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R Software Module

skewkurt.wasp

Title produced by software

Skewness and Kurtosis

Date of computation

Thu, 25 Nov 2010 18:29:18 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/25/t1290709667e7dk3z025d4589i.htm/, Retrieved Sat, 20 Apr 2024 06:35:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101318, Retrieved Sat, 20 Apr 2024 06:35:57 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

125

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Skewness and Kurtosis] [] [2010-11-24 16:04:29] [4dfa50539945b119a90a7606969443b9]
-    D    [Skewness and Kurtosis] [] [2010-11-25 18:29:18] [cf84dc108eae081aed36d3d050e63ee7] [Current]

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Dataseries X:

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Boxplots

1,3898	31,077
1,3067	31,293
1,2894	30,236
1,277	30,160
1,2208	32,436
1,2565	30,695
1,3406	27,525
1,3569	26,434
1,3686	25,739
1,4272	25,204
1,4614	24,977
1,4914	24,320
1,4816	22,680
1,4562	22,052
1,4268	21,467
1,4088	21,383
1,4016	21,777
1,365	21,928
1,319	21,814
1,305	22,937
1,2785	23,595
1,3239	20,830
1,3449	19,650
1,2732	19,195
1,3322	19,644
1,4369	18,483
1,4975	18,079
1,577	19,178
1,5553	18,391
1,5557	18,441
1,575	18,584
1,5527	20,108
1,4748	20,148
1,4718	19,394
1,457	17,745
1,4684	17,696
1,4227	17,032
1,3896	16,438
1,3622	15,683
1,3716	15,594
1,3419	15,713
1,3511	15,937
1,3516	16,171
1,3242	15,928
1,3074	16,348
1,2999	15,579
1,3213	15,305
1,2881	15,648
1,2611	14,954
1,2727	15,137
1,2811	15,839
1,2684	16,050
1,265	15,168
1,277	17,064
1,2271	16,005
1,202	14,886
1,1938	14,931
1,2103	14,544
1,1856	13,812
1,1786	13,031
1,2015	12,574
1,2256	11,964
1,2292	11,451
1,2037	11,346
1,2165	11,353
1,2694	10,702
1,2938	10,646
1,3201	10,556
1,3014	10,463
1,3119	10,407
1,3408	10,625
1,2991	10,872
1,249	10,805
1,2218	10,653
1,2176	10,574
1,2266	10,431
1,2138	10,383
1,2007	10,296
1,1985	10,872
1,2262	10,635
1,2646	10,297
1,2613	10,570
1,2286	10,662
1,1702	10,709
1,1692	10,413
1,1222	10,846
1,1139	10,371
1,1372	9,924
1,1663	9,828
1,1582	9,897
1,0848	9,721
1,0807	10,171
1,0773	10,738
1,0622	10,812
1,0183	10,511
1,0014	10,244
0,9811	10,368
0,9808	10,457
0,9778	10,186
0,9922	10,166
0,9554	10,827
0,917	10,997
0,8858	10,940
0,8758	10,756
0,87	10,893
0,8833	10,236
0,8924	9,960
0,8883	10,018
0,9059	10,063
0,9111	10,002
0,9005	9,728
0,8607	10,002
0,8532	10,177
0,8742	9,948
0,892	9,394
0,9095	9,308
0,9217	9,155
0,9383	9,103
0,8973	9,732
0,8564	9,984

Skewness and Kurtosis - Ungrouped Data
Skewness Measure	Value	Kurtosis Measure	Value
FISHER 3rd Cent. Mom.	-0.002825	FISHER 4th Cent. Mom.	0.003129
FISHER beta 1	0.161321	FISHER beta 2	2.321608
FISHER gamma 1	-0.401648	FISHER gamma 2	-0.678392
FISHER gamma 1 (S.E.)	0.223607	FISHER gamma 2 (S.E.)	0.447214
FISHER Test 1	-1.796222	FISHER Test 2	-1.516932
FISHER Test 1 Probability	0.071800	FISHER Test 2 Probability	0.128600
Pearson 2	-0.644496
Yule using Quartile definition:Weighted Average at Xnp	-0.372229
Yule using Quartile definition:Weighted Average at X(n+1)p	-0.341863
Yule using Quartile definition:Empirical Distribution Function	-0.372229
Yule using Quartile definition:Empirical Distribution Function - Averaging	-0.326368
Yule using Quartile definition:Empirical Distribution Function - Interpolation	-0.309819
Yule using Quartile definition:Closest Observation	-0.372229
Yule using Quartile definition:True Basic - Statistics Graphics Toolkit	-0.309819
Yule using Quartile definition:MS Excel (old versions)	-0.356401
Skewness Measure (small sample)	Value	Kurtosis Measure (small sample)	Value
Skewness (small sample)	-0.406750	Kurtosis (small sample)	-0.655814
Skewness S.E. (small sample)	0.220879	Kurtosis S.E. (small sample)	0.438331
TEST 1 (small sample)	-1.841509	TEST 1 (small sample)	-1.496164
TEST 1 Prob. (small sample)	0.064400	TEST 1 Prob. (small sample)	0.133600
Observations	120

\begin{tabular}{lllllllll}
\hline

Skewness and Kurtosis - Ungrouped Data \tabularnewline

Skewness Measure

Value

Kurtosis Measure

Value \tabularnewline FISHER 3rd Cent. Mom.

