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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 10:46:05 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256057219lc2vk9lc4jvp0th.htm/, Retrieved Thu, 02 May 2024 14:38:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48813, Retrieved Thu, 02 May 2024 14:38:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS3P2O3] [2009-10-20 16:46:05] [9a1fef436e1d399a5ecd6808bfbd8489] [Current]
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Post a new message
Dataseries X:
3922
3759
4138
4634
3995
4308
4143
4429
5219
4929
5755
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5526
4247
3830
4394
4826
4409
4569
4106
4794
3914
3793
4405
4022
4100
4788
3163
3585
3903
4178
3863
4187




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48813&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48813&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48813&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4567.9666666666780.785291099331756.5445343391782
Geometric Mean4526.5221764352
Harmonic Mean4485.73489676997
Quadratic Mean4609.92071515335
Winsorized Mean ( 1 / 20 )4569.2166666666777.297137782819659.1123655769081
Winsorized Mean ( 2 / 20 )4574.2575.944045804923660.2318450580024
Winsorized Mean ( 3 / 20 )4575.975.627307640937160.505922301577
Winsorized Mean ( 4 / 20 )4567.773.139029824135762.4522913550142
Winsorized Mean ( 5 / 20 )4568.2833333333372.558217777473862.9602472781738
Winsorized Mean ( 6 / 20 )4566.3833333333370.78482190583764.5107695461587
Winsorized Mean ( 7 / 20 )4552.7333333333365.970738534213369.011404669545
Winsorized Mean ( 8 / 20 )4544.8666666666763.811279251388571.2235629811132
Winsorized Mean ( 9 / 20 )4534.0666666666761.269142594579874.0024500859879
Winsorized Mean ( 10 / 20 )4544.458.9278607142877.1180209991699
Winsorized Mean ( 11 / 20 )4532.4833333333355.018633164518982.380878488568
Winsorized Mean ( 12 / 20 )4545.4833333333352.191983126113787.0916003009484
Winsorized Mean ( 13 / 20 )4533.1333333333349.583510943042391.4242103295317
Winsorized Mean ( 14 / 20 )4529.8666666666747.912611520867194.5443490320664
Winsorized Mean ( 15 / 20 )4521.8666666666745.246378053169399.9387544645672
Winsorized Mean ( 16 / 20 )4514.443.6197306726532103.494449194989
Winsorized Mean ( 17 / 20 )4508.1666666666742.3652544360056106.411886973945
Winsorized Mean ( 18 / 20 )4489.8666666666738.0124828342494118.115585510276
Winsorized Mean ( 19 / 20 )4484.4833333333335.8199317338294125.195194861247
Winsorized Mean ( 20 / 20 )4485.4833333333335.0935834564052127.814913484267
Trimmed Mean ( 1 / 20 )4565.7413793103575.360587343985860.5852679792671
Trimmed Mean ( 2 / 20 )4562.0178571428672.967100267688862.5215726047291
Trimmed Mean ( 3 / 20 )4555.2222222222270.889179694861764.2583570839712
Trimmed Mean ( 4 / 20 )4547.2692307692368.42224900874966.4589266890041
Trimmed Mean ( 5 / 20 )4541.1466.323979164740268.4690523275208
Trimmed Mean ( 6 / 20 )4534.3541666666763.839278255727371.0276539860454
Trimmed Mean ( 7 / 20 )4527.3913043478361.219155524644473.9538346380044
Trimmed Mean ( 8 / 20 )4522.4545454545559.324389118977176.23263572735
Trimmed Mean ( 9 / 20 )4518.4523809523857.456545235978778.6412124570791
Trimmed Mean ( 10 / 20 )4515.8555.688966245913281.0905697200188
Trimmed Mean ( 11 / 20 )4511.3421052631653.913941175551183.676726406879
Trimmed Mean ( 12 / 20 )4508.1388888888952.56441479577185.7640840558085
Trimmed Mean ( 13 / 20 )4502.6470588235351.362364450174587.6643259519613
Trimmed Mean ( 14 / 20 )4498.2550.334005371857689.368012077875
Trimmed Mean ( 15 / 20 )4493.7333333333349.216877147667491.3047229683144
Trimmed Mean ( 16 / 20 )4489.7142857142948.265273842671793.021626694779
Trimmed Mean ( 17 / 20 )4486.1538461538547.19219923503395.0613431641804
Trimmed Mean ( 18 / 20 )4482.9166666666745.783553335653797.9154377512157
Trimmed Mean ( 19 / 20 )4481.8636363636445.034584855825699.5204829957229
Trimmed Mean ( 20 / 20 )4481.4544.3438404314571101.061386573566
Median4460
Midrange4632.5
Midmean - Weighted Average at Xnp4481.70967741936
Midmean - Weighted Average at X(n+1)p4493.73333333333
Midmean - Empirical Distribution Function4481.70967741936
Midmean - Empirical Distribution Function - Averaging4493.73333333333
Midmean - Empirical Distribution Function - Interpolation4493.73333333333
Midmean - Closest Observation4481.70967741936
Midmean - True Basic - Statistics Graphics Toolkit4493.73333333333
Midmean - MS Excel (old versions)4498.25
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4567.96666666667 & 80.7852910993317 & 56.5445343391782 \tabularnewline
Geometric Mean & 4526.5221764352 &  &  \tabularnewline
Harmonic Mean & 4485.73489676997 &  &  \tabularnewline
