ГОСТ Р ИСО 16269-8-2005 Статистические методы. Статистическое представление данных. Определение предикционных интервалов (Переиздание)

1

2

3

4

5

6

7

8

9

10

15

2

3,770

6,058

7,595

8,730

9,620

10,345

10,954

11,476

11,932

12,335

13,844

3

2,178

3,066

3,615

4,010

4,316

4,566

4,775

4,955

5,112

5,252

5,778

4

1,832

2,484

2,873

3,150

3,364

3,538

3,684

3,810

3,919

4,017

4,386

5

1,680

2,240

2,567

2,798

2,976

3,120

3,241

3,345

3,436

3,517

3,824

6

1,595

2,106

2,400

2,606

2,765

2,893

3,001

3,094

3,175

3,247

3,520

7

1,540

2,020

2,294

2,485

2,632

2,751

2,850

2,935

3,010

3,076

3,328

8

1,501

1,961

2,221

2,402

2,540

2,652

2,746

2,826

2,897

2,959

3,196

9

1,473

1,918

2,168

2,341

2,474

2,580

2,670

2,747

2,814

2,873

3,099

10

1,451

1,885

2,127

2,295

2,422

2,525

2,612

2,686

2,750

2,808

3,025

11

1,434

1,858

2,095

2,258

2,382

2,482

2,566

2,637

2,700

2,756

2,967

12

1,420

1,837

2,069

2,228

2,349

2,447

2,529

2,599

2,660

2,714

2,919

13

1,408

1,820

2,047

2,204

2,322

2,418

2,498

2,566

2,626

2,679

2,880

14

1,398

1,805

2,029

2,183

2,300

2,394

2,472

2,539

2,598

2,650

2,847

15

1,390

1,792

2,013

2,165

2,280

2,373

2,450

2,516

2,574

2,625

2,818

16

1,382

1,781

2,000

2,150

2,264

2,355

2,431

2,496

2,553

2,604

2,794

17

1,376

1,772

1,989

2,137

2,249

2,339

2,415

2,479

2,535

2,585

2,773

18

1,370

1,763

1,978

2,125

2,236

2,326

2,400

2,464

2,519

2,568

2,754

19

1,365

1,756

1,969

2,115

2,225

2,313

2,387

2,450

2,505

2,554

2,737

20

1,361

1,749

1,961

2,106

2,215

2,303

2,376

2,438

2,492

2,541

2,723

25

1,344

1,725

1,931

2,071

2,177

2,262

2,333

2,393

2,445

2,492

2,667

30

1,334

1,709

1,911

2,049

2,153

2,236

2,305

2,363

2,415

2,460

2,631

35

1,326

1,697

1,898

2,033

2,136

2,217

2,285

2,343

2,393

2,438

2,605

40

1,320

1,689

1,887

2,022

2,123

2,204

2,270

2,328

2,377

2,421

2,586

45

1,316

1,683

1,880

2,013

2,113

2,193

2,259

2,316

2,365

2,408

2,572

50

1,312

1,678

1,873

2,006

2,105

2,185

2,250

2,306

2,355

2,398

2,560

60

1,307

1,670

1,864

1,995

2,094

2,172

2,237

2,292

2,341

2,383

2,543

70

1,304

1,664

1,857

1,988

2,085

2,163

2,228

2,282

2,330

2,372

2,530

80

1,301

1,660

1,853

1,982

2,079

2,156

2,221

2,275

2,322

2,364

2,521

90

1,299

1,657

1,849

1,978

2,074

2,151

2,215

2,269

2,316

2,358

2,514

100

1,297

1,655

1,846

1,974

2,071

2,147

2,211

2,265

2,312

2,353

2,508

150

1,292

1,647

1,837

1,964

2,059

2,135

2,198

2,251

2,297

2,338

2,491

200

1,290

1,644

1,832

1,959

2,054

2,129

2,191

2,244

2,290

2,331

2,483

