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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 14:55:21 +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/t12911288009qvhjf58zm4faha.htm/, Retrieved Tue, 30 Nov 2010 15:53:20 +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/t12911288009qvhjf58zm4faha.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 «
9.29 9.52 9.63 9.64 9.91 10.1 10.24 10.07 10.18 10.37 10.45 10.51 10.77 10.82 10.54 10.74 10.86 10.6 10.57 10.52 10.79 10.93 10.81 10.93 11.14 11.23 11.36 10.6 10.59 10.94 10.98 11.11 11.2 10.81 10.98 10.75 10.72 10.55 10.28 10.16 10.31 10.11 9.82 9.79 9.86 9.92 9.82 9.98 9.92 10.1 10.04 9.99 9.81 9.96 10.15 10.19 9.91 9.78 9.48 9.25 9.18 8.98 8.81 8.49 8.61 8.67 8.74 8.61 8.79 9 9.07 9.19 8.97 8.94 8.87 8.92 8.9 9.12 9.43 9.53 9.52 9.51 9.65 9.72 9.61 9.14 9.39 9.27 9.43 9.38 9.22 9.21 9.07 8.96 8.88 8.88 8.87 8.51 8.47 8.35 8.45 8.67 8.4 8.6 8.43 8.64 8.43 8.17 8.22 8.3 8.31 8.5 8.53 8.6 8.87 8.9 8.82 8.76 9.75 9.64
 
Output produced by software:



Skewness and Kurtosis - Ungrouped Data
Skewness MeasureValueKurtosis MeasureValue
FISHER 3rd Cent. Mom.0.107888FISHER 4th Cent. Mom.0.988651
FISHER beta 10.030576FISHER beta 21.882205
FISHER gamma 10.174860FISHER gamma 2-1.117795
FISHER gamma 1 (S.E.)0.223607FISHER gamma 2 (S.E.)0.447214
FISHER Test 10.781997FISHER Test 2-2.499465
FISHER Test 1 Probability0.429600FISHER Test 2 Probability0.012400
Pearson 20.024272
Yule using Quartile definition:
Weighted Average at Xnp
-0.057143
Yule using Quartile definition:
Weighted Average at X(n+1)p
-0.040422
Yule using Quartile definition:
Empirical Distribution Function
-0.057143
Yule using Quartile definition:
Empirical Distribution Function - Averaging
-0.045936
Yule using Quartile definition:
Empirical Distribution Function - Interpolation
-0.051510
Yule using Quartile definition:
Closest Observation
-0.057143
Yule using Quartile definition:
True Basic - Statistics Graphics Toolkit
-0.051510
Yule using Quartile definition:
MS Excel (old versions)
-0.034965
Skewness Measure (small sample)ValueKurtosis Measure (small sample)Value
Skewness (small sample)0.177081Kurtosis (small sample)-1.114090
Skewness S.E. (small sample)0.220879Kurtosis S.E. (small sample)0.438331
TEST 1 (small sample)0.801713TEST 1 (small sample)-2.541667
TEST 1 Prob. (small sample)0.418000TEST 1 Prob. (small sample)0.010800
Observations120



Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data
Skewness Measure (small sample)ValueProbabilityKurtosis Measure (small sample)ValueProbability
Trim. Skewness (0/120)0.1771000.418000Trim. Kurtosis (0/120)-1.1141000.010800
Trim. Skewness (1/120)0.1695000.441200Trim. Kurtosis (1/120)-1.1440000.009600
Trim. Skewness (2/120)0.1677000.453200Trim. Kurtosis (2/120)-1.1583000.009400
Trim. Skewness (3/120)0.1616000.471600Trim. Kurtosis (3/120)-1.1705000.009000
Trim. Skewness (4/120)0.1581000.484000Trim. Kurtosis (4/120)-1.1805000.009000
Trim. Skewness (5/120)0.1530000.502800Trim. Kurtosis (5/120)-1.1906000.009000
Trim. Skewness (6/120)0.1537000.502800Trim. Kurtosis (6/120)-1.1846000.010200
Trim. Skewness (7/120)0.1518000.515600Trim. Kurtosis (7/120)-1.1806000.011000
Trim. Skewness (8/120)0.1522000.515600Trim. Kurtosis (8/120)-1.1755000.012000
Trim. Skewness (9/120)0.1514000.522200Trim. Kurtosis (9/120)-1.1721000.013200
Trim. Skewness (10/120)0.1479000.535200Trim. Kurtosis (10/120)-1.1730000.013800
Trim. Skewness (11/120)0.1483000.541800Trim. Kurtosis (11/120)-1.1668000.015600
Trim. Skewness (12/120)0.1510000.535200Trim. Kurtosis (12/120)-1.1586000.017400
Trim. Skewness (13/120)0.1535000.535200Trim. Kurtosis (13/120)-1.1528000.018800
Trim. Skewness (14/120)0.1537000.535200Trim. Kurtosis (14/120)-1.1514000.020400
Trim. Skewness (15/120)0.1482000.555200Trim. Kurtosis (15/120)-1.1465000.022600
Trim. Skewness (16/120)0.1430000.575400Trim. Kurtosis (16/120)-1.1446000.023800
Trim. Skewness (17/120)0.1371000.596200Trim. Kurtosis (17/120)-1.1460000.025800
Trim. Skewness (18/120)0.1303000.617000Trim. Kurtosis (18/120)-1.1563000.025800
Trim. Skewness (19/120)0.1197000.645600Trim. Kurtosis (19/120)-1.1714000.025800
Trim. Skewness (20/120)0.1209000.652800Trim. Kurtosis (20/120)-1.1622000.028600
Trim. Skewness (21/120)0.1213000.652800Trim. Kurtosis (21/120)-1.1614000.030800
Trim. Skewness (22/120)0.1122000.681800Trim. Kurtosis (22/120)-1.1581000.033200
Trim. Skewness (23/120)0.1004000.718800Trim. Kurtosis (23/120)-1.1569000.035800
Trim. Skewness (24/120)0.0837000.764200Trim. Kurtosis (24/120)-1.1575000.037600
Trim. Skewness (25/120)0.0602000.833600Trim. Kurtosis (25/120)-1.1669000.038400
Trim. Skewness (26/120)0.0317000.912400Trim. Kurtosis (26/120)-1.1858000.038400
Trim. Skewness (27/120)-0.0125000.960200Trim. Kurtosis (27/120)-1.2186000.035800
Trim. Skewness (28/120)-0.0523000.857200Trim. Kurtosis (28/120)-1.2444000.034800
Trim. Skewness (29/120)-0.0800000.787200Trim. Kurtosis (29/120)-1.2515000.036600
Trim. Skewness (30/120)-0.1004000.741400Trim. Kurtosis (30/120)-1.2467000.040400
Trim. Skewness (31/120)-0.1180000.704000Trim. Kurtosis (31/120)-1.2439000.043400
Trim. Skewness (32/120)-0.1330000.674400Trim. Kurtosis (32/120)-1.2337000.048800
Trim. Skewness (33/120)-0.1366000.667200Trim. Kurtosis (33/120)-1.2196000.056200
Trim. Skewness (34/120)-0.1426000.660000Trim. Kurtosis (34/120)-1.2068000.062800
Trim. Skewness (35/120)-0.1487000.652800Trim. Kurtosis (35/120)-1.1928000.070200
Trim. Skewness (36/120)-0.1585000.638400Trim. Kurtosis (36/120)-1.1823000.078400
Trim. Skewness (37/120)-0.1565000.652800Trim. Kurtosis (37/120)-1.1716000.087200
Trim. Skewness (38/120)-0.1501000.674400Trim. Kurtosis (38/120)-1.1795000.091000
Trim. Skewness (39/120)-0.1480000.681800Trim. Kurtosis (39/120)-1.2188000.087200
Trim. Skewness (40/120)-0.1665000.652800Trim. Kurtosis (40/120)-1.2194000.095000
 
Charts produced by software:
 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
 





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