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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Dec 2008 10:39:13 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/11/t1229017197gqg4kng40sx5h73.htm/, Retrieved Thu, 30 May 2024 09:00:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32389, Retrieved Thu, 30 May 2024 09:00:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact253
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Arabica Price in ...] [2008-01-05 23:14:31] [74be16979710d4c4e7c6647856088456]
-   PD  [Univariate Data Series] [Tijdreeks 1 Buite...] [2008-12-11 16:10:45] [2d4aec5ed1856c4828162be37be304d9]
- RMP       [Central Tendency] [Central tendency ...] [2008-12-11 17:39:13] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
- RMP         [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap...] [2008-12-12 08:11:26] [2d4aec5ed1856c4828162be37be304d9]
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Dataseries X:
16283.6
16726.5
14968.9
14861
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17420.4
16704.4
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22160
20664.3
17877.4
21211.2
21423.1
21688.7
23243.2
21490.2
22925.8
23184.8
18562.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32389&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]2 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=32389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32389&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18393.8566666667290.66821828455163.2812791684707
Geometric Mean18259.1622625639
Harmonic Mean18125.3435037864
Quadratic Mean18528.8627780552
Winsorized Mean ( 1 / 20 )18404.83287.46934623415764.023626313911
Winsorized Mean ( 2 / 20 )18405.4533333333283.05840836302665.0235173714682
Winsorized Mean ( 3 / 20 )18372.5583333333272.20416728122267.495507202695
Winsorized Mean ( 4 / 20 )18352.6516666667262.69896399946869.8619110911448
Winsorized Mean ( 5 / 20 )18349.7933333333256.40648243859871.5652473323393
Winsorized Mean ( 6 / 20 )18354.5333333333252.74090248528772.6219347673725
Winsorized Mean ( 7 / 20 )18403.5333333333240.275551157476.5934496651201
Winsorized Mean ( 8 / 20 )18395.4234.62654194792378.4028944350335
Winsorized Mean ( 9 / 20 )18400.71225.96112230849681.4330793368878
Winsorized Mean ( 10 / 20 )18378.16215.89056755523685.127202212287
Winsorized Mean ( 11 / 20 )18349.8166666667208.80991000205487.8780928859467
Winsorized Mean ( 12 / 20 )18228.3566666667180.786574022255100.828044146811
Winsorized Mean ( 13 / 20 )18266.295172.256352902862106.041342987800
Winsorized Mean ( 14 / 20 )18269.0483333333163.501896730332111.736002448124
Winsorized Mean ( 15 / 20 )18272.1983333333162.225150970179112.634805540678
Winsorized Mean ( 16 / 20 )18385.6116666667143.314809263349128.288288985418
Winsorized Mean ( 17 / 20 )18352.8016666667134.471356547003136.481122358958
Winsorized Mean ( 18 / 20 )18340.3216666667120.294981605169152.461236719443
Winsorized Mean ( 19 / 20 )18356.7566666667115.648514792984158.728857863208
Winsorized Mean ( 20 / 20 )18309.323333333398.9713167478068184.996258865466
Trimmed Mean ( 1 / 20 )18388.3051724138277.76694119390966.2004812141303
Trimmed Mean ( 2 / 20 )18370.6265.78156511907169.1191655514931
Trimmed Mean ( 3 / 20 )18351.2370370370253.8889163117872.2805757085568
Trimmed Mean ( 4 / 20 )18343.0365384615244.49670281004675.0236560560598
Trimmed Mean ( 5 / 20 )18340.152236.54819693108477.5324108910592
Trimmed Mean ( 6 / 20 )18337.7416666667228.66353331949080.1953044303091
Trimmed Mean ( 7 / 20 )18334.0913043478219.71433253437383.445131197709
Trimmed Mean ( 8 / 20 )18320.5636363636211.90512407142686.456444678461
Trimmed Mean ( 9 / 20 )18307.2203.29564103911690.0521029689835
Trimmed Mean ( 10 / 20 )18291.615194.35195844302994.1159283731213
Trimmed Mean ( 11 / 20 )18277.95185.28052683365198.6501404781213
Trimmed Mean ( 12 / 20 )18267.0611111111175.005736018365104.379785067126
Trimmed Mean ( 13 / 20 )18272.7529411765169.290111308149107.937509166827
Trimmed Mean ( 14 / 20 )18273.684375163.593895680181111.701505114373
Trimmed Mean ( 15 / 20 )18274.3466666667157.879277372791115.748861856750
Trimmed Mean ( 16 / 20 )18274.6535714286149.604287782162122.153274096249
Trimmed Mean ( 17 / 20 )18258.65143.477592273551127.257850586093
Trimmed Mean ( 18 / 20 )18244.8041666667137.040244073126133.134644425553
Trimmed Mean ( 19 / 20 )18230.3318181818132.095470097157138.008758398553
Trimmed Mean ( 20 / 20 )18210.37124.978838019208145.707627696148
Median17890.65
Midrange18554.85
Midmean - Weighted Average at Xnp18223.7032258065
Midmean - Weighted Average at X(n+1)p18274.3466666667
Midmean - Empirical Distribution Function18223.7032258065
Midmean - Empirical Distribution Function - Averaging18274.3466666667
Midmean - Empirical Distribution Function - Interpolation18274.3466666667