Quadratic Mean & 4609.92071515335 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4569.21666666667 & 77.2971377828196 & 59.1123655769081 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4574.25 & 75.9440458049236 & 60.2318450580024 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4575.9 & 75.6273076409371 & 60.505922301577 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4567.7 & 73.1390298241357 & 62.4522913550142 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4568.28333333333 & 72.5582177774738 & 62.9602472781738 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4566.38333333333 & 70.784821905837 & 64.5107695461587 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4552.73333333333 & 65.9707385342133 & 69.011404669545 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4544.86666666667 & 63.8112792513885 & 71.2235629811132 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4534.06666666667 & 61.2691425945798 & 74.0024500859879 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4544.4 & 58.92786071428 & 77.1180209991699 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4532.48333333333 & 55.0186331645189 & 82.380878488568 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4545.48333333333 & 52.1919831261137 & 87.0916003009484 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4533.13333333333 & 49.5835109430423 & 91.4242103295317 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4529.86666666667 & 47.9126115208671 & 94.5443490320664 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4521.86666666667 & 45.2463780531693 & 99.9387544645672 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4514.4 & 43.6197306726532 & 103.494449194989 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4508.16666666667 & 42.3652544360056 & 106.411886973945 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4489.86666666667 & 38.0124828342494 & 118.115585510276 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4484.48333333333 & 35.8199317338294 & 125.195194861247 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4485.48333333333 & 35.0935834564052 & 127.814913484267 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4565.74137931035 & 75.3605873439858 & 60.5852679792671 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4562.01785714286 & 72.9671002676888 & 62.5215726047291 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4555.22222222222 & 70.8891796948617 & 64.2583570839712 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4547.26923076923 & 68.422249008749 & 66.4589266890041 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4541.14 & 66.3239791647402 & 68.4690523275208 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4534.35416666667 & 63.8392782557273 & 71.0276539860454 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4527.39130434783 & 61.2191555246444 & 73.9538346380044 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4522.45454545455 & 59.3243891189771 & 76.23263572735 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4518.45238095238 & 57.4565452359787 & 78.6412124570791 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4515.85 & 55.6889662459132 & 81.0905697200188 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4511.34210526316 & 53.9139411755511 & 83.676726406879 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4508.13888888889 & 52.564414795771 & 85.7640840558085 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4502.64705882353 & 51.3623644501745 & 87.6643259519613 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4498.25 & 50.3340053718576 & 89.368012077875 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4493.73333333333 & 49.2168771476674 & 91.3047229683144 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4489.71428571429 & 48.2652738426717 & 93.021626694779 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4486.15384615385 & 47.192199235033 & 95.0613431641804 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4482.91666666667 & 45.7835533356537 & 97.9154377512157 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4481.86363636364 & 45.0345848558256 & 99.5204829957229 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4481.45 & 44.3438404314571 & 101.061386573566 \tabularnewline
Median & 4460 &  &  \tabularnewline
Midrange & 4632.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4481.70967741936 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4493.73333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4481.70967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4493.73333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4493.73333333333 &  &  \tabularnewline
