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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 computationFri, 16 Oct 2009 03:59:51 -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/16/t1255687533gmm98r58y6570lf.htm/, Retrieved Tue, 30 Apr 2024 04:34:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46939, Retrieved Tue, 30 Apr 2024 04:34:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsW3uitvoer
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Workshop 2 ] [2009-10-08 16:59:47] [315ba876df544ad397193b5931d5f354]
- RMP     [Central Tendency] [w3 uitvoer] [2009-10-16 09:59:51] [950726a732ba3ca782ecb1a5307d0f6f] [Current]
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Dataseries X:
13132.1
17665.9
16913
17318.8
16224.2
15469.6
16557.5
19414.8
17335
16525.2
18160.4
15553.8
15262.2
18581
17564.1
18948.6
17187.8
17564.8
17668.4
20811.7
17257.8
18984.2
20532.6
17082.3
16894.9
20274.9
20078.6
19900.9
17012.2
19642.9
19024
21691
18835.9
19873.4
21468.2
19406.8
18385.3
20739.3
22268.3
21569
17514.8
21124.7
21251
21393
22145.2
20310.5
23466.9
21264.6
18388.1
22635.4
22014.3
18422.7
16120.2
16037.7
16410.7
17749.8
16349.8
15662.3
17782.3
16398.9




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46939&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46939&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46939&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18620.405288.44950737951764.5534297117065
Geometric Mean18488.1741178971
Harmonic Mean18355.5067492168
Quadratic Mean18751.7590200004
Winsorized Mean ( 1 / 20 )18642.0483333333275.3008897776867.7151764688729
Winsorized Mean ( 2 / 20 )18636.725271.00188003209968.769725869771
Winsorized Mean ( 3 / 20 )18634.78268.79566994217269.3269352293102
Winsorized Mean ( 4 / 20 )18633.2866666667265.49922547118770.1820754226223
Winsorized Mean ( 5 / 20 )18637.6283333333254.16098721921673.3300123565313
Winsorized Mean ( 6 / 20 )18633.6783333333250.28874763482374.4487257594188
Winsorized Mean ( 7 / 20 )18634.0516666667245.93087092507275.76946967485
Winsorized Mean ( 8 / 20 )18640.7716666667241.24331008659077.2695900250078
Winsorized Mean ( 9 / 20 )18628.8766666667236.37922029523378.8092821500958
Winsorized Mean ( 10 / 20 )18628.5766666667235.63714926782279.0561960393336
Winsorized Mean ( 11 / 20 )18626.4133333333227.98796292770581.6991085588135
Winsorized Mean ( 12 / 20 )18570.2733333333215.63661188079286.1183690995817
Winsorized Mean ( 13 / 20 )18627.69201.74459245758292.3330324400969
Winsorized Mean ( 14 / 20 )18583.6833333333192.71207780817796.4323748915792
Winsorized Mean ( 15 / 20 )18552.9583333333179.721719859394103.231586854657
Winsorized Mean ( 16 / 20 )18562.1583333333175.455047509506105.794382075714
Winsorized Mean ( 17 / 20 )18536.4316666667162.120639245731114.337272249281
Winsorized Mean ( 18 / 20 )18504.1216666667150.678338038984122.805453706818
Winsorized Mean ( 19 / 20 )18514.73146.620818911975126.276269205095
Winsorized Mean ( 20 / 20 )18443.2966666667133.997136067858137.639484006037
Trimmed Mean ( 1 / 20 )18631.4706896552269.95212049995869.0176860072418
Trimmed Mean ( 2 / 20 )18620.1375263.30276359229770.7175923486766
Trimmed Mean ( 3 / 20 )18610.9222222222257.85476172802972.175988131846
Trimmed Mean ( 4 / 20 )18601.7461538462252.02815892647273.8082055318
Trimmed Mean ( 5 / 20 )18592.284245.91346037737675.6049871018384
Trimmed Mean ( 6 / 20 )18580.9479166667241.9133568188376.8082761572443
Trimmed Mean ( 7 / 20 )18569.4847826087237.77959873497278.0953659666411
Trimmed Mean ( 8 / 20 )18556.9068181818233.46609634749879.4843752840291
Trimmed Mean ( 9 / 20 )18541.9309523810228.87136412862281.0146390439683
Trimmed Mean ( 10 / 20 )18527.44223.87621143997882.7575197955645
Trimmed Mean ( 11 / 20 )18511.4710526316217.11940094361785.2594055260808
Trimmed Mean ( 12 / 20 )18494.0555555556209.86551999612888.1233637421563
Trimmed Mean ( 13 / 20 )18482.8470588235203.29036104906690.918462456577
Trimmed Mean ( 14 / 20 )18461.95625197.62128773407893.4208883146366
Trimmed Mean ( 15 / 20 )18444.5666666667191.92262882718896.104178956795
Trimmed Mean ( 16 / 20 )18429.0821428571187.24450670826898.4225517043882
Trimmed Mean ( 17 / 20 )18409.8884615385180.917737220065101.758339145846
Trimmed Mean ( 18 / 20 )18391.2791666667175.433666701374104.833237043222
Trimmed Mean ( 19 / 20 )18374.1818181818170.425537641405107.813547620094
Trimmed Mean ( 20 / 20 )18351.99162.605363720039112.862144151634
Median18386.7
Midrange18299.5
Midmean - Weighted Average at Xnp18395.1612903226
Midmean - Weighted Average at X(n+1)p18444.5666666667
Midmean - Empirical Distribution Function18395.1612903226
Midmean - Empirical Distribution Function - Averaging18444.5666666667
Midmean - Empirical Distribution Function - Interpolation18444.5666666667
Midmean - Closest Observation18395.1612903226
