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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 19:06:12 +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/t1291143855f6bd866mlo89sjw.htm/, Retrieved Tue, 30 Nov 2010 20:04:15 +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/t1291143855f6bd866mlo89sjw.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 «

89,45 90,12 87,12 89,61 89,66 88,70 85,57 85,22 87,80 87,28 89,92 90,76 89,36 90,87 90,96 91,55 89,10 87,60 86,74 85,61 87,74 87,20 85,04 84,84 85,17 83,70 84,48 83,26 86,51 85,78 85,42 86,26 84,34 83,55 83,12 83,00 82,43 82,55 79,07 79,74 78,01 77,49 78,97 77,71 78,95 75,10 76,15 77,54 79,84 78,00 76,75 76,94 75,95 76,16 72,86 72,44 72,09 71,41 71,75 69,39 68,16 64,21 64,81 67,00 65,76 65,11 65,13 67,11 68,21 68,02 69,10 69,44 68,14 68,25 68,63 68,96 71,82 73,54 72,38 72,97 73,15 72,34 72,86 70,83 71,52 72,29 73,35 69,12 65,95 64,10 61,35 62,91 62,20 62,67 64,91 66,23 67,07 65,01 65,68 64,38 62,59 59,96 60,41 59,70 60,77 61,79 65,93 66,92 65,25 68,24 69,09 70,60 69,75 70,17 70,14 69,10 67,40 68,53 68,05 65,36 66,59 66,07 68,19 71,03 71,05 68,74 71,65 73,68 69,62 69,40 70,04 72,89 71,29 75,01 74,27 76,94 77,12 79,84 80,99 79,01 79,89 74,09 77,80 81,07 83,76 85,33 84 etc...

Output produced by software:

Skewness and Kurtosis - Ungrouped Data
Skewness Measure	Value	Kurtosis Measure	Value
FISHER 3rd Cent. Mom.	-1379.498322	FISHER 4th Cent. Mom.	112835.923445
FISHER beta 1	0.218225	FISHER beta 2	2.663311
FISHER gamma 1	-0.467145	FISHER gamma 2	-0.336689
FISHER gamma 1 (S.E.)	0.109545	FISHER gamma 2 (S.E.)	0.219089
FISHER Test 1	-4.264434	FISHER Test 2	-1.536770
FISHER Test 1 Probability	0.000000	FISHER Test 2 Probability	0.123600
Pearson 2	-0.423700
Yule using Quartile definition: Weighted Average at Xnp	-0.186331
Yule using Quartile definition: Weighted Average at X(n+1)p	-0.182550
Yule using Quartile definition: Empirical Distribution Function	-0.186331
Yule using Quartile definition: Empirical Distribution Function - Averaging	-0.182581
Yule using Quartile definition: Empirical Distribution Function - Interpolation	-0.182612
Yule using Quartile definition: Closest Observation	-0.186331
Yule using Quartile definition: True Basic - Statistics Graphics Toolkit	-0.182612
Yule using Quartile definition: MS Excel (old versions)	-0.182519
Skewness Measure (small sample)	Value	Kurtosis Measure (small sample)	Value
Skewness (small sample)	-0.468552	Kurtosis (small sample)	-0.327984
Skewness S.E. (small sample)	0.109218	Kurtosis S.E. (small sample)	0.218006
TEST 1 (small sample)	-4.290072	TEST 1 (small sample)	-1.504472
TEST 1 Prob. (small sample)	0.000000	TEST 1 Prob. (small sample)	0.131000
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)	-0.468600	0.000000	Trim. Kurtosis (0/500)	-0.328000	0.131000
Trim. Skewness (1/500)	-0.467300	0.000000	Trim. Kurtosis (1/500)	-0.338800	0.118800
Trim. Skewness (2/500)	-0.465100	0.000000	Trim. Kurtosis (2/500)	-0.350500	0.107400
Trim. Skewness (3/500)	-0.464800	0.000000	Trim. Kurtosis (3/500)	-0.357700	0.101000
Trim. Skewness (4/500)	-0.464900	0.000000	Trim. Kurtosis (4/500)	-0.364400	0.097000
Trim. Skewness (5/500)	-0.465000	0.000000	Trim. Kurtosis (5/500)	-0.368900	0.093000
Trim. Skewness (6/500)	-0.466200	0.000000	Trim. Kurtosis (6/500)	-0.370700	0.091000
Trim. Skewness (7/500)	-0.468500	0.000000	Trim. Kurtosis (7/500)	-0.369300	0.093000
Trim. Skewness (8/500)	-0.470900	0.000000	Trim. Kurtosis (8/500)	-0.368500	0.095000
Trim. Skewness (9/500)	-0.473800	0.000000	Trim. Kurtosis (9/500)	-0.366500	0.097000
Trim. Skewness (10/500)	-0.477000	0.000000	Trim. Kurtosis (10/500)	-0.364500	0.101000
Trim. Skewness (11/500)	-0.480100	0.000000	Trim. Kurtosis (11/500)	-0.362300	0.103200
Trim. Skewness (12/500)	-0.483000	0.000000	Trim. Kurtosis (12/500)	-0.359500	0.107400
Trim. Skewness (13/500)	-0.484500	0.000000	Trim. Kurtosis (13/500)	-0.356400	0.109600
Trim. Skewness (14/500)	-0.486400	0.000000	Trim. Kurtosis (14/500)	-0.352700	0.114200
Trim. Skewness (15/500)	-0.488800	0.000000	Trim. Kurtosis (15/500)	-0.348100	0.121200
Trim. Skewness (16/500)	-0.491400	0.000000	Trim. Kurtosis (16/500)	-0.342000	0.128600
Trim. Skewness (17/500)	-0.493900	0.000000	Trim. Kurtosis (17/500)	-0.336300	0.136200
Trim. Skewness (18/500)	-0.497000	0.000000	Trim. Kurtosis (18/500)	-0.329700	0.144200
Trim. Skewness (19/500)	-0.500600	0.000000	Trim. Kurtosis (19/500)	-0.322000	0.152800
Trim. Skewness (20/500)	-0.504100	0.000000	Trim. Kurtosis (20/500)	-0.314000	0.164600
Trim. Skewness (21/500)	-0.507300	0.000000	Trim. Kurtosis (21/500)	-0.306000	0.177000
Trim. Skewness (22/500)	-0.510300	0.000000	Trim. Kurtosis (22/500)	-0.297900	0.190200
Trim. Skewness (23/500)	-0.512700	0.000000	Trim. Kurtosis (23/500)	-0.289300	0.204000
Trim. Skewness (24/500)	-0.514900	0.000000	Trim. Kurtosis (24/500)	-0.280900	0.218600
Trim. Skewness (25/500)	-0.517100	0.000000	Trim. Kurtosis (25/500)	-0.272700	0.234000
Trim. Skewness (26/500)	-0.519200	0.000000	Trim. Kurtosis (26/500)	-0.264600	0.250200
Trim. Skewness (27/500)	-0.521300	0.000000	Trim. Kurtosis (27/500)	-0.256900	0.262800
Trim. Skewness (28/500)	-0.523700	0.000000	Trim. Kurtosis (28/500)	-0.248700	0.280200
Trim. Skewness (29/500)	-0.525900	0.000000	Trim. Kurtosis (29/500)	-0.241100	0.293800
Trim. Skewness (30/500)	-0.527900	0.000000	Trim. Kurtosis (30/500)	-0.234100	0.312400
Trim. Skewness (31/500)	-0.529800	0.000000	Trim. Kurtosis (31/500)	-0.227600	0.327000
Trim. Skewness (32/500)	-0.532900	0.000000	Trim. Kurtosis (32/500)	-0.217700	0.347200
Trim. Skewness (33/500)	-0.535500	0.000000	Trim. Kurtosis (33/500)	-0.208000	0.373400
Trim. Skewness (34/500)	-0.538100	0.000000	Trim. Kurtosis (34/500)	-0.198400	0.395400
Trim. Skewness (35/500)	-0.540700	0.000000	Trim. Kurtosis (35/500)	-0.188600	0.418000
Trim. Skewness (36/500)	-0.543100	0.000000	Trim. Kurtosis (36/500)	-0.178900	0.447200
Trim. Skewness (37/500)	-0.546500	0.000000	Trim. Kurtosis (37/500)	-0.166500	0.477600
Trim. Skewness (38/500)	-0.549400	0.000000	Trim. Kurtosis (38/500)	-0.154400	0.509200
Trim. Skewness (39/500)	-0.552300	0.000000	Trim. Kurtosis (39/500)	-0.142700	0.541800
Trim. Skewness (40/500)	-0.555000	0.000000	Trim. Kurtosis (40/500)	-0.131700	0.575400

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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