Midmean - Closest Observation & 4481.70967741936 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4493.73333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4498.25 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48813&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]4567.96666666667[/C][C]80.7852910993317[/C][C]56.5445343391782[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4526.5221764352[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4485.73489676997[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4609.92071515335[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4569.21666666667[/C][C]77.2971377828196[/C][C]59.1123655769081[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4574.25[/C][C]75.9440458049236[/C][C]60.2318450580024[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4575.9[/C][C]75.6273076409371[/C][C]60.505922301577[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4567.7[/C][C]73.1390298241357[/C][C]62.4522913550142[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4568.28333333333[/C][C]72.5582177774738[/C][C]62.9602472781738[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4566.38333333333[/C][C]70.784821905837[/C][C]64.5107695461587[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4552.73333333333[/C][C]65.9707385342133[/C][C]69.011404669545[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4544.86666666667[/C][C]63.8112792513885[/C][C]71.2235629811132[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4534.06666666667[/C][C]61.2691425945798[/C][C]74.0024500859879[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4544.4[/C][C]58.92786071428[/C][C]77.1180209991699[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4532.48333333333[/C][C]55.0186331645189[/C][C]82.380878488568[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4545.48333333333[/C][C]52.1919831261137[/C][C]87.0916003009484[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4533.13333333333[/C][C]49.5835109430423[/C][C]91.4242103295317[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4529.86666666667[/C][C]47.9126115208671[/C][C]94.5443490320664[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4521.86666666667[/C][C]45.2463780531693[/C][C]99.9387544645672[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4514.4[/C][C]43.6197306726532[/C][C]103.494449194989[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4508.16666666667[/C][C]42.3652544360056[/C][C]106.411886973945[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4489.86666666667[/C][C]38.0124828342494[/C][C]118.115585510276[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4484.48333333333[/C][C]35.8199317338294[/C][C]125.195194861247[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4485.48333333333[/C][C]35.0935834564052[/C][C]127.814913484267[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4565.74137931035[/C][C]75.3605873439858[/C][C]60.5852679792671[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4562.01785714286[/C][C]72.9671002676888[/C][C]62.5215726047291[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4555.22222222222[/C][C]70.8891796948617[/C][C]64.2583570839712[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4547.26923076923[/C][C]68.422249008749[/C][C]66.4589266890041[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4541.14[/C][C]66.3239791647402[/C][C]68.4690523275208[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4534.35416666667[/C][C]63.8392782557273[/C][C]71.0276539860454[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4527.39130434783[/C][C]61.2191555246444[/C][C]73.9538346380044[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4522.45454545455[/C][C]59.3243891189771[/C][C]76.23263572735[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4518.45238095238[/C][C]57.4565452359787[/C][C]78.6412124570791[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4515.85[/C][C]55.6889662459132[/C][C]81.0905697200188[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4511.34210526316[/C][C]53.9139411755511[/C][C]83.676726406879[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4508.13888888889[/C][C]52.564414795771[/C][C]85.7640840558085[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4502.64705882353[/C][C]51.3623644501745[/C][C]87.6643259519613[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4498.25[/C][C]50.3340053718576[/C][C]89.368012077875[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4493.73333333333[/C][C]49.2168771476674[/C][C]91.3047229683144[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4489.71428571429[/C][C]48.2652738426717[/C][C]93.021626694779[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4486.15384615385[/C][C]47.192199235033[/C][C]95.0613431641804[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4482.91666666667[/C][C]45.7835533356537[/C][C]97.9154377512157[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4481.86363636364[/C][C]45.0345848558256[/C][C]99.5204829957229[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4481.45[/C][C]44.3438404314571[/C][C]101.061386573566[/C][/ROW]