250

1,288

1,641

1,829

1,956

2,050

2,125

2,188

2,240

2,286

2,327

2,478

300

1,287

1,640

1,828

1,954

2,048

2,123

2,185

2,238

2,283

2,324

2,475

350

1,286

1,639

1,826

1,952

2,047

2,121

2,183

2,236

2,281

2,322

2,472

400

1,286

1,638

1,825

1,951

2,045

2,120

2,182

2,234

2,280

2,320

2,470

450

1,285

1,638

1,825

1,950

2,044

2,119

2,181

2,233

2,279

2,319

2,469

500

1,285

1,637

1,824

1,950

2,044

2,118

2,180

2,232

2,278

2,318

2,468

600

1,285

1,636

1,823

1,949

2,043

2,117

2,179

2,231

2,276

2,316

2,466

700

1,284

1,636

1,823

1,948

2,042

2,116

2,178

2,230

2,275

2,315

2,465

800

1,284

1,635

1,822

1,947

2,041

2,116

2,177

2,229

2,275

2,315

2,464

900

1,284

1,635

1,822

1,947

2,041

2,115

2,176

2,229

2,274

2,314

2,463

1000

1,284

1,635

1,821

1,947

2,040

2,115

2,176

2,228

2,274

2,314

2,463

1,282

1,633

1,819

1,944

2,037

2,111

2,172

2,224

2,269

2,309

2,458

20

30

40

50

60

80

100

150

200

250

500

2

14,870

16,249

17,183

17,884

18,442

19,297

19,940

21,068

21,838

22,421

24,153

3

6,139

6,631

6,967

7,221

7,424

7,737

7,973

8,390

8,676

8,894

9,542

4

4,640

4,988

5,227

5,408

5,553

5,777

5,946

6,246

6,453

6,610

7,079

5

4,036

4,326

4,526

4,678

4,800

4,988

5,131

5,384

5,559

5,691

6,089

6

3,708

3,968

4,146

4,282

4,391

4,560

4,689

4,916

5,073

5,192

5,551

7

3,502

3,741

3,907

4,032

4,134

4,290

4,409

4,620

4,766

4,877

5,210

8

3,360

3,585

3,741

3,860

3,955

4,103

4,215

4,415

4,553

4,658

4,974

9

3,256

3,471

3,620

3,733

3,824

3,965

4,073

4,264

4,396

4,497

4,799

10

3,176

3,383

3,526

3,635

3,723

3,859

3,963

4,147

4,275

4,372

4,665

11

3,112

3,313

3,452

3,558

3,643

3,775

3,876

4,055

4,179

4,273

4,557

12

3,061

3,257

3,392

3,495

3,578

3,707

3,805

3,979

4,100

4,192

4,470

13

3,019

3,210

3,342

3,443

3,524

3,650

3,746

3,916

4,035

4,125

4,397

14

2,983

3,170

3,300

3,399

3,478

3,602

3,696

3,863

3,979

4,068

4,334

15

2,952

3,136

3,264

3,361

3,439

3,560

3,653

3,817

3,932

4,019

4,281

16

2,926

3,107

3,232

3,328

3,405

3,525

3,616

3,778

3,890

3,976

4,235

17

2,903

3,081

3,205

3,299

3,375

3,493

3,583

3,743

3,854

3,938

4,194

18

2,882

3,059

3,181

3,274

3,349

3,465

3,554

3,712

3,822

3,905

4,158

19

2,864

3,039

3,160

3,252

3,326

3,441

3,529

3,685

3,793

3,876

4,125

20

2,848

3,021

3,140

3,231

3,305

3,419

3,506

3,660

3,767

3,849

4,096

25

2,788

2,954

3,068

3,156

3,226

3,335

3,419

3,567

3,670

3,749

3,986

30

2,748

2,910

3,021

3,106

3,174

3,280

3,361

3,505

3,605

3,682

3,912

35

2,721

2,878

2,988

