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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, 12 Dec 2008 07:08:41 -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/12/t1229090964pihkousvawjppns.htm/, Retrieved Fri, 17 May 2024 02:02:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32756, Retrieved Fri, 17 May 2024 02:02:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [central tendency ...] [2008-12-12 13:49:21] [005293453b571dbccb80b45226e44173]
-    D    [Central Tendency] [Central tendency ...] [2008-12-12 14:08:41] [b0654df83a8a0e1de3ceb7bf60f0d58f] [Current]
-    D      [Central Tendency] [Central tendency ...] [2008-12-12 14:20:11] [005293453b571dbccb80b45226e44173]
-    D        [Central Tendency] [Central tendency ...] [2008-12-13 12:58:54] [005293453b571dbccb80b45226e44173]
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Dataseries X:
258778
252791
256389
258961
258647
256304
250498
247883
249552
262626
264416
273049
272441
267564
265952
263937
264765
263386
258985
257334
257477
271486
274488
281274
272674
269704
268227
276444
272247
268516
263406
263619
265905
281681
287413
289423
281242
273878
269022
272630
270287
260447
262248
252806
238663
258438
266719
263279
258064
248828
248284
253376
251846
239494
239709
228793
229521
249999
254016
251178




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=32756&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=32756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32756&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 Mean261516.8166666671633.19011550558160.126377317506
Geometric Mean261211.991657146
Harmonic Mean260902.9077648
Quadratic Mean261817.52555304
Winsorized Mean ( 1 / 20 )261495.451619.70486193878161.446357385746
Winsorized Mean ( 2 / 20 )261609.1166666671480.15122606752176.744856916892
Winsorized Mean ( 3 / 20 )261630.3166666671464.71854520312178.621563523922
Winsorized Mean ( 4 / 20 )261642.5166666671460.57359417682179.136825223880
Winsorized Mean ( 5 / 20 )261923.851219.31164284895214.812883593901
Winsorized Mean ( 6 / 20 )261768.351173.75730651204223.017440272961
Winsorized Mean ( 7 / 20 )261760.651148.62114262261227.891199531928
Winsorized Mean ( 8 / 20 )261746.651111.00978419593235.593469763574
Winsorized Mean ( 9 / 20 )261757.451089.00789256581240.363225819488
Winsorized Mean ( 10 / 20 )261833.2833333331072.70048712585244.087969079681
Winsorized Mean ( 11 / 20 )261923.31044.75474788121250.70314399737
Winsorized Mean ( 12 / 20 )262018.11015.13716022407258.111031953716
Winsorized Mean ( 13 / 20 )262057.966666667952.947738966575274.997207035567
Winsorized Mean ( 14 / 20 )261781.7906.637071415865288.73924115102
Winsorized Mean ( 15 / 20 )261778.45859.900203257417304.428873267326
Winsorized Mean ( 16 / 20 )261767.25803.684149537313325.709111161022
Winsorized Mean ( 17 / 20 )262272.15679.973896900537385.709144417883
Winsorized Mean ( 18 / 20 )262210.95662.76161636528395.633880305287
Winsorized Mean ( 19 / 20 )262300.25586.852590093969446.961050232392
Winsorized Mean ( 20 / 20 )262066.25537.898223852026487.204155691902
Trimmed Mean ( 1 / 20 )261599.8793103451515.42520713681172.624737980043
Trimmed Mean ( 2 / 20 )261711.7678571431383.60073485840189.152666129458
Trimmed Mean ( 3 / 20 )261768.7962962961317.25227891358198.723358073970
Trimmed Mean ( 4 / 20 )261822.0576923081241.75143800842210.849007038181
Trimmed Mean ( 5 / 20 )261875.921146.95265024769228.323218001586
Trimmed Mean ( 6 / 20 )261863.93751117.03013802711234.428712874751
Trimmed Mean ( 7 / 20 )261884.7173913041092.60508605377239.688356510557
Trimmed Mean ( 8 / 20 )261908.8863636361067.68662816279245.30501689837
Trimmed Mean ( 9 / 20 )261937.8571428571044.86030862642250.691747959307
Trimmed Mean ( 10 / 20 )261967.9251019.71812997483256.902292211346
Trimmed Mean ( 11 / 20 )261989.184210526989.586930402775264.746002762883
Trimmed Mean ( 12 / 20 )261999.166666667955.66197409448274.15464229904
Trimmed Mean ( 13 / 20 )261996.382352941916.592938549865285.837225374487
Trimmed Mean ( 14 / 20 )261987.5879.794228828904297.782698971249
Trimmed Mean ( 15 / 20 )262016.9840.523925757093311.730448082119
Trimmed Mean ( 16 / 20 )262050.964285714797.523331469665328.580937942982
Trimmed Mean ( 17 / 20 )262091.884615385752.073372703086348.492439871099
Trimmed Mean ( 18 / 20 )262065.375728.388632064403359.787843279834
Trimmed Mean ( 19 / 20 )262043.318181818694.234201990723377.456652856351
Trimmed Mean ( 20 / 20 )262002.75668.811828917521391.743594643136
Median262952.5
Midrange259108
Midmean - Weighted Average at Xnp261719.774193548
Midmean - Weighted Average at X(n+1)p262016.9
Midmean - Empirical Distribution Function261719.774193548
Midmean - Empirical Distribution Function - Averaging262016.9
Midmean - Empirical Distribution Function - Interpolation262016.9
