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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 18:41:32 +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/t12911423748amu0hx1zbv70mb.htm/, Retrieved Tue, 30 Nov 2010 19:39:34 +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/t12911423748amu0hx1zbv70mb.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 «

80,30492817 82,41831292 78,23142005 79,30998555 79,33354838 79,80809546 82,83405312 80,60113118 81,22448193 79,51909061 83,56339358 80,12734212 79,40878211 80,14699197 81,94812726 78,58597756 80,04700687 77,71712537 75,17650884 78,32997066 82,5939708 77,17757947 79,77331028 81,11573716 80,91206771 76,85045195 82,17233136 79,28163541 79,85141977 83,04716922 83,3431549 82,129342 79,2023535 80,20335121 79,21518353 80,71248875 83,16118766 79,87616054 79,77775564 80,38982643 80,10454881 78,17093982 78,42486946 76,75774192 80,45851684 78,78039144 81,19814352 78,57810805 83,40233366 79,59865599 80,10672825 80,75901381 79,98417574 79,21073433 75,65351932 81,07955718 79,73214179 77,3621182 81,52499484 80,4969591 78,73599439 78,33817053 78,44574626 81,48300204 77,3175397 81,69665901 78,55029879 78,73635633 81,30126734 82,24009768 77,91779934 78,58114432 83,55520551 79,41058954 78,38112582 79,77558249 81,73027538 80,9691189 78,05512133 77,819 etc...

Output produced by software:

Skewness and Kurtosis - Ungrouped Data
Skewness Measure	Value	Kurtosis Measure	Value
FISHER 3rd Cent. Mom.	0.135862	FISHER 4th Cent. Mom.	47.909545
FISHER beta 1	0.000279	FISHER beta 2	2.929724
FISHER gamma 1	0.016707	FISHER gamma 2	-0.070276
FISHER gamma 1 (S.E.)	0.109545	FISHER gamma 2 (S.E.)	0.219089
FISHER Test 1	0.152515	FISHER Test 2	-0.320765
FISHER Test 1 Probability	0.872800	FISHER Test 2 Probability	0.741400
Pearson 2	0.172380
Yule using Quartile definition: Weighted Average at Xnp	0.070680
Yule using Quartile definition: Weighted Average at X(n+1)p	0.078751
Yule using Quartile definition: Empirical Distribution Function	0.070680
Yule using Quartile definition: Empirical Distribution Function - Averaging	0.082537
Yule using Quartile definition: Empirical Distribution Function - Interpolation	0.086365
Yule using Quartile definition: Closest Observation	0.070680
Yule using Quartile definition: True Basic - Statistics Graphics Toolkit	0.086365
Yule using Quartile definition: MS Excel (old versions)	0.075008
Skewness Measure (small sample)	Value	Kurtosis Measure (small sample)	Value
Skewness (small sample)	0.016757	Kurtosis (small sample)	-0.058887
Skewness S.E. (small sample)	0.109218	Kurtosis S.E. (small sample)	0.218006
TEST 1 (small sample)	0.153432	TEST 1 (small sample)	-0.270118
TEST 1 Prob. (small sample)	0.872800	TEST 1 Prob. (small sample)	0.779400
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)	0.016800	0.872800	Trim. Kurtosis (0/500)	-0.058900	0.779400
Trim. Skewness (1/500)	0.004600	0.960200	Trim. Kurtosis (1/500)	-0.169300	0.435400
Trim. Skewness (2/500)	0.010800	0.920400	Trim. Kurtosis (2/500)	-0.228300	0.293800
Trim. Skewness (3/500)	0.014600	0.888600	Trim. Kurtosis (3/500)	-0.277700	0.204000
Trim. Skewness (4/500)	0.024200	0.825800	Trim. Kurtosis (4/500)	-0.313500	0.152800
Trim. Skewness (5/500)	0.029800	0.779400	Trim. Kurtosis (5/500)	-0.343300	0.118800
Trim. Skewness (6/500)	0.036800	0.733800	Trim. Kurtosis (6/500)	-0.374200	0.089200
Trim. Skewness (7/500)	0.043200	0.689200	Trim. Kurtosis (7/500)	-0.402900	0.067200
Trim. Skewness (8/500)	0.050200	0.645600	Trim. Kurtosis (8/500)	-0.434500	0.048800
Trim. Skewness (9/500)	0.059900	0.589200	Trim. Kurtosis (9/500)	-0.457100	0.039400
Trim. Skewness (10/500)	0.070000	0.528600	Trim. Kurtosis (10/500)	-0.478100	0.031600
Trim. Skewness (11/500)	0.080800	0.465400	Trim. Kurtosis (11/500)	-0.499300	0.025000
Trim. Skewness (12/500)	0.091000	0.412200	Trim. Kurtosis (12/500)	-0.520900	0.019200
Trim. Skewness (13/500)	0.100400	0.368200	Trim. Kurtosis (13/500)	-0.540300	0.015600
Trim. Skewness (14/500)	0.110100	0.327000	Trim. Kurtosis (14/500)	-0.560500	0.012400
Trim. Skewness (15/500)	0.118800	0.289200	Trim. Kurtosis (15/500)	-0.580000	0.009600
Trim. Skewness (16/500)	0.124400	0.267000	Trim. Kurtosis (16/500)	-0.594600	0.008200
Trim. Skewness (17/500)	0.130500	0.246000	Trim. Kurtosis (17/500)	-0.609200	0.007000
Trim. Skewness (18/500)	0.133800	0.234000	Trim. Kurtosis (18/500)	-0.619800	0.006000
Trim. Skewness (19/500)	0.136400	0.226200	Trim. Kurtosis (19/500)	-0.628400	0.005400
Trim. Skewness (20/500)	0.138500	0.222400	Trim. Kurtosis (20/500)	-0.637800	0.005000
Trim. Skewness (21/500)	0.139800	0.218600	Trim. Kurtosis (21/500)	-0.646900	0.004400
Trim. Skewness (22/500)	0.140700	0.215000	Trim. Kurtosis (22/500)	-0.656700	0.004000
Trim. Skewness (23/500)	0.142000	0.215000	Trim. Kurtosis (23/500)	-0.665200	0.003600
Trim. Skewness (24/500)	0.142400	0.211200	Trim. Kurtosis (24/500)	-0.673600	0.003200
Trim. Skewness (25/500)	0.143000	0.211200	Trim. Kurtosis (25/500)	-0.683400	0.002800
Trim. Skewness (26/500)	0.144000	0.211200	Trim. Kurtosis (26/500)	-0.692200	0.002600
Trim. Skewness (27/500)	0.145800	0.204000	Trim. Kurtosis (27/500)	-0.700200	0.002400
Trim. Skewness (28/500)	0.147600	0.200600	Trim. Kurtosis (28/500)	-0.709600	0.002200
Trim. Skewness (29/500)	0.148500	0.200600	Trim. Kurtosis (29/500)	-0.719200	0.001800
Trim. Skewness (30/500)	0.149100	0.197000	Trim. Kurtosis (30/500)	-0.730200	0.001600
Trim. Skewness (31/500)	0.149100	0.200600	Trim. Kurtosis (31/500)	-0.740300	0.001400
Trim. Skewness (32/500)	0.148700	0.200600	Trim. Kurtosis (32/500)	-0.750800	0.001200
Trim. Skewness (33/500)	0.148500	0.204000	Trim. Kurtosis (33/500)	-0.759600	0.001200
Trim. Skewness (34/500)	0.148500	0.204000	Trim. Kurtosis (34/500)	-0.767800	0.001000
Trim. Skewness (35/500)	0.147400	0.207600	Trim. Kurtosis (35/500)	-0.775800	0.001000
Trim. Skewness (36/500)	0.145300	0.215000	Trim. Kurtosis (36/500)	-0.784200	0.000800
Trim. Skewness (37/500)	0.143100	0.222400	Trim. Kurtosis (37/500)	-0.794000	0.000800
Trim. Skewness (38/500)	0.140700	0.234000	Trim. Kurtosis (38/500)	-0.802500	0.000600
Trim. Skewness (39/500)	0.137800	0.246000	Trim. Kurtosis (39/500)	-0.810600	0.000600
Trim. Skewness (40/500)	0.135700	0.254200	Trim. Kurtosis (40/500)	-0.818200	0.000600

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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