3,071

3,137

3,241

3,320

3,461

3,559

3,634

3,859

40

2,700

2,855

2,963

3,044

3,110

3,212

3,290

3,428

3,524

3,597

3,819

45

2,684

2,837

2,943

3,024

3,089

3,189

3,266

3,402

3,497

3,569

3,788

50

2,671

2,823

2,928

3,008

3,072

3,171

3,247

3,382

3,475

3,547

3,762

60

2,652

2,802

2,905

2,983

3,046

3,144

3,218

3,351

3,442

3,513

3,724

70

2,639

2,787

2,888

2,966

3,028

3,124

3,198

3,328

3,419

3,488

3,697

80

2,629

2,775

2,876

2,953

3,014

3,110

3,183

3,312

3,401

3,470

3,676

90

2,621

2,766

2,867

2,943

3,004

3,099

3,171

3,299

3,388

3,455

3,660

100

2,615

2,759

2,859

2,935

2,995

3,090

3,161

3,288

3,376

3,444

3,647

150

2,596

2,738

2,836

2,911

2,970

3,062

3,133

3,257

3,343

3,409

3,607

200

2,587

2,728

2,825

2,898

2,957

3,049

3,118

3,241

3,327

3,392

3,587

250

2,581

2,722

2,818

2,891

2,950

3,041

3,110

3,232

3,317

3,381

3,575

300

2,577

2,718

2,814

2,886

2,945

3,035

3,104

3,226

3,310

3,374

3,567

350

2,575

2,715

2,810

2,883

2,941

3,031

3,100

3,221

3,305

3,369

3,561

400

2,573

2,712

2,808

2,880

2,939

3,029

3,097

3,218

3,302

3,365

3,557

450

2,571

2,711

2,806

2,878

2,936

3,026

3,094

3,215

3,299

3,362

3,554

500

2,570

2,709

2,805

2,877

2,935

3,024

3,092

3,213

3,296

3,360

3,551

600

2,568

2,707

2,802

2,874

2,932

3,022

3,090

3,210

3,293

3,356

3,547

700

2,567

2,706

2,801

2,873

2,931

3,020

3,088

3,208

3,291

3,354

3,544

800

2,566

2,705

2,800

2,871

2,929

3,018

3,086

3,206

3,289

3,352

3,542

900

2,565

2,704

2,799

2,870

2,928

3,017

3,085

3,205

3,288

3,351

3,540

1000

2,565

2,703

2,798

2,870

2,927

3,016

3,084

3,204

3,286

3,349

3,539

2,559

2,697

2,791

2,862

2,920

3,008

3,075

3,194

3,276

3,339

3,527

1000

2000

5000

10000

20000

50000

100000

200000

500000

1000000

2

25,783

27,327

29,256

30,642

31,972

33,657

34,882

36,068

37,583

38,692

3

10,157

10,741

11,473

12,000

12,508

13,152

13,620

14,074

14,655

15,080

4

7,525

7,949

8,483

8,867

9,238

9,709

10,051

10,384

10,809

11,120

5

6,467

6,828

7,281

7,609

7,925

8,326

8,618

8,902

9,264

9,530

6

5,892

6,218

6,628

6,925

7,211

7,574

7,839

8,096

8,425

8,667

7

5,528

5,832

6,215

6,491

6,758

7,098

7,345

7,586

7,893

8,119

8

5,275

5,564

5,927

6,190

6,444

6,767

7,002

7,231

7,523

7,738

9

5,088

5,365

5,714

5,967

6,211

6,521

6,748

6,968

7,249

7,456

10

4,944

5,212

5,550

5,795

6,031

6,332

6,551

6,764

7,037

7,238

11

4,829

5,090

5,419

5,657

5,887

6,180

6,394

6,602

6,868

7,063

12

4,735

4,990

5,311

5,544

5,769

6,056

6,265

6,468

6,729

6,920

13

4,657

4,906