Midmean - True Basic - Statistics Graphics Toolkit18444.5666666667
Midmean - MS Excel (old versions)18461.95625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18620.405 & 288.449507379517 & 64.5534297117065 \tabularnewline
Geometric Mean & 18488.1741178971 &  &  \tabularnewline
Harmonic Mean & 18355.5067492168 &  &  \tabularnewline
Quadratic Mean & 18751.7590200004 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18642.0483333333 & 275.30088977768 & 67.7151764688729 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18636.725 & 271.001880032099 & 68.769725869771 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18634.78 & 268.795669942172 & 69.3269352293102 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18633.2866666667 & 265.499225471187 & 70.1820754226223 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18637.6283333333 & 254.160987219216 & 73.3300123565313 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18633.6783333333 & 250.288747634823 & 74.4487257594188 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18634.0516666667 & 245.930870925072 & 75.76946967485 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18640.7716666667 & 241.243310086590 & 77.2695900250078 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18628.8766666667 & 236.379220295233 & 78.8092821500958 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18628.5766666667 & 235.637149267822 & 79.0561960393336 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18626.4133333333 & 227.987962927705 & 81.6991085588135 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18570.2733333333 & 215.636611880792 & 86.1183690995817 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18627.69 & 201.744592457582 & 92.3330324400969 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18583.6833333333 & 192.712077808177 & 96.4323748915792 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18552.9583333333 & 179.721719859394 & 103.231586854657 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18562.1583333333 & 175.455047509506 & 105.794382075714 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18536.4316666667 & 162.120639245731 & 114.337272249281 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18504.1216666667 & 150.678338038984 & 122.805453706818 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18514.73 & 146.620818911975 & 126.276269205095 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18443.2966666667 & 133.997136067858 & 137.639484006037 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18631.4706896552 & 269.952120499958 & 69.0176860072418 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18620.1375 & 263.302763592297 & 70.7175923486766 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18610.9222222222 & 257.854761728029 & 72.175988131846 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18601.7461538462 & 252.028158926472 & 73.8082055318 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18592.284 & 245.913460377376 & 75.6049871018384 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18580.9479166667 & 241.91335681883 & 76.8082761572443 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18569.4847826087 & 237.779598734972 & 78.0953659666411 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18556.9068181818 & 233.466096347498 & 79.4843752840291 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18541.9309523810 & 228.871364128622 & 81.0146390439683 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18527.44 & 223.876211439978 & 82.7575197955645 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18511.4710526316 & 217.119400943617 & 85.2594055260808 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18494.0555555556 & 209.865519996128 & 88.1233637421563 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18482.8470588235 & 203.290361049066 & 90.918462456577 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18461.95625 & 197.621287734078 & 93.4208883146366 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18444.5666666667 & 191.922628827188 & 96.104178956795 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18429.0821428571 & 187.244506708268 & 98.4225517043882 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18409.8884615385 & 180.917737220065 & 101.758339145846 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18391.2791666667 & 175.433666701374 & 104.833237043222 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18374.1818181818 & 170.425537641405 & 107.813547620094 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18351.99 & 162.605363720039 & 112.862144151634 \tabularnewline
Median & 18386.7 &  &  \tabularnewline
