ВАРИАНТ № 12
Y |
110 |
130 |
150 |
170 |
190 |
210 |
230 |
250 |
mx |
X |
|
|
|
|
|
|
|
|
|
10 |
1 |
3 |
4 |
|
|
|
|
|
8 |
13 |
|
5 |
6 |
5 |
|
|
|
|
16 |
16 |
|
|
4 |
8 |
6 |
|
|
|
18 |
19 |
|
|
6 |
15 |
9 |
|
|
|
30 |
22 |
|
|
|
|
5 |
6 |
7 |
|
18 |
25 |
|
|
|
|
|
1 |
7 |
2 |
10 |
my |
1 |
8 |
20 |
28 |
20 |
7 |
14 |
2 |
100 |
|
|
|
ВАРИАНТ № 13 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
15-17 |
17-19 |
19-21 |
21-23 |
23-25 |
25-27 |
27-29 |
29-31 |
mx |
X |
|
|
|
|
|
|
|
|
|
2.1-2.5 |
3 |
2 |
4 |
|
|
|
|
|
9 |
2.5-2.9 |
|
5 |
6 |
1 |
|
|
|
|
12 |
2.9-3.3 |
|
|
6 |
9 |
4 |
|
|
|
19 |
3.3-3.7 |
|
|
|
8 |
16 |
7 |
|
|
31 |
3.7-4.1 |
|
|
|
|
8 |
6 |
5 |
|
19 |
4.1-4.5 |
|
|
|
|
|
4 |
5 |
1 |
10 |
my |
3 |
7 |
16 |
18 |
28 |
17 |
10 |
1 |
100 |
|
|
|
ВАРИАНТ № 14 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
12.5- |
15.5- |
18.5- |
21.5- |
24.5- |
27.5- |
30.5- |
33.5- |
mx |
X |
15.5 |
18.5 |
21.5 |
24.5 |
27.5 |
30.5 |
33.5 |
36.5 |
|
1.5-2.1 |
2 |
4 |
6 |
|
|
|
|
|
12 |
2.1-2.7 |
|
2 |
7 |
6 |
|
|
|
|
15 |
2.7-3.3 |
|
|
6 |
8 |
5 |
|
|
|
19 |
3.3-3.9 |
|
|
|
8 |
14 |
4 |
|
|
26 |
3.9-4.5 |
|
|
|
|
3 |
6 |
8 |
|
17 |
4.5-5.1 |
|
|
|
|
|
|
5 |
6 |
11 |
my |
2 |
6 |
19 |
22 |
22 |
10 |
13 |
6 |
100 |
|
|
|
ВАРИАНТ № 15 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
1200 |
2700 |
4200 |
6700 |
8200 |
9700 |
11200 |
12700 |
mx |
X |
|
|
|
|
|
|
|
|
|
20 |
4 |
2 |
5 |
|
|
|
|
|
11 |
520 |
|
|
7 |
5 |
2 |
|
|
|
14 |
1020 |
|
|
|
9 |
14 |
6 |
|
|
29 |
1520 |
|
|
|
7 |
8 |
6 |
|
|
21 |
2020 |
|
|
|
|
4 |
5 |
7 |
|
16 |
2520 |
|
|
|
|
|
3 |
2 |
4 |
9 |
my |
4 |
2 |
12 |
21 |
28 |
20 |
9 |
4 |
100 |
24
ВАРИАНТ № 16
Y |
400- |
500- |
600- |
700- |
800- |
900- |
1000- |
1100- |
mx |
|||||||
X |
500 |
600 |
700 |
800 |
900 |
1000 |
1100 |
1200 |
|
|||||||
40-180 |
|
|
|
|
|
|
|
|
|
2 |
5 |
3 |
10 |
|||
180-220 |
|
|
|
|
|
|
|
5 |
4 |
5 |
|
|
14 |
|||
220-260 |
|
|
|
|
|
15 |
5 |
7 |
|
|
|
|
27 |
|||
260-300 |
|
|
|
4 |
9 |
8 |
|
|
|
|
|
|
21 |
|||
300-340 |
|
4 |
5 |
7 |
|
|
|
|
|
|
|
|
16 |
|||
340-380 |
3 |
4 |
5 |
|
|
|
|
|
|
|
|
|
|
12 |
||
my |
3 |
8 |
14 |
31 |
18 |
13 |
10 |
3 |
100 |
|||||||
|
|
|
|
|
ВАРИАНТ № 17 |