5,221

5,450

5,671

5,952

6,157

6,357

6,612

6,800

14

4,590

4,835

5,145

5,370

5,587

5,863

6,065

6,261

6,513

6,697

15

4,532

4,774

5,079

5,300

5,514

5,787

5,986

6,179

6,427

6,609

16

4,482

4,721

5,022

5,240

5,451

5,720

5,917

6,108

6,352

6,532

17

4,439

4,674

4,971

5,187

5,395

5,661

5,856

6,044

6,286

6,464

18

4,400

4,632

4,926

5,139

5,346

5,609

5,801

5,988

6,228

6,404

19

4,365

4,595

4,886

5,097

5,302

5,562

5,753

5,938

6,175

6,349

20

4,333

4,561

4,850

5,059

5,262

5,520

5,709

5,892

6,128

6,300

25

4,214

4,433

4,711

4,913

5,109

5,358

5,540

5,718

5,945

6,112

30

4,134

4,347

4,618

4,814

5,005

5,248

5,426

5,599

5,821

5,984

35

4,076

4,285

4,550

4,742

4,929

5,167

5,342

5,512

5,729

5,889

40

4,032

4,237

4,498

4,687

4,871

5,106

5,278

5,445

5,659

5,817

45

3,998

4,200

4,457

4,644

4,825

5,057

5,227

5,392

5,604

5,759

50

3,970

4,170

4,424

4,609

4,788

5,017

5,185

5,348

5,558

5,712

60

3,928

4,124

4,373

4,555

4,731

4,956

5,121

5,281

5,487

5,639

70

3,897

4,091

4,336

4,515

4,689

4,911

5,073

5,232

5,435

5,585

80

3,874

4,065

4,308

4,485

4,657

4,876

5,037

5,194

5,395

5,543

90

3,856

4,046

4,286

4,461

4,631

4,849

5,008

5,163

5,363

5,510

100

3,842

4,029

4,268

4,442

4,610

4,826

4,984

5,138

5,336

5,482

150

3,797

3,980

4,213

4,382

4,546

4,756

4,910

5,060

5,253

5,395

200

3,775

3,955

4,184

4,351

4,513

4,719

4,871

5,019

5,209

5,349

250

3,761

3,940

4,167

4,332

4,492

4,697

4,847

4,993

5,181

5,319

300

3,752

3,930

4,155

4,319

4,478

4,681

4,830

4,975

5,162

5,299

350

3,746

3,923

4,147

4,310

4,468

4,670

4,818

4,962

5,148

5,284

400

3,741

3,917

4,141

4,303

4,461

4,662

4,809

4,953

5,137

5,273

450

3,737

3,913

4,136

4,298

4,455

4,655

4,802

4,945

5,129

5,264

500

3,734

3,910

4,132

4,293

4,450

4,650

4,796

4,939

5,122

5,257

600

3,729

3,904

4,126

4,287

4,443

4,642

4,788

4,930

5,112

5,246

700

3,726

3,901

4,122

4,282

4,438

4,636

4,781

4,923

5,105

5,239

800

3,724

3,898

4,118

4,279

4,434

4,632

4,777

4,918

5,099

5,233

900

3,722

3,896

4,116

4,276

4,431

4,628

4,773

4,914

5,095

5,228

1000

3,720

3,894

4,114

4,274

4,428

4,626

4,770

4,911

5,091

5,224

3,706

3,878

4,096

4,254

4,406

4,601

4,743

4,882

5,060

5,190

Примечание - В таблице приведены такие значения коэффициента , которые позволяют с уровнем доверия не менее 90% быть уверенным, что ни одно наблюдение из будущей выборки объема из  нормальной совокупности не будет лежать вне интервала , где и определены по выборке размера из той же совокупности. Аналогично для интервала .