-0.002825 & FISHER 4th Cent. Mom.

0.003129 \tabularnewline FISHER beta 1

0.161321 & FISHER beta 2

2.321608 \tabularnewline FISHER gamma 1

-0.401648 & FISHER gamma 2

-0.678392 \tabularnewline FISHER gamma 1 (S.E.)

0.223607 & FISHER gamma 2 (S.E.)

0.447214 \tabularnewline FISHER Test 1

-1.796222 & FISHER Test 2

-1.516932 \tabularnewline FISHER Test 1 Probability

0.071800 & FISHER Test 2 Probability

0.128600 \tabularnewline Pearson 2

-0.644496 & & \tabularnewline Yule using Quartile definition:Weighted Average at Xnp

-0.372229 & & \tabularnewline Yule using Quartile definition:Weighted Average at X(n+1)p

-0.341863 & & \tabularnewline Yule using Quartile definition:Empirical Distribution Function

-0.372229 & & \tabularnewline Yule using Quartile definition:Empirical Distribution Function - Averaging

-0.326368 & & \tabularnewline Yule using Quartile definition:Empirical Distribution Function - Interpolation

-0.309819 & & \tabularnewline Yule using Quartile definition:Closest Observation

-0.372229 & & \tabularnewline Yule using Quartile definition:True Basic - Statistics Graphics Toolkit

-0.309819 & & \tabularnewline Yule using Quartile definition:MS Excel (old versions)

-0.356401 & & \tabularnewline Skewness Measure (small sample)

Value

Kurtosis Measure (small sample)

Value \tabularnewline Skewness (small sample)

-0.406750 & Kurtosis (small sample)

-0.655814 \tabularnewline Skewness S.E. (small sample)

0.220879 & Kurtosis S.E. (small sample)

0.438331 \tabularnewline TEST 1 (small sample)

-1.841509 & TEST 1 (small sample)

-1.496164 \tabularnewline TEST 1 Prob. (small sample)

0.064400 & TEST 1 Prob. (small sample)

0.133600 \tabularnewline Observations

120 \tabularnewline & \tabularnewline & \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=101318&T=0

[TABLE]

[ROW][C]Skewness and Kurtosis - Ungrouped Data[/C][/ROW]

[ROW][C]Skewness Measure[/C]

Value[/C]

Kurtosis Measure[/C]

Value[/C][/ROW] [ROW][C]FISHER 3rd Cent. Mom.[/C]

-0.002825[/C][C]FISHER 4th Cent. Mom.[/C]

0.003129[/C][/ROW] [ROW][C]FISHER beta 1[/C]

0.161321[/C][C]FISHER beta 2[/C]

2.321608[/C][/ROW] [ROW][C]FISHER gamma 1[/C]

-0.401648[/C][C]FISHER gamma 2[/C]

-0.678392[/C][/ROW] [ROW][C]FISHER gamma 1 (S.E.)[/C]

0.223607[/C][C]FISHER gamma 2 (S.E.)[/C]

0.447214[/C][/ROW] [ROW][C]FISHER Test 1[/C]

-1.796222[/C][C]FISHER Test 2[/C]

-1.516932[/C][/ROW] [ROW][C]FISHER Test 1 Probability[/C]

0.071800[/C][C]FISHER Test 2 Probability[/C]

0.128600[/C][/ROW] [ROW][C]Pearson 2[/C]

-0.644496[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Weighted Average at Xnp[/C]

-0.372229[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Weighted Average at X(n+1)p[/C]

-0.341863[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Empirical Distribution Function[/C]

-0.372229[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Empirical Distribution Function - Averaging[/C]

-0.326368[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Empirical Distribution Function - Interpolation[/C]

-0.309819[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Closest Observation[/C]

-0.372229[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:True Basic - Statistics Graphics Toolkit[/C]

-0.309819[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:MS Excel (old versions)[/C]

-0.356401[/C][C][/C][C][/C][/ROW] [ROW][C]Skewness Measure (small sample)[/C]

Value[/C]

Kurtosis Measure (small sample)[/C]

Value[/C][/ROW] [ROW][C]Skewness (small sample)[/C]

-0.406750[/C][C]Kurtosis (small sample)[/C]

-0.655814[/C][/ROW] [ROW][C]Skewness S.E. (small sample)[/C]

