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*The author of this computation has been verified*

R Software Module: /skewkurt.wasp (opens new window with default values)

Title produced by software: Skewness and Kurtosis

Date of computation: Tue, 30 Nov 2010 18:39:31 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291142252a2ekqtl7um1mrzy.htm/, Retrieved Tue, 30 Nov 2010 19:37:32 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291142252a2ekqtl7um1mrzy.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

58,37708594 61,16112016 56,48725697 56,96663164 59,53376872 59,5866379 59,99357055 57,3154476 62,85409758 61,53287271 59,32695352 59,69493172 60,56339968 57,93999891 57,73449899 58,72178705 55,6721166 61,32071771 59,12948762 58,08172986 62,28183736 59,37105996 59,14171564 59,56696532 62,26037405 61,00913367 60,26957108 54,98176557 58,85766096 60,55552315 59,82559968 62,83306192 62,43594438 60,56281192 62,3945865 59,97746925 60,92222682 61,47935562 62,85565044 59,91682151 57,81241592 55,75297203 61,90724508 59,87953823 58,05548373 58,68553342 59,75742116 59,41307705 58,15827241 60,00618497 59,35447437 63,60965344 59,25905548 60,24817693 60,19957611 58,41838509 60,45026337 61,98671788 59,77722009 62,01461732 57,45711419 58,22613164 57,32364411 61,72886154 61,47752889 59,83242646 61,1166449 62,66588167 60,35098028 61,37523756 57,83912254 62,50930769 58,33732976 61,88210067 58,46909325 55,2554207 60,0506569 60,87779845 59,72977967 60,0 etc...

Output produced by software:

Skewness and Kurtosis - Ungrouped Data
Skewness Measure	Value	Kurtosis Measure	Value
FISHER 3rd Cent. Mom.	-0.430769	FISHER 4th Cent. Mom.	48.399751
FISHER beta 1	0.002778	FISHER beta 2	2.940139
FISHER gamma 1	-0.052709	FISHER gamma 2	-0.059861
FISHER gamma 1 (S.E.)	0.109545	FISHER gamma 2 (S.E.)	0.219089
FISHER Test 1	-0.481168	FISHER Test 2	-0.273226
FISHER Test 1 Probability	0.624200	FISHER Test 2 Probability	0.779400
Pearson 2	0.064188
Yule using Quartile definition: Weighted Average at Xnp	0.054408
Yule using Quartile definition: Weighted Average at X(n+1)p	0.062304
Yule using Quartile definition: Empirical Distribution Function	0.054408
Yule using Quartile definition: Empirical Distribution Function - Averaging	0.063654
Yule using Quartile definition: Empirical Distribution Function - Interpolation	0.065017
Yule using Quartile definition: Closest Observation	0.054408
Yule using Quartile definition: True Basic - Statistics Graphics Toolkit	0.065017
Yule using Quartile definition: MS Excel (old versions)	0.060965
Skewness Measure (small sample)	Value	Kurtosis Measure (small sample)	Value
Skewness (small sample)	-0.052868	Kurtosis (small sample)	-0.048367
Skewness S.E. (small sample)	0.109218	Kurtosis S.E. (small sample)	0.218006
TEST 1 (small sample)	-0.484061	TEST 1 (small sample)	-0.221861
TEST 1 Prob. (small sample)	0.624200	TEST 1 Prob. (small sample)	0.818000
Observations	500

Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data
Skewness Measure (small sample)	Value	Probability	Kurtosis Measure (small sample)	Value	Probability
Trim. Skewness (0/500)	-0.052900	0.624200	Trim. Kurtosis (0/500)	-0.048400	0.818000
Trim. Skewness (1/500)	-0.063800	0.555200	Trim. Kurtosis (1/500)	-0.139400	0.522200
Trim. Skewness (2/500)	-0.056900	0.603000	Trim. Kurtosis (2/500)	-0.188800	0.384400
Trim. Skewness (3/500)	-0.051900	0.631200	Trim. Kurtosis (3/500)	-0.217300	0.317400
Trim. Skewness (4/500)	-0.047900	0.660000	Trim. Kurtosis (4/500)	-0.247000	0.258400
Trim. Skewness (5/500)	-0.042200	0.696600	Trim. Kurtosis (5/500)	-0.276500	0.207600
Trim. Skewness (6/500)	-0.035600	0.741400	Trim. Kurtosis (6/500)	-0.304200	0.167600
Trim. Skewness (7/500)	-0.029600	0.787200	Trim. Kurtosis (7/500)	-0.333100	0.131000
Trim. Skewness (8/500)	-0.025300	0.818000	Trim. Kurtosis (8/500)	-0.356700	0.105200
Trim. Skewness (9/500)	-0.020900	0.849200	Trim. Kurtosis (9/500)	-0.383200	0.083600
Trim. Skewness (10/500)	-0.015100	0.888600	Trim. Kurtosis (10/500)	-0.407100	0.065800
Trim. Skewness (11/500)	-0.008900	0.936200	Trim. Kurtosis (11/500)	-0.431100	0.052400
Trim. Skewness (12/500)	-0.003500	0.968000	Trim. Kurtosis (12/500)	-0.454900	0.041400
Trim. Skewness (13/500)	0.002400	0.976000	Trim. Kurtosis (13/500)	-0.482300	0.030800
Trim. Skewness (14/500)	0.008800	0.936200	Trim. Kurtosis (14/500)	-0.507900	0.023200
Trim. Skewness (15/500)	0.015500	0.888600	Trim. Kurtosis (15/500)	-0.533400	0.017400
Trim. Skewness (16/500)	0.021700	0.841400	Trim. Kurtosis (16/500)	-0.554900	0.013600
Trim. Skewness (17/500)	0.024000	0.825800	Trim. Kurtosis (17/500)	-0.570000	0.011400
Trim. Skewness (18/500)	0.027800	0.802600	Trim. Kurtosis (18/500)	-0.584800	0.009600
Trim. Skewness (19/500)	0.033100	0.764200	Trim. Kurtosis (19/500)	-0.597800	0.008200
Trim. Skewness (20/500)	0.038000	0.733800	Trim. Kurtosis (20/500)	-0.609900	0.007200
Trim. Skewness (21/500)	0.043700	0.696600	Trim. Kurtosis (21/500)	-0.622400	0.006200
Trim. Skewness (22/500)	0.049100	0.667200	Trim. Kurtosis (22/500)	-0.635100	0.005200
Trim. Skewness (23/500)	0.056000	0.624200	Trim. Kurtosis (23/500)	-0.648300	0.004600
Trim. Skewness (24/500)	0.062700	0.582400	Trim. Kurtosis (24/500)	-0.662600	0.003800
Trim. Skewness (25/500)	0.069200	0.541800	Trim. Kurtosis (25/500)	-0.675600	0.003200
Trim. Skewness (26/500)	0.075900	0.509200	Trim. Kurtosis (26/500)	-0.690200	0.002600
Trim. Skewness (27/500)	0.083500	0.465400	Trim. Kurtosis (27/500)	-0.704900	0.002200
Trim. Skewness (28/500)	0.089500	0.435400	Trim. Kurtosis (28/500)	-0.717200	0.001800
Trim. Skewness (29/500)	0.092400	0.423800	Trim. Kurtosis (29/500)	-0.724100	0.001800
Trim. Skewness (30/500)	0.095500	0.406600	Trim. Kurtosis (30/500)	-0.729800	0.001600
Trim. Skewness (31/500)	0.098700	0.395400	Trim. Kurtosis (31/500)	-0.736700	0.001600
Trim. Skewness (32/500)	0.101600	0.384400	Trim. Kurtosis (32/500)	-0.741900	0.001400
Trim. Skewness (33/500)	0.104500	0.368200	Trim. Kurtosis (33/500)	-0.745900	0.001400
Trim. Skewness (34/500)	0.107400	0.357600	Trim. Kurtosis (34/500)	-0.750500	0.001400
Trim. Skewness (35/500)	0.109700	0.347200	Trim. Kurtosis (35/500)	-0.755100	0.001200
Trim. Skewness (36/500)	0.111900	0.342200	Trim. Kurtosis (36/500)	-0.760200	0.001200
Trim. Skewness (37/500)	0.114600	0.332000	Trim. Kurtosis (37/500)	-0.764800	0.001200
Trim. Skewness (38/500)	0.117600	0.317400	Trim. Kurtosis (38/500)	-0.770000	0.001200
Trim. Skewness (39/500)	0.120100	0.307800	Trim. Kurtosis (39/500)	-0.774600	0.001000
Trim. Skewness (40/500)	0.123100	0.298400	Trim. Kurtosis (40/500)	-0.779600	0.001000

Charts produced by software:

Parameters (Session):

Parameters (R input):

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

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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