1

2

3

4

5

6

7

8

9

10

15

2

7,733

12,253

15,309

17,572

19,347

20,794

22,01

23,053

23,964

24,770

27,786

3

3,372

4,572

5,328

5,876

6,303

6,652

6,946

7,198

7,420

7,616

8,359

4

2,632

3,402

3,871

4,209

4,472

4,687

4,868

5,024

5,161

5,282

5,744

5

2,336

2,952

3,321

3,584

3,788

3,955

4,096

4,217

4,323

4,418

4,779

6

2,177

2,716

3,033

3,259

3,434

3,576

3,696

3,800

3,891

3,972

4,280

7

2,078

2,570

2,857

3,061

3,218

3,345

3,453

3,546

3,627

3,700

3,976

8

2,010

2,472

2,738

2,927

3,072

3,190

3,289

3,374

3,449

3,516

3,771

9

1,961

2,400

2,653

2,830

2,967

3,077

3,171

3,251

3,321

3,384

3,623

10

1,923

2,346

2,588

2,757

2,887

2,993

3,081

3,158

3,225

3,285

3,512

11

1,894

2,304

2,537

2,700

2,825

2,927

3,012

3,085

3,149

3,207

3,424

12

1,870

2,270

2,497

2,655

2,776

2,874

2,956

3,027

3,089

3,144

3,354

13

1,850

2,242

2,463

2,617

2,735

2,830

2,910

2,979

3,039

3,093

3,297

14

1,834

2,219

2,435

2,586

2,701

2,794

2,872

2,939

2,997

3,050

3,248

15

1,820

2,199

2,411

2,559

2,672

2,763

2,839

2,905

2,962

3,013

3,207

16

1,808

2,182

2,391

2,536

2,647

2,736

2,811

2,875

2,932

2,982

3,172

17

1,797

2,167

2,373

2,516

2,625

2,713

2,787

2,850

2,906

2,955

3,142

18

1,788

2,154

2,358

2,499

2,606

2,693

2,766

2,828

2,882

2,931

3,115

19

1,780

2,142

2,344

2,484

2,590

2,675

2,747

2,808

2,862

2,910

3,091

20

1,772

2,132

2,332

2,470

2,575

2,659

2,730

2,791

2,844

2,891

3,070

25

1,745

2,094

2,287

2,419

2,520

2,601

2,668

2,726

2,777

2,822

2,992

30

1,728

2,070

2,258

2,386

2,484

2,563

2,628

2,684

2,733

2,777

2,941

35

1,715

2,052

2,237

2,364

2,459

2,536

2,600

2,655

2,703

2,745

2,906

40

1,706

2,040

2,222

2,347

2,441

2,517

2,580

2,633

2,680

2,722

2,880

45

1,699

2,030

2,210

2,334

2,427

2,502

2,564

2,617

2,663

2,704

2,859

50

1,694

2,022

2,201

2,323

2,416

2,490

2,551

2,604

2,650

2,690

2,843

60

1,685

2,011

2,188

2,308

2,399

2,472

2,532

2,584

2,629

2,669

2,820

70

1,680

2,002

2,178

2,297

2,387

2,459

2,519

2,570

2,615

2,655

2,803

80

1,675

1,996

2,171

2,289

2,379

2,450

2,509

2,560

2,604

2,643

2,791

90

1,672

1,992

2,165

2,283

2,372

2,443

2,502

2,552

2,596

2,635

2,781

100

1,669

1,988

2,161

2,278

2,367

2,437

2,496

2,546

2,590

2,628

2,773

150

1,661

1,977

2,148

2,263

2,351

2,420

2,478

2,527

2,570

2,608

2,750

200

1,657

1,971

2,141

2,256

2,343

2,412

2,469

2,518

2,560

2,598

2,739

250

1,655

1,968

2,137

2,252

2,338

2,407

2,464

2,512

2,555

2,592

2,732

300

1,653

1,966

2,135

2,249

2,335

2,403

2,460

2,509

2,551

2,588

2,728

350

1,652

1,964

2,133

2,247

2,333

2,401

2,458

2,506

2,548

2,585

2,725

400

1,651

1,963

2,131

2,245

2,331

2,399

2,456

2,504

2,546

2,583

2,722

450

1,651

1,962

2,130

2,244

2,330

2,398

2,454

2,502

2,544

2,581

2,720

500

1,650

1,962

2,129

2,243

2,329