Midrange & 18299.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18395.1612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18444.5666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18395.1612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18444.5666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18444.5666666667 &  &  \tabularnewline
Midmean - Closest Observation & 18395.1612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18444.5666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18461.95625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46939&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]18620.405[/C][C]288.449507379517[/C][C]64.5534297117065[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18488.1741178971[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18355.5067492168[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18751.7590200004[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18642.0483333333[/C][C]275.30088977768[/C][C]67.7151764688729[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18636.725[/C][C]271.001880032099[/C][C]68.769725869771[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18634.78[/C][C]268.795669942172[/C][C]69.3269352293102[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18633.2866666667[/C][C]265.499225471187[/C][C]70.1820754226223[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18637.6283333333[/C][C]254.160987219216[/C][C]73.3300123565313[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18633.6783333333[/C][C]250.288747634823[/C][C]74.4487257594188[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18634.0516666667[/C][C]245.930870925072[/C][C]75.76946967485[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18640.7716666667[/C][C]241.243310086590[/C][C]77.2695900250078[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18628.8766666667[/C][C]236.379220295233[/C][C]78.8092821500958[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18628.5766666667[/C][C]235.637149267822[/C][C]79.0561960393336[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18626.4133333333[/C][C]227.987962927705[/C][C]81.6991085588135[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18570.2733333333[/C][C]215.636611880792[/C][C]86.1183690995817[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18627.69[/C][C]201.744592457582[/C][C]92.3330324400969[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18583.6833333333[/C][C]192.712077808177[/C][C]96.4323748915792[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18552.9583333333[/C][C]179.721719859394[/C][C]103.231586854657[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18562.1583333333[/C][C]175.455047509506[/C][C]105.794382075714[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18536.4316666667[/C][C]162.120639245731[/C][C]114.337272249281[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18504.1216666667[/C][C]150.678338038984[/C][C]122.805453706818[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18514.73[/C][C]146.620818911975[/C][C]126.276269205095[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18443.2966666667[/C][C]133.997136067858[/C][C]137.639484006037[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18631.4706896552[/C][C]269.952120499958[/C][C]69.0176860072418[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18620.1375[/C][C]263.302763592297[/C][C]70.7175923486766[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18610.9222222222[/C][C]257.854761728029[/C][C]72.175988131846[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18601.7461538462[/C][C]252.028158926472[/C][C]73.8082055318[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18592.284[/C][C]245.913460377376[/C][C]75.6049871018384[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18580.9479166667[/C][C]241.91335681883[/C][C]76.8082761572443[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18569.4847826087[/C][C]237.779598734972[/C][C]78.0953659666411[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18556.9068181818[/C][C]233.466096347498[/C][C]79.4843752840291[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18541.9309523810[/C][C]228.871364128622[/C][C]81.0146390439683[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18527.44[/C][C]223.876211439978[/C][C]82.7575197955645[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18511.4710526316[/C][C]217.119400943617[/C][C]85.2594055260808[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18494.0555555556[/C][C]209.865519996128[/C][C]88.1233637421563[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18482.8470588235[/C][C]203.290361049066[/C][C]90.918462456577[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18461.95625[/C][C]197.621287734078[/C][C]93.4208883146366[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18444.5666666667[/C][C]191.922628827188[/C][C]96.104178956795[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18429.0821428571[/C][C]187.244506708268[/C][C]98.4225517043882[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18409.8884615385[/C][C]180.917737220065[/C][C]101.758339145846[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18391.2791666667[/C][C]175.433666701374[/C][C]104.833237043222[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18374.1818181818[/C][C]170.425537641405[/C][C]107.813547620094[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18351.99[/C][C]162.605363720039[/C][C]112.862144151634[/C][/ROW]
