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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 04:21:33 -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/18/t12558614251xu8kii2pxml7bc.htm/, Retrieved Mon, 29 Apr 2024 10:08:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47255, Retrieved Mon, 29 Apr 2024 10:08:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173
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      [Variability] [WS3 Part2 Vraag2 b] [2009-10-18 09:23:05] [42ad1186d39724f834063794eac7cea3]
- RM D          [Central Tendency] [WS3 Part2 Vraag 4] [2009-10-18 10:21:33] [37de18e38c1490dd77c2b362ed87f3bb] [Current]
-                 [Central Tendency] [BDM 13] [2009-10-21 08:43:48] [f5d341d4bbba73282fc6e80153a6d315]
-                 [Central Tendency] [TG 13] [2009-10-21 09:06:28] [a21bac9c8d3d56fdec8be4e719e2c7ed]
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Dataseries X:
190.6
196.6
185.1
192.9
188.7
190.2
175.8
163.4
186.2
202.2
194.5
183.6
186.6
187.4
186.6
185.3
179.1
186
176.3
158.9
192.9
199
190.2
182.8
197.4
211.7
237.5
224.9
218.9
234.9
213.6
205
243.8
238.7
240.3
233.6
230.6
233.6
256.7
250.7
240.8
258.2
239.2
241.1
257.5
274.5
286.3
275.4
309.1
307.4
367.4
377.1
405.4
424.9
357.6
363.2
384
407
398.9
361.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47255&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47255&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47255&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean244.4959.298475187857926.2940960813947
Geometric Mean235.545359680709
Harmonic Mean228.018327794453
Quadratic Mean254.713646735571
Winsorized Mean ( 1 / 20 )244.2716666666679.1932028107194926.5708993585826
Winsorized Mean ( 2 / 20 )244.6316666666679.1199661424149326.8237472427599
Winsorized Mean ( 3 / 20 )244.3316666666679.0210179852188627.0847111786064
Winsorized Mean ( 4 / 20 )243.5258.7173560966834527.9356489856655
Winsorized Mean ( 5 / 20 )243.2583333333338.524449148552228.5365457748843
Winsorized Mean ( 6 / 20 )242.3683333333338.2612660592715229.3379164397358
Winsorized Mean ( 7 / 20 )242.0533333333338.1154631876146929.8261883194467
Winsorized Mean ( 8 / 20 )241.9066666666678.06851797404929.9815489591419
Winsorized Mean ( 9 / 20 )241.3666666666677.8942529573848230.5749851150736
Winsorized Mean ( 10 / 20 )233.3166666666675.9961622220881438.9109997403331
Winsorized Mean ( 11 / 20 )233.0783333333335.919856508637939.3722944117377
Winsorized Mean ( 12 / 20 )228.8583333333335.0616472451441145.2142004863908
Winsorized Mean ( 13 / 20 )226.674.5968346392452549.3100182601341
Winsorized Mean ( 14 / 20 )226.7633333333334.5155224852170750.2186256575428
Winsorized Mean ( 15 / 20 )223.0633333333333.7703129443962259.1630818510357
Winsorized Mean ( 16 / 20 )222.8766666666673.7409290415833859.577892066173
Winsorized Mean ( 17 / 20 )222.7633333333333.6887130996392360.3905284352747
Winsorized Mean ( 18 / 20 )221.6533333333333.3125011175068366.9141912622695
Winsorized Mean ( 19 / 20 )219.4683333333332.9993092346609473.1729595591843
Winsorized Mean ( 20 / 20 )219.1016666666672.7976013653211478.3176864948076
Trimmed Mean ( 1 / 20 )242.8603448275868.9707253737098327.0725425994344
Trimmed Mean ( 2 / 20 )241.3482142857148.6913701754348227.7687187881904
Trimmed Mean ( 3 / 20 )239.5240740740748.3860741672370728.5621220725489
Trimmed Mean ( 4 / 20 )237.6758.0462918185122829.5384514209609
Trimmed Mean ( 5 / 20 )235.927.7381087179369830.4880699663906
Trimmed Mean ( 6 / 20 )234.0854166666677.407431689451831.6014276581186
Trimmed Mean ( 7 / 20 )232.2847826086967.0647837027799932.8792490161152
Trimmed Mean ( 8 / 20 )230.3818181818186.6548709471107334.6185252896362
Trimmed Mean ( 9 / 20 )228.3238095238106.1099249141640537.3693314944851
Trimmed Mean ( 10 / 20 )226.155.4060531126146241.83273735737
Trimmed Mean ( 11 / 20 )225.0184210526325.134484223354343.8249318264785
Trimmed Mean ( 12 / 20 )223.7972222222224.7767533739365846.8513244672267
Trimmed Mean ( 13 / 20 )223.0529411764714.5707768080632348.7997884261132
Trimmed Mean ( 14 / 20 )222.531254.4246342055386450.2937055726417
Trimmed Mean ( 15 / 20 )221.9266666666674.2296841906329652.4688503123104
Trimmed Mean ( 16 / 20 )221.7642857142864.1851059113288952.9889303670857
Trimmed Mean ( 17 / 20 )221.6038461538464.1076681791282153.9488187677511
Trimmed Mean ( 18 / 20 )221.4333333333333.9867837218043955.5418474602164
Trimmed Mean ( 19 / 20 )221.43.9210333031615756.464707867052
Trimmed Mean ( 20 / 20 )221.7053.9024788006437256.8113271911763
Median227.75
Midrange291.9
Midmean - Weighted Average at Xnp220.854838709677
Midmean - Weighted Average at X(n+1)p221.926666666667
Midmean - Empirical Distribution Function220.854838709677
Midmean - Empirical Distribution Function - Averaging221.926666666667
Midmean - Empirical Distribution Function - Interpolation221.926666666667
