ni 14
6 9 11
12 11 13
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 1 5 8
ni 12 28 20
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2,5
wi 0 ,1
4
0 ,4
5 ,5
0 ,3
8
0 ,2
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
|
1-3
|
4
|
2
|
2
|
3-5
|
8
|
4
|
3
|
5-7
|
10
|
5
|
4
|
7-9
|
16
|
8
|
5
|
9-11
|
12
|
6
|
6
|
11-13
|
6
|
3
|
7
|
13-15
|
4
|
2
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
7 10 15 21
14 12 14 10
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
10,
14,
36,
92,
86 ,
42,
21, 14
Nazariy chastotalar:
ni :
12,
16 ,
42,
94,
92,
38,
18, 13
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
|
5
|
13
|
2
|
5
|
8
|
26
|
3
|
8
|
11
|
20
|
4
|
11
|
14
|
36
|
5
|
14
|
17
|
32
|
6
|
17
|
20
|
28
|
7
|
20
|
23
|
25
|
8
|
23
|
26
|
12
|
9
|
26
|
29
|
8
|
variant 1.Tanlanma taqsimot berilgan:
xi 6 7
ni 12 15
9 12
13 10
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 3
wi 0 ,22
5
0 ,26
7
0 ,24
9
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
|
3-8
8-13
13-18
18-23
23-28
28-33
33-38
|
8
14
20
25
15
12
6
|
1,6
2,8
4
5
3
2,4
1,4
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
4 11 15 19
12 14 12 12
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
12,
16,
42,
98,
104,
46 ,
18, 10
Nazariy chastotalar:
ni :
11,
18,
44,
98,
99,
42,
16 , 10
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
|
6
|
6
|
2
|
6
|
10
|
25
|
3
|
10
|
14
|
24
|
4
|
14
|
18
|
32
|
5
|
18
|
22
|
36
|
6
7
8
9
|
22
26
30
34
|
26
30
34
38
|
30
20
22
5
|
variant 1.Tanlanma taqsimot berilgan:
xi 2
ni 10
6 7 11
15 15 10
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 4 7 9
ni 12 40 28
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2,4
wi 0 ,18
5
0 ,34
6 ,6
0 ,26
8
0 ,22
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
|
3-7
|
8
|
2
|
2
|
7-11
|
14
|
3,5
|
3
|
11-15
|
16
|
4
|
4
|
15-19
|
22
|
5,5
|
5
|
19-23
|
18
|
4,5
|
6
|
23-27
|
12
|
3
|
7
|
27-31
|
10
|
2,5
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
5 7 10 16
15 10 11 14
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
8, 14,
40,
96 ,
106,
48,
16 , 12
Nazariy chastotalar:
ni :
8, 16 ,
42,
98,
96 ,
44,
15, 9
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
|
4
|
7
|
8
|
2
|
7
|
10
|
18
|
3
|
10
|
13
|
30
|
4
|
13
|
16
|
26
|
5
|
16
|
19
|
38
|
6
|
19
|
22
|
40
|
7
|
22
|
25
|
26
|
8
|
25
|
28
|
8
|
9
|
28
|
31
|
6
|
variant 1.Tanlanma taqsimot berilgan:
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