0.220879[/C][C]Kurtosis S.E. (small sample)[/C]

0.438331[/C][/ROW] [ROW][C]TEST 1 (small sample)[/C]

-1.841509[/C][C]TEST 1 (small sample)[/C]

-1.496164[/C][/ROW] [ROW][C]TEST 1 Prob. (small sample)[/C]

0.064400[/C][C]TEST 1 Prob. (small sample)[/C]

0.133600[/C][/ROW] [ROW][C]Observations[/C]

120[/C][/ROW] [ROW][C] [/C][C] [/C][/ROW] [ROW][C] [/C][C] [/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=101318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101318&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Skewness and Kurtosis - Ungrouped Data
Skewness Measure	Value	Kurtosis Measure	Value
FISHER 3rd Cent. Mom.	-0.002825	FISHER 4th Cent. Mom.	0.003129
FISHER beta 1	0.161321	FISHER beta 2	2.321608
FISHER gamma 1	-0.401648	FISHER gamma 2	-0.678392
FISHER gamma 1 (S.E.)	0.223607	FISHER gamma 2 (S.E.)	0.447214
FISHER Test 1	-1.796222	FISHER Test 2	-1.516932
FISHER Test 1 Probability	0.071800	FISHER Test 2 Probability	0.128600
Pearson 2	-0.644496
Yule using Quartile definition:Weighted Average at Xnp	-0.372229
Yule using Quartile definition:Weighted Average at X(n+1)p	-0.341863
Yule using Quartile definition:Empirical Distribution Function	-0.372229
Yule using Quartile definition:Empirical Distribution Function - Averaging	-0.326368
Yule using Quartile definition:Empirical Distribution Function - Interpolation	-0.309819
Yule using Quartile definition:Closest Observation	-0.372229
Yule using Quartile definition:True Basic - Statistics Graphics Toolkit	-0.309819
Yule using Quartile definition:MS Excel (old versions)	-0.356401
Skewness Measure (small sample)	Value	Kurtosis Measure (small sample)	Value
Skewness (small sample)	-0.406750	Kurtosis (small sample)	-0.655814
Skewness S.E. (small sample)	0.220879	Kurtosis S.E. (small sample)	0.438331
TEST 1 (small sample)	-1.841509	TEST 1 (small sample)	-1.496164
TEST 1 Prob. (small sample)	0.064400	TEST 1 Prob. (small sample)	0.133600
Observations	120

Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data
Skewness Measure (small sample)	Value	Probability	Kurtosis Measure (small sample)	Value	Probability
Trim. Skewness (0/120)	-0.406700	0.064400	Trim. Kurtosis (0/120)	-0.655800	0.133600
Trim. Skewness (1/120)	-0.438700	0.047800	Trim. Kurtosis (1/120)	-0.630500	0.152800
Trim. Skewness (2/120)	-0.475700	0.034000	Trim. Kurtosis (2/120)	-0.607800	0.170600
Trim. Skewness (3/120)	-0.509600	0.023800	Trim. Kurtosis (3/120)	-0.577800	0.197000
Trim. Skewness (4/120)	-0.551600	0.015600	Trim. Kurtosis (4/120)	-0.547300	0.226200
Trim. Skewness (5/120)	-0.600600	0.009000	Trim. Kurtosis (5/120)	-0.518800	0.254200
Trim. Skewness (6/120)	-0.626000	0.007000	Trim. Kurtosis (6/120)	-0.468200	0.307800
Trim. Skewness (7/120)	-0.653600	0.005200	Trim. Kurtosis (7/120)	-0.410800	0.373400
Trim. Skewness (8/120)	-0.679900	0.004000	Trim. Kurtosis (8/120)	-0.348600	0.453200
Trim. Skewness (9/120)	-0.706100	0.003000	Trim. Kurtosis (9/120)	-0.282300	0.548400
Trim. Skewness (10/120)	-0.734500	0.002200	Trim. Kurtosis (10/120)	-0.211400	0.652800
Trim. Skewness (11/120)	-0.763400	0.001600	Trim. Kurtosis (11/120)	-0.140200	0.764200
Trim. Skewness (12/120)	-0.792700	0.001200	Trim. Kurtosis (12/120)	-0.063800	0.888600
Trim. Skewness (13/120)	-0.822700	0.001000	Trim. Kurtosis (13/120)	0.014100	0.976000
Trim. Skewness (14/120)	-0.857800	0.000600	Trim. Kurtosis (14/120)	0.094500	0.849200
Trim. Skewness (15/120)	-0.881200	0.000600	Trim. Kurtosis (15/120)	0.173900	0.726400
Trim. Skewness (16/120)	-0.895700	0.000400	Trim. Kurtosis (16/120)	0.238500	0.638400
Trim. Skewness (17/120)	-0.909700	0.000400	Trim. Kurtosis (17/120)	0.289700	0.568600
Trim. Skewness (18/120)	-0.916900	0.000400	Trim. Kurtosis (18/120)	0.307500	0.548400
Trim. Skewness (19/120)	-0.919300	0.000600	Trim. Kurtosis (19/120)	0.334600	0.522200
Trim. Skewness (20/120)	-0.924600	0.000600	Trim. Kurtosis (20/120)	0.379900	0.471600
Trim. Skewness (21/120)	-0.936600	0.000600	Trim. Kurtosis (21/120)	0.479300	0.368200
Trim. Skewness (22/120)	-0.941600	0.000600	Trim. Kurtosis (22/120)	0.550900	0.307800
Trim. Skewness (23/120)	-0.902500	0.001200	Trim. Kurtosis (23/120)	0.524500	0.337000
Trim. Skewness (24/120)	-0.844200	0.002800	Trim. Kurtosis (24/120)	0.435300	0.435400
Trim. Skewness (25/120)	-0.749300	0.008800	Trim. Kurtosis (25/120)	0.207700	0.711400
Trim. Skewness (26/120)	-0.630400	0.030000	Trim. Kurtosis (26/120)	-0.125800	0.825800
Trim. Skewness (27/120)	-0.585600	0.046600	Trim. Kurtosis (27/120)	-0.180200	0.756600
Trim. Skewness (28/120)	-0.542900	0.068800	Trim. Kurtosis (28/120)	-0.208800	0.718800
Trim. Skewness (29/120)	-0.472200	0.118800	Trim. Kurtosis (29/120)	-0.336200	0.568600
Trim. Skewness (30/120)	-0.343400	0.262800	Trim. Kurtosis (30/120)	-0.644900	0.289200
Trim. Skewness (31/120)	-0.273900	0.378800	Trim. Kurtosis (31/120)	-0.771600	0.211200
Trim. Skewness (32/120)	-0.193100	0.541800	Trim. Kurtosis (32/120)	-0.957100	0.126000
Trim. Skewness (33/120)	-0.138800	0.667200	Trim. Kurtosis (33/120)	-1.125000	0.076800
Trim. Skewness (34/120)	-0.122900	0.704000	Trim. Kurtosis (34/120)	-1.167500	0.071800
Trim. Skewness (35/120)	-0.104100	0.756600	Trim. Kurtosis (35/120)	-1.176800	0.075000
Trim. Skewness (36/120)	-0.084200	0.802600	Trim. Kurtosis (36/120)	-1.204500	0.073400
Trim. Skewness (37/120)	-0.046300	0.888600	Trim. Kurtosis (37/120)	-1.275000	0.062800
Trim. Skewness (38/120)	-0.026700	0.936200	Trim. Kurtosis (38/120)	-1.335000	0.056200
Trim. Skewness (39/120)	-0.027200	0.936200	Trim. Kurtosis (39/120)	-1.399100	0.050000
Trim. Skewness (40/120)	-0.032000	0.928200	Trim. Kurtosis (40/120)	-1.412200	0.053600

\begin{tabular}{lllllllll}
\hline

Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data \tabularnewline

Skewness Measure (small sample)

Value

Probability

Kurtosis Measure (small sample)

Value

Probability \tabularnewline Trim. Skewness (0/120)

-0.406700

0.064400 & Trim. Kurtosis (0/120)

-0.655800

0.133600 \tabularnewline Trim. Skewness (1/120)

-0.438700

0.047800 & Trim. Kurtosis (1/120)

-0.630500

0.152800 \tabularnewline Trim. Skewness (2/120)

-0.475700

0.034000 & Trim. Kurtosis (2/120)

-0.607800

0.170600 \tabularnewline Trim. Skewness (3/120)

-0.509600

0.023800 & Trim. Kurtosis (3/120)

-0.577800

0.197000 \tabularnewline Trim. Skewness (4/120)

-0.551600

0.015600 & Trim. Kurtosis (4/120)

-0.547300

0.226200 \tabularnewline Trim. Skewness (5/120)

-0.600600

0.009000 & Trim. Kurtosis (5/120)

-0.518800

0.254200 \tabularnewline Trim. Skewness (6/120)

-0.626000

0.007000 & Trim. Kurtosis (6/120)

-0.468200

0.307800 \tabularnewline Trim. Skewness (7/120)

-0.653600

0.005200 & Trim. Kurtosis (7/120)

-0.410800

0.373400 \tabularnewline Trim. Skewness (8/120)

-0.679900

0.004000 & Trim. Kurtosis (8/120)

-0.348600

0.453200 \tabularnewline Trim. Skewness (9/120)

-0.706100

0.003000 & Trim. Kurtosis (9/120)

-0.282300

0.548400 \tabularnewline Trim. Skewness (10/120)

-0.734500

0.002200 & Trim. Kurtosis (10/120)