Midmean - Closest Observation18223.7032258065
Midmean - True Basic - Statistics Graphics Toolkit18274.3466666667
Midmean - MS Excel (old versions)18273.684375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18393.8566666667 & 290.668218284551 & 63.2812791684707 \tabularnewline
Geometric Mean & 18259.1622625639 &  &  \tabularnewline
Harmonic Mean & 18125.3435037864 &  &  \tabularnewline
Quadratic Mean & 18528.8627780552 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18404.83 & 287.469346234157 & 64.023626313911 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18405.4533333333 & 283.058408363026 & 65.0235173714682 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18372.5583333333 & 272.204167281222 & 67.495507202695 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18352.6516666667 & 262.698963999468 & 69.8619110911448 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18349.7933333333 & 256.406482438598 & 71.5652473323393 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18354.5333333333 & 252.740902485287 & 72.6219347673725 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18403.5333333333 & 240.2755511574 & 76.5934496651201 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18395.4 & 234.626541947923 & 78.4028944350335 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18400.71 & 225.961122308496 & 81.4330793368878 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18378.16 & 215.890567555236 & 85.127202212287 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18349.8166666667 & 208.809910002054 & 87.8780928859467 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18228.3566666667 & 180.786574022255 & 100.828044146811 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18266.295 & 172.256352902862 & 106.041342987800 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18269.0483333333 & 163.501896730332 & 111.736002448124 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18272.1983333333 & 162.225150970179 & 112.634805540678 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18385.6116666667 & 143.314809263349 & 128.288288985418 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18352.8016666667 & 134.471356547003 & 136.481122358958 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18340.3216666667 & 120.294981605169 & 152.461236719443 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18356.7566666667 & 115.648514792984 & 158.728857863208 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18309.3233333333 & 98.9713167478068 & 184.996258865466 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18388.3051724138 & 277.766941193909 & 66.2004812141303 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18370.6 & 265.781565119071 & 69.1191655514931 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18351.2370370370 & 253.88891631178 & 72.2805757085568 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18343.0365384615 & 244.496702810046 & 75.0236560560598 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18340.152 & 236.548196931084 & 77.5324108910592 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18337.7416666667 & 228.663533319490 & 80.1953044303091 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18334.0913043478 & 219.714332534373 & 83.445131197709 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18320.5636363636 & 211.905124071426 & 86.456444678461 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18307.2 & 203.295641039116 & 90.0521029689835 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18291.615 & 194.351958443029 & 94.1159283731213 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18277.95 & 185.280526833651 & 98.6501404781213 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18267.0611111111 & 175.005736018365 & 104.379785067126 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18272.7529411765 & 169.290111308149 & 107.937509166827 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18273.684375 & 163.593895680181 & 111.701505114373 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18274.3466666667 & 157.879277372791 & 115.748861856750 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18274.6535714286 & 149.604287782162 & 122.153274096249 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18258.65 & 143.477592273551 & 127.257850586093 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18244.8041666667 & 137.040244073126 & 133.134644425553 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18230.3318181818 & 132.095470097157 & 138.008758398553 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18210.37 & 124.978838019208 & 145.707627696148 \tabularnewline
Median & 17890.65 &  &  \tabularnewline
