xi 2 1 3 6
ni 12
11 17 10
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 4 1 9
ni 12
30 18
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 6
wi 0 ,24
9
0 ,32
10
0 ,16
13
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
|
xi 1 xi
|
ni
|
ni h
|
1
2
3
4
5
6
7
|
3-7
7-11
11-15
15-19
19-23
23-27
27-31
|
4
12
20
28
16
6
4
|
1
3
5
7
4
1,5
1
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
8 14 18 24
16 10 9 15
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
8, 16,
42,
76,
108,
44,
18, 10
Nazariy chastotalar:
ni :
9, 18,
44,
96 ,
98,
46 ,
16 , 8
H0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plam normal taqsimlangan deb faraz qilib, n=200 hajmli tanlanmaning, bir xil uzunlikdagi intervallar ketma-ketligiva 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
|
11
|
8
|
2
|
11
|
15
|
16
|
3
|
15
|
19
|
28
|
4
|
19
|
23
|
22
|
5
|
23
|
27
|
38
|
6
|
27
|
31
|
34
|
7
|
31
|
35
|
18
|
8
|
35
|
39
|
14
|
9
|
39
|
43
|
12
|
variant 1.Tanlanma taqsimot berilgan:
xi 8
ni 14
15 18 20
12 10 14
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 2 4 8
ni 25 50 25
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2,5
wi 0 ,27
3,5
0 ,28
5 ,5
0 ,33
8
0 ,12
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini 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
|
(-4)-2
2-8
8-14
14-20
20-26
26-32
32-38
|
6
9
15
36
21
9
4
|
1
1,5
2,5
6
3,5
1,5
2/3
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
9 13
8 16
16 29
12 14
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
6 , 15,
40,
74,
106 ,
38,
14, 8
Nazariy chastotalar:
ni :
6 , 16 ,
38,
94,
96 ,
36 ,
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-ketligiva 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
|
3
|
7
|
9
|
2
|
7
|
11
|
12
|
3
|
11
|
15
|
30
|
4
|
15
|
19
|
24
|
5
|
19
|
23
|
38
|
6
|
23
|
27
|
45
|
7
|
27
|
31
|
17
|
8
|
31
|
35
|
12
|
9
|
35
|
39
|
8
|
variant 1.Tanlanma taqsimot berilgan:
xi 5 7
ni 13 14
9 12
11 12
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 5 2 7
ni 12
28 40
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2
wi 0 ,21
4
0 ,24
6
0 ,16
9
0 ,39
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
|
(-3)-0
|
6
|
2
|
2
|
0-3
|
12
|
3
|
3
|
3-6
|
15
|
5
|
4
|
6-9
|
24
|
8
|
5
6
7
|
9-12
12-15
15-18
|
21
15
7
|
7
5
7/3
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
12 15 18 24
14 10 12 14
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
8, 16 ,
42,
76,
99,
38,
18, 10
Nazariy chastotalar:
ni :
8, 18,
44,
90,
92,
40,
16 , 9
H0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plam normal taqsimlangan deb faraz qilib, n=200 hajmli tanlanmaning, bir xil uzunlikdagi intervallar ketma-ketligiva 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
|
4
|
6
|
7
|
2
|
6
|
8
|
13
|
3
|
8
|
10
|
25
|
4
|
10
|
12
|
45
|
5
|
12
|
14
|
39
|
6
|
14
|
16
|
23
|
7
|
16
|
18
|
32
|
8
|
18
|
20
|
19
|
9
|
20
|
22
|
6
|
variant 1.Tanlanma taqsimot berilgan:
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