2,397

2,453

2,501

2,543

2,580

2,719

600

1,649

1,960

2,128

2,242

2,327

2,395

2,451

2,499

2,541

2,578

2,717

700

1,649

1,960

2,127

2,241

2,326

2,394

2,450

2,498

2,540

2,577

2,715

800

1,648

1,959

2,127

2,240

2,325

2,393

2,449

2,497

2,539

2,576

2,714

900

1,648

1,959

2,126

2,239

2,324

2,392

2,448

2,496

2,538

2,575

2,713

1000

1,648

1,958

2,126

2,239

2,324

2,392

2,448

2,496

2,537

2,574

2,712

1,645

1,955

2,122

2,235

2,319

2,387

2,443

2,490

2,532

2,568

2,706

20

30

40

50

60

80

100

150

200

250

500

2

29,837

32,597

34,466

35,868

36,985

38,696

39,984

42,242

43,785

44,952

48,421

3

8,869

9,566

10,043

10,404

10,692

11,138

11,474

12,068

12,477

12,786

13,712

4

6,064

6,503

6,805

7,034

7,219

7,503

7,719

8,101

8,365

8,565

9,165

5

5,029

5,374

5,613

5,794

5,940

6,166

6,338

6,643

6,853

7,013

7,494

6

4,495

4,791

4,997

5,154

5,280

5,475

5,624

5,888

6,071

6,210

6,629

7

4,169

4,435

4,620

4,762

4,875

5,052

5,187

5,426

5,592

5,718

6,098

8

3,949

4,195

4,366

4,497

4,602

4,766

4,890

5,112

5,266

5,384

5,738

9

3,790

4,021

4,182

4,305

4,404

4,558

4,676

4,885

5,031

5,142

5,476

10

3,670

3,890

4,043

4,160

4,254

4,401

4,513

4,713

4,851

4,957

5,277

11

3,576

3,787

3,934

4,046

4,136

4,277

4,385

4,577

4,710

4,812

5,120

12

3,501

3,704

3,846

3,954

4,041

4,177

4,282

4,467

4,596

4,695

4,993

13

3,439

3,636

3,773

3,878

3,963

4,095

4,196

4,376

4,502

4,598

4,888

14

3,387

3,579

3,712

3,815

3,897

4,026

4,124

4,300

4,422

4,516

4,799

15

3,343

3,530

3,661

3,761

3,841

3,967

4,063

4,235

4,355

4,446

4,723

16

3,305

3,488

3,616

3,714

3,793

3,916

4,011

4,179

4,296

4,386

4,657

17

3,272

3,452

3,577

3,673

3,751

3,872

3,965

4,130

4,245

4,333

4,600

18

3,243

3,420

3,543

3,638

3,714

3,833

3,924

4,087

4,200

4,287

4,549

19

3,217

3,392

3,513

3,606

3,681

3,799

3,888

4,048

4,160

4,245

4,504

20

3,194

3,367

3,486

3,578

3,652

3,768

3,856

4,014

4,124

4,208

4,464

25

3,110

3,273

3,386

3,473

3,543

3,653

3,736

3,886

3,990

4,070

4,312

30

3,055

3,212

3,321

3,405

3,472

3,578

3,658

3,802

3,902

3,979

4,211

35

3,017

3,170

3,276

3,357

3,423

3,525

3,603

3,742

3,839

3,914

4,140

40

2,988

3,138

3,242

3,322

3,386

3,485

3,562

3,698

3,793

3,866

4,086

45

2,967

3,114

3,216

3,294

3,357

3,455

3,530

3,664

3,757

3,828

4,045

50

2,949

3,095

3,196

3,272

3,334

3,431

3,505

3,637

3,728

3,799

4,012

60

2,924

3,066

3,165

3,240

3,301

3,395

3,467

3,596

3,685

3,754

3,962

70

2,905

3,046

3,143

3,217

3,277

3,370

3,441

3,567

3,655

3,722

3,926

80

2,892

3,031

3,127

3,200

3,259

3,351

3,421

3,545

3,632

3,698

3,899

90

2,881

3,019

3,114

3,187

3,245

3,336

3,405

3,529

3,614

3,680

3,879

100

2,873

3,010

3,104

3,176

3,234

3,324

3,393

3,515

3,600

3,665

3,862

150

2,848

2,982

3,075

3,145

3,202

3,289

3,356

3,475

3,558