[ROW][C]Median[/C][C]4460[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4632.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4481.70967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4493.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4481.70967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4493.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4493.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4481.70967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4493.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4498.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48813&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48813&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4567.9666666666780.785291099331756.5445343391782
Geometric Mean4526.5221764352
Harmonic Mean4485.73489676997
Quadratic Mean4609.92071515335
Winsorized Mean ( 1 / 20 )4569.2166666666777.297137782819659.1123655769081
Winsorized Mean ( 2 / 20 )4574.2575.944045804923660.2318450580024
Winsorized Mean ( 3 / 20 )4575.975.627307640937160.505922301577
Winsorized Mean ( 4 / 20 )4567.773.139029824135762.4522913550142
Winsorized Mean ( 5 / 20 )4568.2833333333372.558217777473862.9602472781738
Winsorized Mean ( 6 / 20 )4566.3833333333370.78482190583764.5107695461587
Winsorized Mean ( 7 / 20 )4552.7333333333365.970738534213369.011404669545
Winsorized Mean ( 8 / 20 )4544.8666666666763.811279251388571.2235629811132
Winsorized Mean ( 9 / 20 )4534.0666666666761.269142594579874.0024500859879
Winsorized Mean ( 10 / 20 )4544.458.9278607142877.1180209991699
Winsorized Mean ( 11 / 20 )4532.4833333333355.018633164518982.380878488568
Winsorized Mean ( 12 / 20 )4545.4833333333352.191983126113787.0916003009484
Winsorized Mean ( 13 / 20 )4533.1333333333349.583510943042391.4242103295317
Winsorized Mean ( 14 / 20 )4529.8666666666747.912611520867194.5443490320664
Winsorized Mean ( 15 / 20 )4521.8666666666745.246378053169399.9387544645672
Winsorized Mean ( 16 / 20 )4514.443.6197306726532103.494449194989
Winsorized Mean ( 17 / 20 )4508.1666666666742.3652544360056106.411886973945
Winsorized Mean ( 18 / 20 )4489.8666666666738.0124828342494118.115585510276
Winsorized Mean ( 19 / 20 )4484.4833333333335.8199317338294125.195194861247
Winsorized Mean ( 20 / 20 )4485.4833333333335.0935834564052127.814913484267
Trimmed Mean ( 1 / 20 )4565.7413793103575.360587343985860.5852679792671
Trimmed Mean ( 2 / 20 )4562.0178571428672.967100267688862.5215726047291
Trimmed Mean ( 3 / 20 )4555.2222222222270.889179694861764.2583570839712
Trimmed Mean ( 4 / 20 )4547.2692307692368.42224900874966.4589266890041
Trimmed Mean ( 5 / 20 )4541.1466.323979164740268.4690523275208
Trimmed Mean ( 6 / 20 )4534.3541666666763.839278255727371.0276539860454
Trimmed Mean ( 7 / 20 )4527.3913043478361.219155524644473.9538346380044
Trimmed Mean ( 8 / 20 )4522.4545454545559.324389118977176.23263572735
Trimmed Mean ( 9 / 20 )4518.4523809523857.456545235978778.6412124570791
Trimmed Mean ( 10 / 20 )4515.8555.688966245913281.0905697200188
Trimmed Mean ( 11 / 20 )4511.3421052631653.913941175551183.676726406879
Trimmed Mean ( 12 / 20 )4508.1388888888952.56441479577185.7640840558085
Trimmed Mean ( 13 / 20 )4502.6470588235351.362364450174587.6643259519613
Trimmed Mean ( 14 / 20 )4498.2550.334005371857689.368012077875
Trimmed Mean ( 15 / 20 )4493.7333333333349.216877147667491.3047229683144
Trimmed Mean ( 16 / 20 )4489.7142857142948.265273842671793.021626694779
Trimmed Mean ( 17 / 20 )4486.1538461538547.19219923503395.0613431641804
Trimmed Mean ( 18 / 20 )4482.9166666666745.783553335653797.9154377512157
Trimmed Mean ( 19 / 20 )4481.8636363636445.034584855825699.5204829957229
Trimmed Mean ( 20 / 20 )4481.4544.3438404314571101.061386573566
Median4460
Midrange4632.5
Midmean - Weighted Average at Xnp4481.70967741936
Midmean - Weighted Average at X(n+1)p4493.73333333333
Midmean - Empirical Distribution Function4481.70967741936
Midmean - Empirical Distribution Function - Averaging4493.73333333333
Midmean - Empirical Distribution Function - Interpolation4493.73333333333
Midmean - Closest Observation4481.70967741936
Midmean - True Basic - Statistics Graphics Toolkit4493.73333333333
Midmean - MS Excel (old versions)4498.25
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')