Midmean - Closest Observation261719.774193548
Midmean - True Basic - Statistics Graphics Toolkit262016.9
Midmean - MS Excel (old versions)261987.5
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 261516.816666667 & 1633.19011550558 & 160.126377317506 \tabularnewline
Geometric Mean & 261211.991657146 &  &  \tabularnewline
Harmonic Mean & 260902.9077648 &  &  \tabularnewline
Quadratic Mean & 261817.52555304 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 261495.45 & 1619.70486193878 & 161.446357385746 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 261609.116666667 & 1480.15122606752 & 176.744856916892 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 261630.316666667 & 1464.71854520312 & 178.621563523922 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 261642.516666667 & 1460.57359417682 & 179.136825223880 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 261923.85 & 1219.31164284895 & 214.812883593901 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 261768.35 & 1173.75730651204 & 223.017440272961 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 261760.65 & 1148.62114262261 & 227.891199531928 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 261746.65 & 1111.00978419593 & 235.593469763574 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 261757.45 & 1089.00789256581 & 240.363225819488 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 261833.283333333 & 1072.70048712585 & 244.087969079681 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 261923.3 & 1044.75474788121 & 250.70314399737 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 262018.1 & 1015.13716022407 & 258.111031953716 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 262057.966666667 & 952.947738966575 & 274.997207035567 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 261781.7 & 906.637071415865 & 288.73924115102 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 261778.45 & 859.900203257417 & 304.428873267326 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 261767.25 & 803.684149537313 & 325.709111161022 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 262272.15 & 679.973896900537 & 385.709144417883 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 262210.95 & 662.76161636528 & 395.633880305287 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 262300.25 & 586.852590093969 & 446.961050232392 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 262066.25 & 537.898223852026 & 487.204155691902 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 261599.879310345 & 1515.42520713681 & 172.624737980043 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 261711.767857143 & 1383.60073485840 & 189.152666129458 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 261768.796296296 & 1317.25227891358 & 198.723358073970 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 261822.057692308 & 1241.75143800842 & 210.849007038181 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 261875.92 & 1146.95265024769 & 228.323218001586 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 261863.9375 & 1117.03013802711 & 234.428712874751 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 261884.717391304 & 1092.60508605377 & 239.688356510557 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 261908.886363636 & 1067.68662816279 & 245.30501689837 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 261937.857142857 & 1044.86030862642 & 250.691747959307 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 261967.925 & 1019.71812997483 & 256.902292211346 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 261989.184210526 & 989.586930402775 & 264.746002762883 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 261999.166666667 & 955.66197409448 & 274.15464229904 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 261996.382352941 & 916.592938549865 & 285.837225374487 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 261987.5 & 879.794228828904 & 297.782698971249 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 262016.9 & 840.523925757093 & 311.730448082119 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 262050.964285714 & 797.523331469665 & 328.580937942982 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 262091.884615385 & 752.073372703086 & 348.492439871099 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 262065.375 & 728.388632064403 & 359.787843279834 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 262043.318181818 & 694.234201990723 & 377.456652856351 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 262002.75 & 668.811828917521 & 391.743594643136 \tabularnewline
Median & 262952.5 &  &  \tabularnewline