Midmean - Closest Observation220.854838709677
Midmean - True Basic - Statistics Graphics Toolkit221.926666666667
Midmean - MS Excel (old versions)222.53125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 244.495 & 9.2984751878579 & 26.2940960813947 \tabularnewline
Geometric Mean & 235.545359680709 &  &  \tabularnewline
Harmonic Mean & 228.018327794453 &  &  \tabularnewline
Quadratic Mean & 254.713646735571 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 244.271666666667 & 9.19320281071949 & 26.5708993585826 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 244.631666666667 & 9.11996614241493 & 26.8237472427599 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 244.331666666667 & 9.02101798521886 & 27.0847111786064 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 243.525 & 8.71735609668345 & 27.9356489856655 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 243.258333333333 & 8.5244491485522 & 28.5365457748843 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 242.368333333333 & 8.26126605927152 & 29.3379164397358 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 242.053333333333 & 8.11546318761469 & 29.8261883194467 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 241.906666666667 & 8.068517974049 & 29.9815489591419 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 241.366666666667 & 7.89425295738482 & 30.5749851150736 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 233.316666666667 & 5.99616222208814 & 38.9109997403331 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 233.078333333333 & 5.9198565086379 & 39.3722944117377 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 228.858333333333 & 5.06164724514411 & 45.2142004863908 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 226.67 & 4.59683463924525 & 49.3100182601341 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 226.763333333333 & 4.51552248521707 & 50.2186256575428 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 223.063333333333 & 3.77031294439622 & 59.1630818510357 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 222.876666666667 & 3.74092904158338 & 59.577892066173 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 222.763333333333 & 3.68871309963923 & 60.3905284352747 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 221.653333333333 & 3.31250111750683 & 66.9141912622695 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 219.468333333333 & 2.99930923466094 & 73.1729595591843 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 219.101666666667 & 2.79760136532114 & 78.3176864948076 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 242.860344827586 & 8.97072537370983 & 27.0725425994344 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 241.348214285714 & 8.69137017543482 & 27.7687187881904 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 239.524074074074 & 8.38607416723707 & 28.5621220725489 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 237.675 & 8.04629181851228 & 29.5384514209609 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 235.92 & 7.73810871793698 & 30.4880699663906 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 234.085416666667 & 7.4074316894518 & 31.6014276581186 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 232.284782608696 & 7.06478370277999 & 32.8792490161152 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 230.381818181818 & 6.65487094711073 & 34.6185252896362 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 228.323809523810 & 6.10992491416405 & 37.3693314944851 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 226.15 & 5.40605311261462 & 41.83273735737 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 225.018421052632 & 5.1344842233543 & 43.8249318264785 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 223.797222222222 & 4.77675337393658 & 46.8513244672267 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 223.052941176471 & 4.57077680806323 & 48.7997884261132 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 222.53125 & 4.42463420553864 & 50.2937055726417 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 221.926666666667 & 4.22968419063296 & 52.4688503123104 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 221.764285714286 & 4.18510591132889 & 52.9889303670857 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 221.603846153846 & 4.10766817912821 & 53.9488187677511 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 221.433333333333 & 3.98678372180439 & 55.5418474602164 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 221.4 & 3.92103330316157 & 56.464707867052 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 221.705 & 3.90247880064372 & 56.8113271911763 \tabularnewline
Median & 227.75 &  &  \tabularnewline