-0.211400

0.652800 \tabularnewline Trim. Skewness (11/120)

-0.763400

0.001600 & Trim. Kurtosis (11/120)

-0.140200

0.764200 \tabularnewline Trim. Skewness (12/120)

-0.792700

0.001200 & Trim. Kurtosis (12/120)

-0.063800

0.888600 \tabularnewline Trim. Skewness (13/120)

-0.822700

0.001000 & Trim. Kurtosis (13/120)

0.014100

0.976000 \tabularnewline Trim. Skewness (14/120)

-0.857800

0.000600 & Trim. Kurtosis (14/120)

0.094500

0.849200 \tabularnewline Trim. Skewness (15/120)

-0.881200

0.000600 & Trim. Kurtosis (15/120)

0.173900

0.726400 \tabularnewline Trim. Skewness (16/120)

-0.895700

0.000400 & Trim. Kurtosis (16/120)

0.238500

0.638400 \tabularnewline Trim. Skewness (17/120)

-0.909700

0.000400 & Trim. Kurtosis (17/120)

0.289700

0.568600 \tabularnewline Trim. Skewness (18/120)

-0.916900

0.000400 & Trim. Kurtosis (18/120)

0.307500

0.548400 \tabularnewline Trim. Skewness (19/120)

-0.919300

0.000600 & Trim. Kurtosis (19/120)

0.334600

0.522200 \tabularnewline Trim. Skewness (20/120)

-0.924600

0.000600 & Trim. Kurtosis (20/120)

0.379900

0.471600 \tabularnewline Trim. Skewness (21/120)

-0.936600

0.000600 & Trim. Kurtosis (21/120)

0.479300

0.368200 \tabularnewline Trim. Skewness (22/120)

-0.941600

0.000600 & Trim. Kurtosis (22/120)

0.550900

0.307800 \tabularnewline Trim. Skewness (23/120)

-0.902500

0.001200 & Trim. Kurtosis (23/120)

0.524500

0.337000 \tabularnewline Trim. Skewness (24/120)

-0.844200

0.002800 & Trim. Kurtosis (24/120)

0.435300

0.435400 \tabularnewline Trim. Skewness (25/120)

-0.749300

0.008800 & Trim. Kurtosis (25/120)

0.207700

0.711400 \tabularnewline Trim. Skewness (26/120)

-0.630400

0.030000 & Trim. Kurtosis (26/120)

-0.125800

0.825800 \tabularnewline Trim. Skewness (27/120)

-0.585600

0.046600 & Trim. Kurtosis (27/120)

-0.180200

0.756600 \tabularnewline Trim. Skewness (28/120)

-0.542900

0.068800 & Trim. Kurtosis (28/120)

-0.208800

0.718800 \tabularnewline Trim. Skewness (29/120)

-0.472200

0.118800 & Trim. Kurtosis (29/120)

-0.336200

0.568600 \tabularnewline Trim. Skewness (30/120)

-0.343400

0.262800 & Trim. Kurtosis (30/120)

-0.644900

0.289200 \tabularnewline Trim. Skewness (31/120)

-0.273900

0.378800 & Trim. Kurtosis (31/120)

-0.771600

0.211200 \tabularnewline Trim. Skewness (32/120)

-0.193100

0.541800 & Trim. Kurtosis (32/120)

-0.957100

0.126000 \tabularnewline Trim. Skewness (33/120)

-0.138800

0.667200 & Trim. Kurtosis (33/120)

-1.125000

0.076800 \tabularnewline Trim. Skewness (34/120)

-0.122900

0.704000 & Trim. Kurtosis (34/120)

-1.167500

0.071800 \tabularnewline Trim. Skewness (35/120)

-0.104100

0.756600 & Trim. Kurtosis (35/120)

-1.176800

0.075000 \tabularnewline Trim. Skewness (36/120)

-0.084200

0.802600 & Trim. Kurtosis (36/120)

-1.204500

0.073400 \tabularnewline Trim. Skewness (37/120)

-0.046300

0.888600 & Trim. Kurtosis (37/120)

-1.275000

0.062800 \tabularnewline Trim. Skewness (38/120)

-0.026700

0.936200 & Trim. Kurtosis (38/120)

-1.335000

0.056200 \tabularnewline Trim. Skewness (39/120)

-0.027200

0.936200 & Trim. Kurtosis (39/120)

-1.399100

0.050000 \tabularnewline Trim. Skewness (40/120)

-0.032000

0.928200 & Trim. Kurtosis (40/120)

-1.412200

0.053600 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=101318&T=1

[TABLE]

[ROW][C]Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data[/C][/ROW]

[ROW][C]Skewness Measure (small sample)[/C]

Value[/C]

Probability[/C]

Kurtosis Measure (small sample)[/C]

Value[/C]

