## Free Statistics

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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135

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

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

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 <- 3nodenom <- n/denomif (nodenom>40) denom <- n/40sqrtn = 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])/nwin[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 <- 3nodenom <- n/denomif (nodenom>40) denom <- n/40sqrtn = 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 - iqvalue <- (1-f)*data[i] + f*data[i+1]}q2 <- function(data,n,p,i,f) {np <- (n+1)*pi <<- floor(np)f <<- np - iqvalue <- (1-f)*data[i] + f*data[i+1]}q3 <- function(data,n,p,i,f) {np <- n*pi <<- floor(np)f <<- np - iif (f==0) {qvalue <- data[i]} else {qvalue <- data[i+1]}}q4 <- function(data,n,p,i,f) {np <- n*pi <<- floor(np)f <<- np - iif (f==0) {qvalue <- (data[i]+data[i+1])/2} else {qvalue <- data[i+1]}}q5 <- function(data,n,p,i,f) {np <- (n-1)*pi <<- floor(np)f <<- np - iif (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+0.5i <<- floor(np)f <<- np - iqvalue <- data[i]}q7 <- function(data,n,p,i,f) {np <- (n+1)*pi <<- floor(np)f <<- np - iif (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)*pi <<- floor(np)f <<- np - iif (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 <- 0myn <- 0roundno4 <- 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 / mynreturn(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)midmbitmap(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')