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Descriptive Statistics Formulas: Sigma, Kurtosis, Skewness, and More

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Standard normal table

z

x.x0

x.x1

x.x2

x.x3

x.x4

x.x5

x.x6

x.x7

x.x8

x.x9

4.0

.00003

3.9

.00005

.00005

.00004

.00004

.00004

.00004

.00004

.00004

.00003

.00003

3.8

.00007

.00007

.00007

.00006

.00006

.00006

.00006

.00005

.00005

.00005

3.7

.00011

.00010

.00010

.00010

.00009

.00009

.00008

.00008

.00008

.00008

3.6

.00016

.00015

.00015

.00014

.00014

.00013

.00013

.00012

.00012

.00011

3.5

.00023

.00022

.00022

.00021

.00020

.00019

.00019

.00018

.00017

.00017

3.4

.00034

.00032

.00031

.00030

.00029

.00028

.00027

.00026

.00025

.00024

3.3

.00048

.00047

.00045

.00043

.00042

.00040

.00039

.00038

.00036

.00035

3.2

.00069

.00066

.00064

.00062

.00060

.00058

.00056

.00054

.00052

.00050

3.1

.00097

.00094

.00090

.00087

.00084

.00082

.00079

.00076

.00074

.00071

3.0

.00135

.00131

.00126

.00122

.00118

.00114

.00111

.00107

.00104

.00100

2.9

.0019

.0018

.0018

.0017

.0016

.0016

.0015

.0015

.0014

.0014

2.8

.0026

.0025

.0024

.0023

.0023

.0022

.0021

.0021

.0020

.0019

2.7

.0035

.0034

.0033

.0032

.0031

.0030

.0029

.0028

.0027

.0026

2.6

.0047

.0045

.0044

.0043

.0041

.0040

.0039

.0038

.0037

.0036

2.5

.0062

.0060

.0059

.0057

.0055

.0054

.0052

.0051

.0049

.0048

2.4

.0082

.0080

.0078

.0075

.0073

.0071

.0069

.0068

.0066

.0064

2.3

.0107

.0104

.0102

.0099

.0096

.0094

.0091

.0089

.0087

.0084

2.2

.0139

.0136

.0132

.0129

.0125

.0122

.0119

.0116

.0113

.0110

2.1

.0179

.0174

.0170

.0166

.0162

.0158

.0154

.0150

.0146

.0143

2.0

.0228

.0222

.0217

.0212

.0207

.0202

.0197

.0192

.0188

.0183

z

x.x0

x.x1

x.x2

x.x3

x.x4

x.x5

x.x6

x.x7

x.x8

x.x9

1.9

.0287

.0281

.0274

.0268

.0262

.0256

.0250

.0244

.0239

.0233

1.8

.0359

.0351

.0344

.0336

.0329

.0322

.0314

.0307

.0301

.0294

1.7

.0446

.0436

.0427

.0418

.0409

.0401

.0392

.0384

.0375

.0367

1.6

.0548

.0537

.0526

.0516

.0505

.0495

.0485

.0475

.0465

.0455

1.5

.0668

.0655

.0643

.0630

.0618

.0606

.0594

.0582

.0571

.0559

1.4

.0808

.0793

.0778

.0764

.0749

.0735

.0721

.0708

.0694

.0681

1.3

.0968

.0951

.0934

.0918

.0901

.0885

.0869

.0853

.0838

.0823

1.2

.1151

.1131

.1112

.1093

.1075

.1056

.1038

.1020

.1003

.0985

1.1

.1357

.1335

.1314

.1292

.1271

.1251

.1230

.1210

.1190

.1170

1.0

.1587

.1562

.1539

.1515

.1492

.1469

.1446

.1423

.1401

.1379

0.9

.1841

.1814

.1788

.1762

.1736

.1711

.1685

.1660

.1635

.1611

0.8

.2119

.2090

.2061

.2033

.2005

.1977

.1949

.1922

.1894

.1867

0.7

.2420

.2389

.2358

.2327

.2297

.2266

.2236

.2206

.2177

.2148

0.6

.2743

.2709

.2676

.2643

.2611

.2578

.2546

.2514

.2483

.2451

0.5

.3085

.3050

.3015

.2981

.2946

.2912

.2877

.2843

.2810

.2776

0.4

.3446

.3409

.3372

.3336

.3300

.3264

.3228

.3192

.3156

.3121

0.3

.3821

.3783

.3745

.3707

.3669

.3632

.3594

.3557

.3520

.3483

0.2

.4207

.4168

.4129

.4090

.4052

.4013

.3974

.3936

.3897

.3859

0.1

.4602

.4562

.4522

.4483

.4443

.4404

.4364

.4325

.4286

.4247

0.0

.5000

.4960

.4920

.4880

.4840

.4801

.4761

.4721

.4681

.4641

Additional reference material

Additional sections from legacy sigma-f:

Sigma

Sigma of the individuals (actual sigma)

Estimated sigma

Subgroup Size

d2

Subgroup Size

d2

2

1.128

14

3.407

3

1.693

15

3.472

4

2.059

16

3.532

5

2.326

17

3.588

6

2.534

18

3.640

7

2.704

19

3.689

8

2.847

20

3.735

9

2.970

21

3.778

10

3.078

22

3.819

11

3.173

23

3.858

12

3.258

24

3.895

13

3.336

25

3.931

Additional sections from legacy kurtosis-f:

Kurtosis formula

Additional sections from legacy skewness-f:

Skewness formula

Additional sections from legacy coefficient-f:

Coefficient of variance formula

Where

Additional sections from legacy chi-square-f:

Chi-square formula and degrees of freedom table

Alpha value = 5%

Alpha value = 1%

Degrees of freedom

Value

Degrees of freedom

Value

1

3.84

1

6.63

2

5.99

2

9.21

3

7.82

3

11.3

4

9.49

4

13.3

5

11.10

5

15.1

6

12.60

6

16.8

7

14.10

7

18.5

8

15.50

8

20.1

9

16.90

9

23.2

10

18.30

10

24.7

11

19.70

11

26.2

12

21.00

12

27.7

13

22.40

13

29.1

14

23.70

14

30.6

15

25.00

15

30.6

16

26.30

16

32.0

17

27.60

17

33.4

18

28.90

18

34.8

19

30.10

19

36.2

20

31.40

20

37.6

21

32.70

21

38.9

22

33.90

22

40.3

23

35.20

23

41.6

24

36.40

24

43.0

25

37.70

25

44.3

26

38.90

26

45.6

27

40.10

27

47.0

28

41.30

28

48.3

29

42.60

29

49.6

30

43.80

30

50.9

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