Probability[/C][/ROW] [ROW][C]Trim. Skewness (0/120)[/C]

-0.406700[/C]

0.064400[/C][C]Trim. Kurtosis (0/120)[/C]

-0.655800[/C]

0.133600[/C][/ROW] [ROW][C]Trim. Skewness (1/120)[/C]

-0.438700[/C]

0.047800[/C][C]Trim. Kurtosis (1/120)[/C]

-0.630500[/C]

0.152800[/C][/ROW] [ROW][C]Trim. Skewness (2/120)[/C]

-0.475700[/C]

0.034000[/C][C]Trim. Kurtosis (2/120)[/C]

-0.607800[/C]

0.170600[/C][/ROW] [ROW][C]Trim. Skewness (3/120)[/C]

-0.509600[/C]

0.023800[/C][C]Trim. Kurtosis (3/120)[/C]

-0.577800[/C]

0.197000[/C][/ROW] [ROW][C]Trim. Skewness (4/120)[/C]

-0.551600[/C]

0.015600[/C][C]Trim. Kurtosis (4/120)[/C]

-0.547300[/C]

0.226200[/C][/ROW] [ROW][C]Trim. Skewness (5/120)[/C]

-0.600600[/C]

0.009000[/C][C]Trim. Kurtosis (5/120)[/C]

-0.518800[/C]

0.254200[/C][/ROW] [ROW][C]Trim. Skewness (6/120)[/C]

-0.626000[/C]

0.007000[/C][C]Trim. Kurtosis (6/120)[/C]

-0.468200[/C]

0.307800[/C][/ROW] [ROW][C]Trim. Skewness (7/120)[/C]

-0.653600[/C]

0.005200[/C][C]Trim. Kurtosis (7/120)[/C]

-0.410800[/C]

0.373400[/C][/ROW] [ROW][C]Trim. Skewness (8/120)[/C]

-0.679900[/C]

0.004000[/C][C]Trim. Kurtosis (8/120)[/C]

-0.348600[/C]

0.453200[/C][/ROW] [ROW][C]Trim. Skewness (9/120)[/C]

-0.706100[/C]

0.003000[/C][C]Trim. Kurtosis (9/120)[/C]

-0.282300[/C]

0.548400[/C][/ROW] [ROW][C]Trim. Skewness (10/120)[/C]

-0.734500[/C]

0.002200[/C][C]Trim. Kurtosis (10/120)[/C]

-0.211400[/C]

0.652800[/C][/ROW] [ROW][C]Trim. Skewness (11/120)[/C]

-0.763400[/C]

0.001600[/C][C]Trim. Kurtosis (11/120)[/C]

-0.140200[/C]

0.764200[/C][/ROW] [ROW][C]Trim. Skewness (12/120)[/C]

-0.792700[/C]

0.001200[/C][C]Trim. Kurtosis (12/120)[/C]

-0.063800[/C]

0.888600[/C][/ROW] [ROW][C]Trim. Skewness (13/120)[/C]

-0.822700[/C]

0.001000[/C][C]Trim. Kurtosis (13/120)[/C]

0.014100[/C]

0.976000[/C][/ROW] [ROW][C]Trim. Skewness (14/120)[/C]

-0.857800[/C]

0.000600[/C][C]Trim. Kurtosis (14/120)[/C]

0.094500[/C]

0.849200[/C][/ROW] [ROW][C]Trim. Skewness (15/120)[/C]

-0.881200[/C]

0.000600[/C][C]Trim. Kurtosis (15/120)[/C]

0.173900[/C]

0.726400[/C][/ROW] [ROW][C]Trim. Skewness (16/120)[/C]

-0.895700[/C]

0.000400[/C][C]Trim. Kurtosis (16/120)[/C]

0.238500[/C]

0.638400[/C][/ROW] [ROW][C]Trim. Skewness (17/120)[/C]

-0.909700[/C]

0.000400[/C][C]Trim. Kurtosis (17/120)[/C]

0.289700[/C]

0.568600[/C][/ROW] [ROW][C]Trim. Skewness (18/120)[/C]

-0.916900[/C]

0.000400[/C][C]Trim. Kurtosis (18/120)[/C]

0.307500[/C]

0.548400[/C][/ROW] [ROW][C]Trim. Skewness (19/120)[/C]

-0.919300[/C]

0.000600[/C][C]Trim. Kurtosis (19/120)[/C]

0.334600[/C]

0.522200[/C][/ROW] [ROW][C]Trim. Skewness (20/120)[/C]

-0.924600[/C]

0.000600[/C][C]Trim. Kurtosis (20/120)[/C]

0.379900[/C]

0.471600[/C][/ROW] [ROW][C]Trim. Skewness (21/120)[/C]

-0.936600[/C]

0.000600[/C][C]Trim. Kurtosis (21/120)[/C]

0.479300[/C]