Midrange & 259108 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 261719.774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 262016.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 261719.774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 262016.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 262016.9 &  &  \tabularnewline
Midmean - Closest Observation & 261719.774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 262016.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 261987.5 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32756&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]261516.816666667[/C][C]1633.19011550558[/C][C]160.126377317506[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]261211.991657146[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]260902.9077648[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]261817.52555304[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]261495.45[/C][C]1619.70486193878[/C][C]161.446357385746[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]261609.116666667[/C][C]1480.15122606752[/C][C]176.744856916892[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]261630.316666667[/C][C]1464.71854520312[/C][C]178.621563523922[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]261642.516666667[/C][C]1460.57359417682[/C][C]179.136825223880[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]261923.85[/C][C]1219.31164284895[/C][C]214.812883593901[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]261768.35[/C][C]1173.75730651204[/C][C]223.017440272961[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]261760.65[/C][C]1148.62114262261[/C][C]227.891199531928[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]261746.65[/C][C]1111.00978419593[/C][C]235.593469763574[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]261757.45[/C][C]1089.00789256581[/C][C]240.363225819488[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]261833.283333333[/C][C]1072.70048712585[/C][C]244.087969079681[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]261923.3[/C][C]1044.75474788121[/C][C]250.70314399737[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]262018.1[/C][C]1015.13716022407[/C][C]258.111031953716[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]262057.966666667[/C][C]952.947738966575[/C][C]274.997207035567[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]261781.7[/C][C]906.637071415865[/C][C]288.73924115102[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]261778.45[/C][C]859.900203257417[/C][C]304.428873267326[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]261767.25[/C][C]803.684149537313[/C][C]325.709111161022[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]262272.15[/C][C]679.973896900537[/C][C]385.709144417883[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]262210.95[/C][C]662.76161636528[/C][C]395.633880305287[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]262300.25[/C][C]586.852590093969[/C][C]446.961050232392[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]262066.25[/C][C]537.898223852026[/C][C]487.204155691902[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]261599.879310345[/C][C]1515.42520713681[/C][C]172.624737980043[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]261711.767857143[/C][C]1383.60073485840[/C][C]189.152666129458[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]261768.796296296[/C][C]1317.25227891358[/C][C]198.723358073970[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]261822.057692308[/C][C]1241.75143800842[/C][C]210.849007038181[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]261875.92[/C][C]1146.95265024769[/C][C]228.323218001586[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]261863.9375[/C][C]1117.03013802711[/C][C]234.428712874751[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]261884.717391304[/C][C]1092.60508605377[/C][C]239.688356510557[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]261908.886363636[/C][C]1067.68662816279[/C][C]245.30501689837[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]261937.857142857[/C][C]1044.86030862642[/C][C]250.691747959307[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]261967.925[/C][C]1019.71812997483[/C][C]256.902292211346[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]261989.184210526[/C][C]989.586930402775[/C][C]264.746002762883[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]261999.166666667[/C][C]955.66197409448[/C][C]274.15464229904[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]261996.382352941[/C][C]916.592938549865[/C][C]285.837225374487[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]261987.5[/C][C]879.794228828904[/C][C]297.782698971249[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]262016.9[/C][C]840.523925757093[/C][C]311.730448082119[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]262050.964285714[/C][C]797.523331469665[/C][C]328.580937942982[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]262091.884615385[/C][C]752.073372703086[/C][C]348.492439871099[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]262065.375[/C][C]728.388632064403[/C][C]359.787843279834[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]262043.318181818[/C][C]694.234201990723[/C][C]377.456652856351[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]262002.75[/C][C]668.811828917521[/C][C]391.743594643136[/C][/ROW]