Midrange & 291.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 220.854838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 221.926666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 220.854838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 221.926666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 221.926666666667 &  &  \tabularnewline
Midmean - Closest Observation & 220.854838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 221.926666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 222.53125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47255&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]244.495[/C][C]9.2984751878579[/C][C]26.2940960813947[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]235.545359680709[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]228.018327794453[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]254.713646735571[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]244.271666666667[/C][C]9.19320281071949[/C][C]26.5708993585826[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]244.631666666667[/C][C]9.11996614241493[/C][C]26.8237472427599[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]244.331666666667[/C][C]9.02101798521886[/C][C]27.0847111786064[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]243.525[/C][C]8.71735609668345[/C][C]27.9356489856655[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]243.258333333333[/C][C]8.5244491485522[/C][C]28.5365457748843[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]242.368333333333[/C][C]8.26126605927152[/C][C]29.3379164397358[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]242.053333333333[/C][C]8.11546318761469[/C][C]29.8261883194467[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]241.906666666667[/C][C]8.068517974049[/C][C]29.9815489591419[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]241.366666666667[/C][C]7.89425295738482[/C][C]30.5749851150736[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]233.316666666667[/C][C]5.99616222208814[/C][C]38.9109997403331[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]233.078333333333[/C][C]5.9198565086379[/C][C]39.3722944117377[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]228.858333333333[/C][C]5.06164724514411[/C][C]45.2142004863908[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]226.67[/C][C]4.59683463924525[/C][C]49.3100182601341[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]226.763333333333[/C][C]4.51552248521707[/C][C]50.2186256575428[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]223.063333333333[/C][C]3.77031294439622[/C][C]59.1630818510357[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]222.876666666667[/C][C]3.74092904158338[/C][C]59.577892066173[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]222.763333333333[/C][C]3.68871309963923[/C][C]60.3905284352747[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]221.653333333333[/C][C]3.31250111750683[/C][C]66.9141912622695[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]219.468333333333[/C][C]2.99930923466094[/C][C]73.1729595591843[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]219.101666666667[/C][C]2.79760136532114[/C][C]78.3176864948076[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]242.860344827586[/C][C]8.97072537370983[/C][C]27.0725425994344[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]241.348214285714[/C][C]8.69137017543482[/C][C]27.7687187881904[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]239.524074074074[/C][C]8.38607416723707[/C][C]28.5621220725489[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]237.675[/C][C]8.04629181851228[/C][C]29.5384514209609[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]235.92[/C][C]7.73810871793698[/C][C]30.4880699663906[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]234.085416666667[/C][C]7.4074316894518[/C][C]31.6014276581186[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]232.284782608696[/C][C]7.06478370277999[/C][C]32.8792490161152[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]230.381818181818[/C][C]6.65487094711073[/C][C]34.6185252896362[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]228.323809523810[/C][C]6.10992491416405[/C][C]37.3693314944851[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]226.15[/C][C]5.40605311261462[/C][C]41.83273735737[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]225.018421052632[/C][C]5.1344842233543[/C][C]43.8249318264785[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]223.797222222222[/C][C]4.77675337393658[/C][C]46.8513244672267[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]223.052941176471[/C][C]4.57077680806323[/C][C]48.7997884261132[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]222.53125[/C][C]4.42463420553864[/C][C]50.2937055726417[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]221.926666666667[/C][C]4.22968419063296[/C][C]52.4688503123104[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]221.764285714286[/C][C]4.18510591132889[/C][C]52.9889303670857[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]221.603846153846[/C][C]4.10766817912821[/C][C]53.9488187677511[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]221.433333333333[/C][C]3.98678372180439[/C][C]55.5418474602164[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]221.4[/C][C]3.92103330316157[/C][C]56.464707867052[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]221.705[/C][C]3.90247880064372[/C][C]56.8113271911763[/C][/ROW]