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Y |
12000 |
12570 |
13140 |
13710 |
14280 |
14850 |
15420 |
15990 |
mx |
|||||||
X |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1500 |
1 |
6 |
4 |
|
|
|
|
|
|
|
|
|
|
11 |
||
1600 |
|
|
|
4 |
7 |
5 |
|
|
|
|
|
|
16 |
|||
1700 |
|
|
|
|
|
6 |
15 |
6 |
|
|
|
|
27 |
|||
1800 |
|
|
|
|
|
8 |
8 |
4 |
|
|
|
|
20 |
|||
1900 |
|
|
|
|
|
|
|
5 |
5 |
6 |
|
|
16 |
|||
2000 |
|
|
|
|
|
|
|
|
|
5 |
2 |
3 |
10 |
|||
my |
1 |
6 |
8 |
21 |
33 |
20 |
8 |
3 |
100 |
|||||||
|
|
|
|
|
ВАРИАНТ № 18 |
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Y |
120- |
140- |
160- |
180- |
200- |
220- |
240- |
260- |
mx |
|||||||
X |
140 |
160 |
180 |
200 |
220 |
240 |
260 |
280 |
|
|||||||
80-90 |
3 |
4 |
2 |
|
|
|
|
|
|
|
|
|
|
9 |
||
90-100 |
|
5 |
7 |
5 |
|
|
|
|
|
|
|
|
17 |
|||
100-110 |
|
|
|
|
|
8 |
14 |
6 |
|
|
|
|
28 |
|||
110-120 |
|
|
|
|
|
|
|
8 |
9 |
|
|
|
|
23 |
||
120-130 |
|
|
|
|
|
|
|
|
|
5 |
6 |
3 |
14 |
|||
130-140 |
|
|
|
|
|
|
|
|
|
|
|
5 |
4 |
9 |
||
my |
3 |
9 |
9 |
13 |
22 |
20 |
11 |
7 |
100 |
|||||||
|
|
|
|
|
ВАРИАНТ № 19 |
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
11.6- |
|
|
|
|
|
Y |
7.6-8.4 |
|
8.4- |
|
9.2- |
|
10.0- |
|
10.8- |
|
12.4- |
|
13.2- |
mx |
||
X |
|
|
9.2 |
|
10.0 |
|
10.8 |
|
11.6 |
|
12.4 |
|
13.2 |
|
14.0 |
|
115-125 |
5 |
|
6 |
|
|
|
|
|
|
|
|
|
|
|
|
11 |
125-135 |
|
|
3 |
|
4 |
|
6 |
|
|
|
|
|
|
|
|
13 |
135-145 |
|
|
|
|
4 |
|
5 |
|
6 |
|
7 |
|
|
|
|
15 |
145-155 |
|
|
|
|
|
|
6 |
|
13 |
|
|
|
|
|
26 |
|
155-165 |
|
|
|
|
|
|
|
|
|
|
6 |
|
9 |
|
5 |
20 |
165-175 |
|
|
|
|
|
|
|
|
|
|
13 |
|
7 |
|
8 |
15 |
my |
5 |
|
9 |
|
8 |
|
17 |
|
19 |
|
|
16 |
|
13 |
100 |
|
25
ВАРИАНТ № 20
Y |
7.5 |
8.0 |
8.5 |
9.0 |
9.5 |
10.0 |
10.5 |
11.0 |
mx |
X |
|
|
|
|
|
|
|
|
|
115 |
|
|
|
|
|
4 |
3 |
2 |
9 |
120 |
|
|
|
|
8 |
7 |
|
|
15 |
125 |
|
|
|
8 |
7 |
4 |
|
|
19 |
130 |
|
|
7 |
15 |
3 |
|
|
|
25 |
135 |
|
2 |
9 |
8 |
|
|
|
|
19 |
140 |
1 |
4 |
8 |
|
|
|
|
|
13 |
my |
1 |
6 |
24 |
31 |
18 |
15 |
3 |
2 |
100 |
|
|
|
ВАРИАНТ № 21 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
200- |
400- |
600- |
800- |
1000- |
1200- |
1400- |
1600- |
mx |
X |
400 |
600 |
800 |