[ROW][C]Median[/C][C]18386.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18299.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18395.1612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18444.5666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18395.1612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18444.5666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18444.5666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18395.1612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18444.5666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18461.95625[/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=46939&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46939&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 Mean18620.405288.44950737951764.5534297117065
Geometric Mean18488.1741178971
Harmonic Mean18355.5067492168
Quadratic Mean18751.7590200004
Winsorized Mean ( 1 / 20 )18642.0483333333275.3008897776867.7151764688729
Winsorized Mean ( 2 / 20 )18636.725271.00188003209968.769725869771
Winsorized Mean ( 3 / 20 )18634.78268.79566994217269.3269352293102
Winsorized Mean ( 4 / 20 )18633.2866666667265.49922547118770.1820754226223
Winsorized Mean ( 5 / 20 )18637.6283333333254.16098721921673.3300123565313
Winsorized Mean ( 6 / 20 )18633.6783333333250.28874763482374.4487257594188
Winsorized Mean ( 7 / 20 )18634.0516666667245.93087092507275.76946967485
Winsorized Mean ( 8 / 20 )18640.7716666667241.24331008659077.2695900250078
Winsorized Mean ( 9 / 20 )18628.8766666667236.37922029523378.8092821500958
Winsorized Mean ( 10 / 20 )18628.5766666667235.63714926782279.0561960393336
Winsorized Mean ( 11 / 20 )18626.4133333333227.98796292770581.6991085588135
Winsorized Mean ( 12 / 20 )18570.2733333333215.63661188079286.1183690995817
Winsorized Mean ( 13 / 20 )18627.69201.74459245758292.3330324400969
Winsorized Mean ( 14 / 20 )18583.6833333333192.71207780817796.4323748915792
Winsorized Mean ( 15 / 20 )18552.9583333333179.721719859394103.231586854657
Winsorized Mean ( 16 / 20 )18562.1583333333175.455047509506105.794382075714
Winsorized Mean ( 17 / 20 )18536.4316666667162.120639245731114.337272249281
Winsorized Mean ( 18 / 20 )18504.1216666667150.678338038984122.805453706818
Winsorized Mean ( 19 / 20 )18514.73146.620818911975126.276269205095
Winsorized Mean ( 20 / 20 )18443.2966666667133.997136067858137.639484006037
Trimmed Mean ( 1 / 20 )18631.4706896552269.95212049995869.0176860072418
Trimmed Mean ( 2 / 20 )18620.1375263.30276359229770.7175923486766
Trimmed Mean ( 3 / 20 )18610.9222222222257.85476172802972.175988131846
Trimmed Mean ( 4 / 20 )18601.7461538462252.02815892647273.8082055318
Trimmed Mean ( 5 / 20 )18592.284245.91346037737675.6049871018384
Trimmed Mean ( 6 / 20 )18580.9479166667241.9133568188376.8082761572443
Trimmed Mean ( 7 / 20 )18569.4847826087237.77959873497278.0953659666411
Trimmed Mean ( 8 / 20 )18556.9068181818233.46609634749879.4843752840291
Trimmed Mean ( 9 / 20 )18541.9309523810228.87136412862281.0146390439683
Trimmed Mean ( 10 / 20 )18527.44223.87621143997882.7575197955645
Trimmed Mean ( 11 / 20 )18511.4710526316217.11940094361785.2594055260808
Trimmed Mean ( 12 / 20 )18494.0555555556209.86551999612888.1233637421563
Trimmed Mean ( 13 / 20 )18482.8470588235203.29036104906690.918462456577
Trimmed Mean ( 14 / 20 )18461.95625197.62128773407893.4208883146366
Trimmed Mean ( 15 / 20 )18444.5666666667191.92262882718896.104178956795
Trimmed Mean ( 16 / 20 )18429.0821428571187.24450670826898.4225517043882
Trimmed Mean ( 17 / 20 )18409.8884615385180.917737220065101.758339145846
Trimmed Mean ( 18 / 20 )18391.2791666667175.433666701374104.833237043222
Trimmed Mean ( 19 / 20 )18374.1818181818170.425537641405107.813547620094
Trimmed Mean ( 20 / 20 )18351.99162.605363720039112.862144151634
Median18386.7
Midrange18299.5
Midmean - Weighted Average at Xnp18395.1612903226
Midmean - Weighted Average at X(n+1)p18444.5666666667
Midmean - Empirical Distribution Function18395.1612903226
Midmean - Empirical Distribution Function - Averaging18444.5666666667
Midmean - Empirical Distribution Function - Interpolation18444.5666666667
Midmean - Closest Observation18395.1612903226
Midmean - True Basic - Statistics Graphics Toolkit18444.5666666667
Midmean - MS Excel (old versions)18461.95625
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')