
19-22
22-15
|
6
9
15
21
18
12
9
|
2
3
5
7
6
4
3
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
12 15 18 22
10 14 12 14
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
5, 12,
38,
94,
100,
42,
18, 10
Nazariy chastotalar:
ni :
8, 16 ,
40,
96 ,
98,
46 ,
10, 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
|
5
|
9
|
10
|
2
|
9
|
13
|
15
|
3
|
13
|
17
|
32
|
4
|
17
|
21
|
39
|
5
|
21
|
25
|
45
|
6
|
25
|
29
|
26
|
7
|
29
|
33
|
24
|
8
|
33
|
37
|
16
|
9
|
37
|
41
|
3
|
variant 1.Tanlanma taqsimot berilgan:
xi 4 7 8 11
ni 11 15 14 10
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 7
ni 12
10 15
24 24
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 5
wi 0 ,24
8
0 ,23
10
0 ,17
13
0 ,36
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
|
2-8
8-14
|
9
15
|
1,5
2,5
|
3
4
5
6
7
|
14-20
20-26
26-32
32-38
38-44
|
18
24
18
12
4
|
3
4
3
2
2/3
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
15 18 20 24
12 11 14 13
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
14,
20,
42,
96,
102,
52,
22, 16
Nazariy chastotalar:
ni :
12,
24,
48,
98,
104,
44,
20, 14
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
|
8
|
10
|
9
|
2
|
10
|
12
|
21
|
3
|
12
|
14
|
19
|
4
|
14
|
16
|
34
|
5
|
16
|
18
|
38
|
6
|
18
|
20
|
41
|
7
|
20
|
22
|
18
|
8
|
22
|
24
|
12
|
9
|
24
|
26
|
8
|
variant 1.Tanlanma taqsimot berilgan:
xi 5 8 9 12
ni 8 15 17 10
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 8
ni 15
12 16
50 35
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 4 ,5
wi 0 ,1
6
0 ,3
7 ,5
0 ,4
8
0 ,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
2
3
4
5
6
7
|
4-6
6-8
8-10
10-12
12-14
14-16
16-18
|
8
12
16
18
16
12
10
|
4
6
7
9
8
6
5
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taqsi- moti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
8 12 16 20
14 11 10 15
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
10,
16 ,
40,
95,
108,
42,
23, 12
Nazariy chastotalar:
ni :
10,
18,
42,
96 ,
98,
46 ,
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
|
xi1
|
h i
|
1
|
5
|
8
|
7
|
2
|
8
|
11
|
18
|
3
|
11
|
14
|
35
|
4
|
14
|
17
|
38
|
5
|
17
|
20
|
39
|
6
|
20
|
23
|
21
|
7
|
23
|
26
|
25
|
8
|
26
|
29
|
13
|
9
|
29
|
32
|
14
|
variant 1.Tanlanma taqsimot berilgan:
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