1000 |
1200 |
1400 |
1600 |
1800 |
|
2.5-7.5 |
1 |
2 |
5 |
|
|
|
|
|
8 |
7.5-12.5 |
|
2 |
7 |
4 |
|
|
|
|
13 |
12.5-17.5 |
|
|
9 |
6 |
4 |
|
|
|
19 |
17.5-22.5 |
|
|
|
14 |
6 |
7 |
|
|
27 |
22.5-27.5 |
|
|
|
|
1 |
8 |
9 |
|
18 |
27.5-32.5 |
|
|
|
|
|
4 |
5 |
6 |
15 |
my |
1 |
4 |
21 |
24 |
11 |
19 |
14 |
6 |
100 |
|
|
|
ВАРИАНТ № 22 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
210- |
310- |
410- |
510- |
610- |
710- |
810- |
910- |
mx |
X |
310 |
410 |
510 |
610 |
710 |
810 |
910 |
1010 |
|
1-5 |
|
|
|
|
|
|
7 |
2 |
9 |
5-9 |
|
|
|
|
|
7 |
8 |
|
15 |
9-13 |
|
|
|
15 |
5 |
9 |
|
|
29 |
13-17 |
|
|
6 |
6 |
7 |
|
|
|
19 |
17-21 |
|
5 |
9 |
2 |
|
|
|
|
16 |
21-25 |
2 |
4 |
6 |
|
|
|
|
|
12 |
my |
2 |
9 |
21 |
23 |
12 |
16 |
15 |
2 |
100 |
|
|
|
ВАРИАНТ № 23 |
|
|
|
|
||
|
|
|
|
|
|
|
|
||
Y |
1435- |
1505- |
1575- |
1645- |
1715- |
1785- |
1855- |
1925- |
mx |
X |
1505 |
1575 |
1645 |
1715 |
1785 |
1855 |
1925 |
1995 |
|
205-215 |
3 |
2 |
3 |
|
|
|
|
|
8 |
215-225 |
|
1 |
4 |
5 |
|
|
|
|
10 |
225-235 |
|
|
7 |
13 |
8 |
|
|
|
28 |
235-245 |
|
|
|
|
9 |
6 |
6 |
|
21 |
245-255 |
|
|
|
|
|
7 |
8 |
3 |
18 |
255-265 |
|
|
|
|
|
4 |
6 |
5 |
15 |
my |
3 |
3 |
14 |
18 |
17 |
17 |
20 |
8 |
100 |
26
ВАРИАНТ № 24
Y |
2400 |
2440 |
2480 |
2520 |
2560 |
2600 |
2640 |
2680 |
mx |
X |
|
|
|
|
|
|
|
|
|
300 |
5 |
4 |
2 |
|
|
|
|
|
11 |
305 |
|
1 |
3 |
3 |
|
|
|
|
7 |
310 |
|
|
7 |
10 |
14 |
|
|
|
31 |
315 |
|
|
|
9 |
6 |
4 |
|
|
19 |
320 |
|
|
|
|
|
8 |
5 |
7 |
20 |
325 |
|
|
|
|
|
|
6 |
6 |
12 |
my |
5 |
5 |
12 |
22 |
20 |
12 |
11 |
13 |
100 |
|
|
|
ВАРИАНТ № 25 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
80- |
160- |
240- |
320- |
400- |
480- |
560- |
640- |
mx |
X |
160 |
240 |
320 |
400 |
480 |
560 |
640 |
720 |
|
8.5-12.5 |
4 |
5 |
2 |
|
|
|
|
|
11 |
12.5-16.5 |
|
6 |
7 |
5 |
|
|
|
|
18 |
16.5-20.5 |
|
|
6 |
8 |
14 |
|
|
|
28 |
20.5-24.5 |
|
|
|
|
12 |
9 |
2 |
|
23 |
24.5-28.5 |
|
|
|
|
6 |
4 |
|
|
10 |
28.5-32.5 |
|
|
|
|
|
5 |
3 |
2 |
10 |
my |
4 |
11 |
15 |
13 |
32 |
18 |
5 |
2 |
100 |
|
|
|
ВАРИАНТ № 26 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
235- |
375- |
425- |
475- |
525- |
575- |
625- |
675- |
mx |
X |
375 |
425 |
475 |