0.368200[/C][/ROW] [ROW][C]Trim. Skewness (22/120)[/C]

-0.941600[/C]

0.000600[/C][C]Trim. Kurtosis (22/120)[/C]

0.550900[/C]

0.307800[/C][/ROW] [ROW][C]Trim. Skewness (23/120)[/C]

-0.902500[/C]

0.001200[/C][C]Trim. Kurtosis (23/120)[/C]

0.524500[/C]

0.337000[/C][/ROW] [ROW][C]Trim. Skewness (24/120)[/C]

-0.844200[/C]

0.002800[/C][C]Trim. Kurtosis (24/120)[/C]

0.435300[/C]

0.435400[/C][/ROW] [ROW][C]Trim. Skewness (25/120)[/C]

-0.749300[/C]

0.008800[/C][C]Trim. Kurtosis (25/120)[/C]

0.207700[/C]

0.711400[/C][/ROW] [ROW][C]Trim. Skewness (26/120)[/C]

-0.630400[/C]

0.030000[/C][C]Trim. Kurtosis (26/120)[/C]

-0.125800[/C]

0.825800[/C][/ROW] [ROW][C]Trim. Skewness (27/120)[/C]

-0.585600[/C]

0.046600[/C][C]Trim. Kurtosis (27/120)[/C]

-0.180200[/C]

0.756600[/C][/ROW] [ROW][C]Trim. Skewness (28/120)[/C]

-0.542900[/C]

0.068800[/C][C]Trim. Kurtosis (28/120)[/C]

-0.208800[/C]

0.718800[/C][/ROW] [ROW][C]Trim. Skewness (29/120)[/C]

-0.472200[/C]

0.118800[/C][C]Trim. Kurtosis (29/120)[/C]

-0.336200[/C]

0.568600[/C][/ROW] [ROW][C]Trim. Skewness (30/120)[/C]

-0.343400[/C]

0.262800[/C][C]Trim. Kurtosis (30/120)[/C]

-0.644900[/C]

0.289200[/C][/ROW] [ROW][C]Trim. Skewness (31/120)[/C]

-0.273900[/C]

0.378800[/C][C]Trim. Kurtosis (31/120)[/C]

-0.771600[/C]

0.211200[/C][/ROW] [ROW][C]Trim. Skewness (32/120)[/C]

-0.193100[/C]

0.541800[/C][C]Trim. Kurtosis (32/120)[/C]

-0.957100[/C]

0.126000[/C][/ROW] [ROW][C]Trim. Skewness (33/120)[/C]

-0.138800[/C]

0.667200[/C][C]Trim. Kurtosis (33/120)[/C]

-1.125000[/C]

0.076800[/C][/ROW] [ROW][C]Trim. Skewness (34/120)[/C]

-0.122900[/C]

0.704000[/C][C]Trim. Kurtosis (34/120)[/C]

-1.167500[/C]

0.071800[/C][/ROW] [ROW][C]Trim. Skewness (35/120)[/C]

-0.104100[/C]

0.756600[/C][C]Trim. Kurtosis (35/120)[/C]

-1.176800[/C]

0.075000[/C][/ROW] [ROW][C]Trim. Skewness (36/120)[/C]

-0.084200[/C]

0.802600[/C][C]Trim. Kurtosis (36/120)[/C]

-1.204500[/C]

0.073400[/C][/ROW] [ROW][C]Trim. Skewness (37/120)[/C]

-0.046300[/C]

0.888600[/C][C]Trim. Kurtosis (37/120)[/C]

-1.275000[/C]

0.062800[/C][/ROW] [ROW][C]Trim. Skewness (38/120)[/C]

-0.026700[/C]

0.936200[/C][C]Trim. Kurtosis (38/120)[/C]

-1.335000[/C]

0.056200[/C][/ROW] [ROW][C]Trim. Skewness (39/120)[/C]

-0.027200[/C]

0.936200[/C][C]Trim. Kurtosis (39/120)[/C]

-1.399100[/C]

0.050000[/C][/ROW] [ROW][C]Trim. Skewness (40/120)[/C]

-0.032000[/C]

0.928200[/C][C]Trim. Kurtosis (40/120)[/C]

-1.412200[/C]