[ROW][C]Median[/C][C]227.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]291.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]220.854838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]221.926666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]220.854838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]221.926666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]221.926666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]220.854838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]221.926666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]222.53125[/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=47255&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47255&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 Mean244.4959.298475187857926.2940960813947
Geometric Mean235.545359680709
Harmonic Mean228.018327794453
Quadratic Mean254.713646735571
Winsorized Mean ( 1 / 20 )244.2716666666679.1932028107194926.5708993585826
Winsorized Mean ( 2 / 20 )244.6316666666679.1199661424149326.8237472427599
Winsorized Mean ( 3 / 20 )244.3316666666679.0210179852188627.0847111786064
Winsorized Mean ( 4 / 20 )243.5258.7173560966834527.9356489856655
Winsorized Mean ( 5 / 20 )243.2583333333338.524449148552228.5365457748843
Winsorized Mean ( 6 / 20 )242.3683333333338.2612660592715229.3379164397358
Winsorized Mean ( 7 / 20 )242.0533333333338.1154631876146929.8261883194467
Winsorized Mean ( 8 / 20 )241.9066666666678.06851797404929.9815489591419
Winsorized Mean ( 9 / 20 )241.3666666666677.8942529573848230.5749851150736
Winsorized Mean ( 10 / 20 )233.3166666666675.9961622220881438.9109997403331
Winsorized Mean ( 11 / 20 )233.0783333333335.919856508637939.3722944117377
Winsorized Mean ( 12 / 20 )228.8583333333335.0616472451441145.2142004863908
Winsorized Mean ( 13 / 20 )226.674.5968346392452549.3100182601341
Winsorized Mean ( 14 / 20 )226.7633333333334.5155224852170750.2186256575428
Winsorized Mean ( 15 / 20 )223.0633333333333.7703129443962259.1630818510357
Winsorized Mean ( 16 / 20 )222.8766666666673.7409290415833859.577892066173
Winsorized Mean ( 17 / 20 )222.7633333333333.6887130996392360.3905284352747
Winsorized Mean ( 18 / 20 )221.6533333333333.3125011175068366.9141912622695
Winsorized Mean ( 19 / 20 )219.4683333333332.9993092346609473.1729595591843
Winsorized Mean ( 20 / 20 )219.1016666666672.7976013653211478.3176864948076
Trimmed Mean ( 1 / 20 )242.8603448275868.9707253737098327.0725425994344
Trimmed Mean ( 2 / 20 )241.3482142857148.6913701754348227.7687187881904
Trimmed Mean ( 3 / 20 )239.5240740740748.3860741672370728.5621220725489
Trimmed Mean ( 4 / 20 )237.6758.0462918185122829.5384514209609
Trimmed Mean ( 5 / 20 )235.927.7381087179369830.4880699663906
Trimmed Mean ( 6 / 20 )234.0854166666677.407431689451831.6014276581186
Trimmed Mean ( 7 / 20 )232.2847826086967.0647837027799932.8792490161152
Trimmed Mean ( 8 / 20 )230.3818181818186.6548709471107334.6185252896362
Trimmed Mean ( 9 / 20 )228.3238095238106.1099249141640537.3693314944851
Trimmed Mean ( 10 / 20 )226.155.4060531126146241.83273735737
Trimmed Mean ( 11 / 20 )225.0184210526325.134484223354343.8249318264785
Trimmed Mean ( 12 / 20 )223.7972222222224.7767533739365846.8513244672267
Trimmed Mean ( 13 / 20 )223.0529411764714.5707768080632348.7997884261132
Trimmed Mean ( 14 / 20 )222.531254.4246342055386450.2937055726417
Trimmed Mean ( 15 / 20 )221.9266666666674.2296841906329652.4688503123104
Trimmed Mean ( 16 / 20 )221.7642857142864.1851059113288952.9889303670857
Trimmed Mean ( 17 / 20 )221.6038461538464.1076681791282153.9488187677511
Trimmed Mean ( 18 / 20 )221.4333333333333.9867837218043955.5418474602164
Trimmed Mean ( 19 / 20 )221.43.9210333031615756.464707867052
Trimmed Mean ( 20 / 20 )221.7053.9024788006437256.8113271911763
Median227.75
Midrange291.9
Midmean - Weighted Average at Xnp220.854838709677
Midmean - Weighted Average at X(n+1)p221.926666666667
Midmean - Empirical Distribution Function220.854838709677
Midmean - Empirical Distribution Function - Averaging221.926666666667
Midmean - Empirical Distribution Function - Interpolation221.926666666667
Midmean - Closest Observation220.854838709677
Midmean - True Basic - Statistics Graphics Toolkit221.926666666667
Midmean - MS Excel (old versions)222.53125
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')