525 |
575 |
625 |
675 |
725 |
|
22-34 |
6 |
6 |
4 |
3 |
|
|
|
|
19 |
34-46 |
|
|
6 |
9 |
5 |
|
|
|
20 |
46-58 |
|
|
|
|
12 |
8 |
6 |
|
26 |
58-70 |
|
|
|
|
|
7 |
5 |
3 |
15 |
70-82 |
|
|
|
|
|
|
4 |
9 |
13 |
82-96 |
|
|
|
|
|
|
|
7 |
7 |
my |
6 |
6 |
10 |
12 |
17 |
15 |
15 |
19 |
100 |
|
|
|
ВАРИАНТ № 27 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
26-46 |
46-66 |
66-86 |
86- |
106- |
126- |
146- |
166- |
mx |
X |
|
|
|
106 |
126 |
146 |
166 |
186 |
|
4.6-6.2 |
6 |
4 |
4 |
|
|
|
|
|
14 |
6.2-7.8 |
|
8 |
7 |
2 |
|
|
|
|
17 |
7.8-9.4 |
|
|
3 |
8 |
9 |
|
|
|
20 |
9.4-11.0 |
|
|
|
16 |
5 |
8 |
|
|
29 |
11.0-12.6 |
|
|
|
|
|
6 |
5 |
|
11 |
12.6-14.2 |
|
|
|
|
|
4 |
3 |
2 |
9 |
my |
6 |
12 |
14 |
26 |
14 |
18 |
8 |
2 |
100 |
27
ВАРИАНТ № 28
Y |
18.5 |
19.7 |
20.9 |
22.1 |
23.3 |
24.5 |
25.7 |
26.9 |
mx |
X |
|
|
|
|
|
|
|
|
|
125 |
4 |
3 |
6 |
|
|
|
|
|
13 |
200 |
|
7 |
4 |
7 |
|
|
|
|
18 |
275 |
|
|
|
15 |
9 |
7 |
|
|
31 |
350 |
|
|
|
|
8 |
5 |
6 |
|
19 |
425 |
|
|
|
|
|
4 |
3 |
1 |
8 |
500 |
|
|
|
|
|
|
6 |
5 |
11 |
my |
4 |
10 |
10 |
22 |
17 |
16 |
15 |
6 |
100 |
|
|
|
ВАРИАНТ № 29 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
1.5- |
8.5- |
15.5- |
22.5- |
29.5- |
36.5- |
43.5- |
50.5- |
mx |
X |
8.5 |
15.5 |
22.5 |
29.5 |
36.5 |
43.5 |
50.5 |
57.5 |
|
0.47-0.61 |
5 |
3 |
2 |
2 |
|
|
|
|
12 |
0.61-0.75 |
|
4 |
8 |
9 |
4 |
|
|
|
25 |
0.75-0.89 |
|
|
|
|
17 |
9 |
6 |
|
32 |
0.89-1.03 |
|
|
|
|
1 |
6 |
5 |
|
12 |
1.03-1.17 |
|
|
|
|
|
6 |
3 |
2 |
11 |
1.17-1.31 |
|
|
|
|
|
|
4 |
4 |
8 |
my |
5 |
7 |
10 |
11 |
22 |
21 |
18 |
6 |
100 |
|
|
|
ВАРИАНТ № 30 |
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
Y |
0.33- |
0.83- |
1.33- |
1.83- |
2.33- |
2.83- |
3.33- |
3.88- |
mx |
X |
0.83 |
1.33 |
1.83 |
2.33 |
2.83 |
3.33 |
3.88 |
4.33 |
|
38-62 |
3 |
3 |
4 |
6 |
|
|
|
|
16 |
62-86 |
|
5 |
8 |
9 |
|
|
|
|
22 |
86-110 |
|
|
|
13 |
8 |
9 |
|
|
30 |
110-134 |
|
|
|
|
9 |
2 |
4 |
|
15 |
134-158 |
|
|
|
|
|
1 |
3 |
5 |
9 |
158-182 |
|
|
|
|
|
|
5 |
3 |
8 |
my |
3 |
8 |
12 |
28 |
17 |
12 |
12 |
8 |
100 |
28
Решение типового варианта
ЗАДАНИЕ 1. В результате эксперимента получена выборка из 100 чисел
24.8 |
26.2 |
25.6 |
24.0 |
26.4 |
25.2 |