0.053600[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=101318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101318&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data
Skewness Measure (small sample)	Value	Probability	Kurtosis Measure (small sample)	Value	Probability
Trim. Skewness (0/120)	-0.406700	0.064400	Trim. Kurtosis (0/120)	-0.655800	0.133600
Trim. Skewness (1/120)	-0.438700	0.047800	Trim. Kurtosis (1/120)	-0.630500	0.152800
Trim. Skewness (2/120)	-0.475700	0.034000	Trim. Kurtosis (2/120)	-0.607800	0.170600
Trim. Skewness (3/120)	-0.509600	0.023800	Trim. Kurtosis (3/120)	-0.577800	0.197000
Trim. Skewness (4/120)	-0.551600	0.015600	Trim. Kurtosis (4/120)	-0.547300	0.226200
Trim. Skewness (5/120)	-0.600600	0.009000	Trim. Kurtosis (5/120)	-0.518800	0.254200
Trim. Skewness (6/120)	-0.626000	0.007000	Trim. Kurtosis (6/120)	-0.468200	0.307800
Trim. Skewness (7/120)	-0.653600	0.005200	Trim. Kurtosis (7/120)	-0.410800	0.373400
Trim. Skewness (8/120)	-0.679900	0.004000	Trim. Kurtosis (8/120)	-0.348600	0.453200
Trim. Skewness (9/120)	-0.706100	0.003000	Trim. Kurtosis (9/120)	-0.282300	0.548400
Trim. Skewness (10/120)	-0.734500	0.002200	Trim. Kurtosis (10/120)	-0.211400	0.652800
Trim. Skewness (11/120)	-0.763400	0.001600	Trim. Kurtosis (11/120)	-0.140200	0.764200
Trim. Skewness (12/120)	-0.792700	0.001200	Trim. Kurtosis (12/120)	-0.063800	0.888600
Trim. Skewness (13/120)	-0.822700	0.001000	Trim. Kurtosis (13/120)	0.014100	0.976000
Trim. Skewness (14/120)	-0.857800	0.000600	Trim. Kurtosis (14/120)	0.094500	0.849200
Trim. Skewness (15/120)	-0.881200	0.000600	Trim. Kurtosis (15/120)	0.173900	0.726400
Trim. Skewness (16/120)	-0.895700	0.000400	Trim. Kurtosis (16/120)	0.238500	0.638400
Trim. Skewness (17/120)	-0.909700	0.000400	Trim. Kurtosis (17/120)	0.289700	0.568600
Trim. Skewness (18/120)	-0.916900	0.000400	Trim. Kurtosis (18/120)	0.307500	0.548400
Trim. Skewness (19/120)	-0.919300	0.000600	Trim. Kurtosis (19/120)	0.334600	0.522200
Trim. Skewness (20/120)	-0.924600	0.000600	Trim. Kurtosis (20/120)	0.379900	0.471600
Trim. Skewness (21/120)	-0.936600	0.000600	Trim. Kurtosis (21/120)	0.479300	0.368200
Trim. Skewness (22/120)	-0.941600	0.000600	Trim. Kurtosis (22/120)	0.550900	0.307800
Trim. Skewness (23/120)	-0.902500	0.001200	Trim. Kurtosis (23/120)	0.524500	0.337000
Trim. Skewness (24/120)	-0.844200	0.002800	Trim. Kurtosis (24/120)	0.435300	0.435400
Trim. Skewness (25/120)	-0.749300	0.008800	Trim. Kurtosis (25/120)	0.207700	0.711400
Trim. Skewness (26/120)	-0.630400	0.030000	Trim. Kurtosis (26/120)	-0.125800	0.825800
Trim. Skewness (27/120)	-0.585600	0.046600	Trim. Kurtosis (27/120)	-0.180200	0.756600
Trim. Skewness (28/120)	-0.542900	0.068800	Trim. Kurtosis (28/120)	-0.208800	0.718800
Trim. Skewness (29/120)	-0.472200	0.118800	Trim. Kurtosis (29/120)	-0.336200	0.568600
Trim. Skewness (30/120)	-0.343400	0.262800	Trim. Kurtosis (30/120)	-0.644900	0.289200
Trim. Skewness (31/120)	-0.273900	0.378800	Trim. Kurtosis (31/120)	-0.771600	0.211200
Trim. Skewness (32/120)	-0.193100	0.541800	Trim. Kurtosis (32/120)	-0.957100	0.126000
Trim. Skewness (33/120)	-0.138800	0.667200	Trim. Kurtosis (33/120)	-1.125000	0.076800
Trim. Skewness (34/120)	-0.122900	0.704000	Trim. Kurtosis (34/120)	-1.167500	0.071800
Trim. Skewness (35/120)	-0.104100	0.756600	Trim. Kurtosis (35/120)	-1.176800	0.075000
Trim. Skewness (36/120)	-0.084200	0.802600	Trim. Kurtosis (36/120)	-1.204500	0.073400
Trim. Skewness (37/120)	-0.046300	0.888600	Trim. Kurtosis (37/120)	-1.275000	0.062800
Trim. Skewness (38/120)	-0.026700	0.936200	Trim. Kurtosis (38/120)	-1.335000	0.056200
Trim. Skewness (39/120)	-0.027200	0.936200	Trim. Kurtosis (39/120)	-1.399100	0.050000
Trim. Skewness (40/120)	-0.032000	0.928200	Trim. Kurtosis (40/120)	-1.412200	0.053600

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code