Midrange & 18554.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18223.7032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18274.3466666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18223.7032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18274.3466666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18274.3466666667 &  &  \tabularnewline
Midmean - Closest Observation & 18223.7032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18274.3466666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18273.684375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32389&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]18393.8566666667[/C][C]290.668218284551[/C][C]63.2812791684707[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18259.1622625639[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18125.3435037864[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18528.8627780552[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18404.83[/C][C]287.469346234157[/C][C]64.023626313911[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18405.4533333333[/C][C]283.058408363026[/C][C]65.0235173714682[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18372.5583333333[/C][C]272.204167281222[/C][C]67.495507202695[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18352.6516666667[/C][C]262.698963999468[/C][C]69.8619110911448[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18349.7933333333[/C][C]256.406482438598[/C][C]71.5652473323393[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18354.5333333333[/C][C]252.740902485287[/C][C]72.6219347673725[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18403.5333333333[/C][C]240.2755511574[/C][C]76.5934496651201[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18395.4[/C][C]234.626541947923[/C][C]78.4028944350335[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18400.71[/C][C]225.961122308496[/C][C]81.4330793368878[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18378.16[/C][C]215.890567555236[/C][C]85.127202212287[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18349.8166666667[/C][C]208.809910002054[/C][C]87.8780928859467[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18228.3566666667[/C][C]180.786574022255[/C][C]100.828044146811[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18266.295[/C][C]172.256352902862[/C][C]106.041342987800[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18269.0483333333[/C][C]163.501896730332[/C][C]111.736002448124[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18272.1983333333[/C][C]162.225150970179[/C][C]112.634805540678[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18385.6116666667[/C][C]143.314809263349[/C][C]128.288288985418[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18352.8016666667[/C][C]134.471356547003[/C][C]136.481122358958[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18340.3216666667[/C][C]120.294981605169[/C][C]152.461236719443[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18356.7566666667[/C][C]115.648514792984[/C][C]158.728857863208[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18309.3233333333[/C][C]98.9713167478068[/C][C]184.996258865466[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18388.3051724138[/C][C]277.766941193909[/C][C]66.2004812141303[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18370.6[/C][C]265.781565119071[/C][C]69.1191655514931[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18351.2370370370[/C][C]253.88891631178[/C][C]72.2805757085568[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18343.0365384615[/C][C]244.496702810046[/C][C]75.0236560560598[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18340.152[/C][C]236.548196931084[/C][C]77.5324108910592[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18337.7416666667[/C][C]228.663533319490[/C][C]80.1953044303091[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18334.0913043478[/C][C]219.714332534373[/C][C]83.445131197709[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18320.5636363636[/C][C]211.905124071426[/C][C]86.456444678461[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18307.2[/C][C]203.295641039116[/C][C]90.0521029689835[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18291.615[/C][C]194.351958443029[/C][C]94.1159283731213[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18277.95[/C][C]185.280526833651[/C][C]98.6501404781213[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18267.0611111111[/C][C]175.005736018365[/C][C]104.379785067126[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18272.7529411765[/C][C]169.290111308149[/C][C]107.937509166827[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18273.684375[/C][C]163.593895680181[/C][C]111.701505114373[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18274.3466666667[/C][C]157.879277372791[/C][C]115.748861856750[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18274.6535714286[/C][C]149.604287782162[/C][C]122.153274096249[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18258.65[/C][C]143.477592273551[/C][C]127.257850586093[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18244.8041666667[/C][C]137.040244073126[/C][C]133.134644425553[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18230.3318181818[/C][C]132.095470097157[/C][C]138.008758398553[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18210.37[/C][C]124.978838019208[/C][C]145.707627696148[/C][/ROW]