[ROW][C]Median[/C][C]262952.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]259108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]261719.774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]262016.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]261719.774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]262016.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]262016.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]261719.774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]262016.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]261987.5[/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=32756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32756&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 Mean261516.8166666671633.19011550558160.126377317506
Geometric Mean261211.991657146
Harmonic Mean260902.9077648
Quadratic Mean261817.52555304
Winsorized Mean ( 1 / 20 )261495.451619.70486193878161.446357385746
Winsorized Mean ( 2 / 20 )261609.1166666671480.15122606752176.744856916892
Winsorized Mean ( 3 / 20 )261630.3166666671464.71854520312178.621563523922
Winsorized Mean ( 4 / 20 )261642.5166666671460.57359417682179.136825223880
Winsorized Mean ( 5 / 20 )261923.851219.31164284895214.812883593901
Winsorized Mean ( 6 / 20 )261768.351173.75730651204223.017440272961
Winsorized Mean ( 7 / 20 )261760.651148.62114262261227.891199531928
Winsorized Mean ( 8 / 20 )261746.651111.00978419593235.593469763574
Winsorized Mean ( 9 / 20 )261757.451089.00789256581240.363225819488
Winsorized Mean ( 10 / 20 )261833.2833333331072.70048712585244.087969079681
Winsorized Mean ( 11 / 20 )261923.31044.75474788121250.70314399737
Winsorized Mean ( 12 / 20 )262018.11015.13716022407258.111031953716
Winsorized Mean ( 13 / 20 )262057.966666667952.947738966575274.997207035567
Winsorized Mean ( 14 / 20 )261781.7906.637071415865288.73924115102
Winsorized Mean ( 15 / 20 )261778.45859.900203257417304.428873267326
Winsorized Mean ( 16 / 20 )261767.25803.684149537313325.709111161022
Winsorized Mean ( 17 / 20 )262272.15679.973896900537385.709144417883
Winsorized Mean ( 18 / 20 )262210.95662.76161636528395.633880305287
Winsorized Mean ( 19 / 20 )262300.25586.852590093969446.961050232392
Winsorized Mean ( 20 / 20 )262066.25537.898223852026487.204155691902
Trimmed Mean ( 1 / 20 )261599.8793103451515.42520713681172.624737980043
Trimmed Mean ( 2 / 20 )261711.7678571431383.60073485840189.152666129458
Trimmed Mean ( 3 / 20 )261768.7962962961317.25227891358198.723358073970
Trimmed Mean ( 4 / 20 )261822.0576923081241.75143800842210.849007038181
Trimmed Mean ( 5 / 20 )261875.921146.95265024769228.323218001586
Trimmed Mean ( 6 / 20 )261863.93751117.03013802711234.428712874751
Trimmed Mean ( 7 / 20 )261884.7173913041092.60508605377239.688356510557
Trimmed Mean ( 8 / 20 )261908.8863636361067.68662816279245.30501689837
Trimmed Mean ( 9 / 20 )261937.8571428571044.86030862642250.691747959307
Trimmed Mean ( 10 / 20 )261967.9251019.71812997483256.902292211346
Trimmed Mean ( 11 / 20 )261989.184210526989.586930402775264.746002762883
Trimmed Mean ( 12 / 20 )261999.166666667955.66197409448274.15464229904
Trimmed Mean ( 13 / 20 )261996.382352941916.592938549865285.837225374487
Trimmed Mean ( 14 / 20 )261987.5879.794228828904297.782698971249
Trimmed Mean ( 15 / 20 )262016.9840.523925757093311.730448082119
Trimmed Mean ( 16 / 20 )262050.964285714797.523331469665328.580937942982
Trimmed Mean ( 17 / 20 )262091.884615385752.073372703086348.492439871099
Trimmed Mean ( 18 / 20 )262065.375728.388632064403359.787843279834
Trimmed Mean ( 19 / 20 )262043.318181818694.234201990723377.456652856351
Trimmed Mean ( 20 / 20 )262002.75668.811828917521391.743594643136
Median262952.5
Midrange259108
Midmean - Weighted Average at Xnp261719.774193548
Midmean - Weighted Average at X(n+1)p262016.9
Midmean - Empirical Distribution Function261719.774193548
Midmean - Empirical Distribution Function - Averaging262016.9
Midmean - Empirical Distribution Function - Interpolation262016.9
Midmean - Closest Observation261719.774193548
Midmean - True Basic - Statistics Graphics Toolkit262016.9
Midmean - MS Excel (old versions)261987.5
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')