26.7 |
25.4 |
25.3 |
26.1 |
24.3 |
25.3 |
25.6 |
26.7 |
24.5 |
26.0 |
25.7 |
25.0 |
26.4 |
25.9 |
24.4 |
25.4 |
26.1 |
23.4 |
26.5 |
25.9 |
23.9 |
25.7 |
27.1 |
24.9 |
23.8 |
25.6 |
25.2 |
26.4 |
24.2 |
26.5 |
25.7 |
24.7 |
26.0 |
25.8 |
24.3 |
25.5 |
26.7 |
24.9 |
26.2 |
26.7 |
24.6 |
26.0 |
25.4 |
25.0 |
25.4 |
25.3 |
24.1 |
26.6 |
24.8 |
25.6 |
23.7 |
26.8 |
25.2 |
26.1 |
24.5 |
25.4 |
25.1 |
26.2 |
24.2 |
26.4 |
25.7 |
23.9 |
27.2 |
25.0 |
23.9 |
25.6 |
24.9 |
24.5 |
26.2 |
26.7 |
24.3 |
26.1 |
27.7 |
25.8 |
25.6 |
25.2 |
24.2 |
26.0 |
24.7 |
26.5 |
23.5 |
25.4 |
27.1 |
24.0 |
26.2 |
24.2 |
25.5 |
26.0 |
25.7 |
26.4 |
24.6 |
27.0 |
25.2 |
26.9 |
1. Записываем числовые значения (варианты) в порядке возрастания, получим вариационный ряд
23.4 |
23.5 |
23.7 |
23.8 |
23.9 |
23.9 |
23.9 |
24.0 |
24.0 |
24.1 |
24.2 |
24.2 |
24.2 |
24.3 |
24.3 |
24.3 |
24.4 |
24.5 |
24.5 |
24.5 |
24.6 |
24.6 |
24.7 |
24.7 |
24.8 |
24.8 |
24.8 |
24.9 |
24.9 |
24.9 |
25.0 |
25.0 |
25.1 |
25.2 |
25.2 |
25.2 |
25.2 |
25.2 |
25.3 |
25.3 |
25.3 |
25.4 |
25.4 |
25.4 |
25.4 |
25.4 |
25.4 |
25.5 |
25.5 |
25.6 |
25.6 |
25.6 |
25.6 |
25.6 |
25.7 |
25.7 |
25.7 |
25.7 |
25.7 |
25.7 |
25.8 |
25.8 |
25.9 |
25.9 |
26.0 |
26.0 |
26.0 |
26.0 |
26.0 |
26.0 |
26.1 |
26.1 |
26.1 |
26.1 |
26.2 |
26.2 |
26.2 |
26.2 |
26.2 |
26.4 |
26.4 |
26.4 |
26.4 |
26.4 |
26.5 |
26.5 |
26.5 |
26.6 |
26.7 |
26.7 |
26.7 |
26.7 |
26.7 |
26.8 |
26.9 |
27.0 |
27.1 |
27.1 |
27.2 |
27.7 |
2. Находим размах вариации
xmax − xmin = 27.7 − 23.4 = 4.3;
оптимальное число интервалов
k=1 + 3.322 lg n =1 + 3.322 lg100 = 7.644 ≈8
идлину частичного интервала
|
h = |
xmax − xmin |
= |
4.3 |
= 0.54. |
|
|
|
|
|
|
||
|
|
8 |
|
|
|
|
|
|
|||||
|
|
|
8 |
|
|
|
|
|
|
|
|
||
Выпишем границы интервалов: *) |
|
|
|
|
|
|
|
|
|||||
a1 = 23.4; |
a2 = 23.94; |
a3 = 24.48; |
a4 = 25.02; |
a5 = 25.56; |
|
|
|
||||||
a6 = 26.10; |
a7 = 26.64; |
a8 = 27.18; |
a9 = 27.72. |
|
|
|
|
h |
|
||||
*) Отметим другой способ построения интервалов: |
a |
= x |
min |
− |
, |
||||||||
|
|||||||||||||
|
|
|
|
|
|
|
1 |
|
2 |
|
|||
a2 = a1 +h , a3 = a2 +h , и |
|
|
|
|
|
|
|
|
|||||
т.д.. При |
этом последний |
интервал |
|||||||||||
“накроет” xmax .
29