[ROW][C]Median[/C][C]17890.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18554.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18223.7032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18274.3466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18223.7032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18274.3466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18274.3466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18223.7032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18274.3466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18273.684375[/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=32389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32389&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 Mean18393.8566666667290.66821828455163.2812791684707
Geometric Mean18259.1622625639
Harmonic Mean18125.3435037864
Quadratic Mean18528.8627780552
Winsorized Mean ( 1 / 20 )18404.83287.46934623415764.023626313911
Winsorized Mean ( 2 / 20 )18405.4533333333283.05840836302665.0235173714682
Winsorized Mean ( 3 / 20 )18372.5583333333272.20416728122267.495507202695
Winsorized Mean ( 4 / 20 )18352.6516666667262.69896399946869.8619110911448
Winsorized Mean ( 5 / 20 )18349.7933333333256.40648243859871.5652473323393
Winsorized Mean ( 6 / 20 )18354.5333333333252.74090248528772.6219347673725
Winsorized Mean ( 7 / 20 )18403.5333333333240.275551157476.5934496651201
Winsorized Mean ( 8 / 20 )18395.4234.62654194792378.4028944350335
Winsorized Mean ( 9 / 20 )18400.71225.96112230849681.4330793368878
Winsorized Mean ( 10 / 20 )18378.16215.89056755523685.127202212287
Winsorized Mean ( 11 / 20 )18349.8166666667208.80991000205487.8780928859467
Winsorized Mean ( 12 / 20 )18228.3566666667180.786574022255100.828044146811
Winsorized Mean ( 13 / 20 )18266.295172.256352902862106.041342987800
Winsorized Mean ( 14 / 20 )18269.0483333333163.501896730332111.736002448124
Winsorized Mean ( 15 / 20 )18272.1983333333162.225150970179112.634805540678
Winsorized Mean ( 16 / 20 )18385.6116666667143.314809263349128.288288985418
Winsorized Mean ( 17 / 20 )18352.8016666667134.471356547003136.481122358958
Winsorized Mean ( 18 / 20 )18340.3216666667120.294981605169152.461236719443
Winsorized Mean ( 19 / 20 )18356.7566666667115.648514792984158.728857863208
Winsorized Mean ( 20 / 20 )18309.323333333398.9713167478068184.996258865466
Trimmed Mean ( 1 / 20 )18388.3051724138277.76694119390966.2004812141303
Trimmed Mean ( 2 / 20 )18370.6265.78156511907169.1191655514931
Trimmed Mean ( 3 / 20 )18351.2370370370253.8889163117872.2805757085568
Trimmed Mean ( 4 / 20 )18343.0365384615244.49670281004675.0236560560598
Trimmed Mean ( 5 / 20 )18340.152236.54819693108477.5324108910592
Trimmed Mean ( 6 / 20 )18337.7416666667228.66353331949080.1953044303091
Trimmed Mean ( 7 / 20 )18334.0913043478219.71433253437383.445131197709
Trimmed Mean ( 8 / 20 )18320.5636363636211.90512407142686.456444678461
Trimmed Mean ( 9 / 20 )18307.2203.29564103911690.0521029689835
Trimmed Mean ( 10 / 20 )18291.615194.35195844302994.1159283731213
Trimmed Mean ( 11 / 20 )18277.95185.28052683365198.6501404781213
Trimmed Mean ( 12 / 20 )18267.0611111111175.005736018365104.379785067126
Trimmed Mean ( 13 / 20 )18272.7529411765169.290111308149107.937509166827
Trimmed Mean ( 14 / 20 )18273.684375163.593895680181111.701505114373
Trimmed Mean ( 15 / 20 )18274.3466666667157.879277372791115.748861856750
Trimmed Mean ( 16 / 20 )18274.6535714286149.604287782162122.153274096249
Trimmed Mean ( 17 / 20 )18258.65143.477592273551127.257850586093
Trimmed Mean ( 18 / 20 )18244.8041666667137.040244073126133.134644425553
Trimmed Mean ( 19 / 20 )18230.3318181818132.095470097157138.008758398553
Trimmed Mean ( 20 / 20 )18210.37124.978838019208145.707627696148
Median17890.65
Midrange18554.85
Midmean - Weighted Average at Xnp18223.7032258065
Midmean - Weighted Average at X(n+1)p18274.3466666667
Midmean - Empirical Distribution Function18223.7032258065
Midmean - Empirical Distribution Function - Averaging18274.3466666667
Midmean - Empirical Distribution Function - Interpolation18274.3466666667
Midmean - Closest Observation18223.7032258065
Midmean - True Basic - Statistics Graphics Toolkit18274.3466666667
Midmean - MS Excel (old versions)18273.684375
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')