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Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 13:52:26 -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/20/t12560684718o64efzb6daorx7.htm/, Retrieved Thu, 02 May 2024 18:49:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49099, Retrieved Thu, 02 May 2024 18:49:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-20 19:52:26] [99bf2a1e962091d45abf4c2600a412f9] [Current]
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Dataseries X:
0.116742833
0.143551689
0.105714286
0.138176276
0.134115884
0.097661871
0.15145334
0.16254323
0.148139198
0.131851532
0.148648649
0.138115135
0.142650253
0.13298713
0.111898831
0.116250761
0.098523023
0.101752504
0.149171271
0.126763402
0.120583717
0.128706625
0.132487197
0.104152128
0.103472343
0.117063492
0.095050803
0.117047308
0.106723785
0.102724991
0.134228188
0.132318749
0.123727799
0.110964333
0.136517125
0.120432432
0.118454392
0.130125622
0.10398749
0.12508918
0.123999029
0.097785616
0.129069767
0.123416339
0.142294566
0.095367354
0.120084766
0.134203655
0.117660446
0.105263158
0.111816738
0.107244474
0.114223088
0.099707968
0.134900358
0.140785658
0.117593644
0.125808056
0.122439024
0.107769424





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49099&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49099&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49099&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.1222000320833330.0020909216668904158.443142092964
Geometric Mean0.121147916978902
Harmonic Mean0.120102151470360
Quadratic Mean0.123250935464097
Winsorized Mean ( 1 / 20 )0.1220204764333330.0020367995181995159.9079464341178
Winsorized Mean ( 2 / 20 )0.1220208913666670.0020023661761219460.9383502486989
Winsorized Mean ( 3 / 20 )0.1220009475166670.0019951313758076661.1493303127866
Winsorized Mean ( 4 / 20 )0.1220161445833330.0019774781025674261.7029055466738
Winsorized Mean ( 5 / 20 )0.1217325975833330.0018771244299648764.8505744425326
Winsorized Mean ( 6 / 20 )0.1218469075833330.0018200327970238866.9476439010207
Winsorized Mean ( 7 / 20 )0.1219188675833330.0017910905735637868.0696271773393
Winsorized Mean ( 8 / 20 )0.1218173267833330.0017350628995648570.209170407531
Winsorized Mean ( 9 / 20 )0.1215031915333330.0016513723810445273.5771004335684
Winsorized Mean ( 10 / 20 )0.1215204410333330.0016447069893755873.8857692089393
Winsorized Mean ( 11 / 20 )0.1214311613666670.0015594772911506177.866578792611
Winsorized Mean ( 12 / 20 )0.1211980335666670.0014919081561095581.236926730607
Winsorized Mean ( 13 / 20 )0.1212711215166670.0014313113295193484.727284005634
Winsorized Mean ( 14 / 20 )0.121386891250.0014096357296668686.1122406983025
Winsorized Mean ( 15 / 20 )0.1214961860.0013840598179365487.7824675100644
Winsorized Mean ( 16 / 20 )0.1220471606666670.00119882018166706101.806061103300
Winsorized Mean ( 17 / 20 )0.1221470277333330.00113948511879291107.194930165238
Winsorized Mean ( 18 / 20 )0.1221211212333330.00112794339386845108.268838575756
Winsorized Mean ( 19 / 20 )0.12270918390.000995175524002767123.304061384511
Winsorized Mean ( 20 / 20 )0.1228097715666670.000810887529653717151.45105464763
Trimmed Mean ( 1 / 20 )0.1219725498620690.0019912892160670161.253055999056
Trimmed Mean ( 2 / 20 )0.1219211999642860.0019349786358804263.0090677506687
Trimmed Mean ( 3 / 20 )0.1218658158518520.0018879062029581164.5507788792175
Trimmed Mean ( 4 / 20 )0.1218138421346150.0018322766721697066.4822316328291
Trimmed Mean ( 5 / 20 )0.12175315140.0017690910693892868.8224328903719
Trimmed Mean ( 6 / 20 )0.1217582898541670.0017241706106747870.6184695994294
Trimmed Mean ( 7 / 20 )0.1217390251304350.0016839442979625472.2939739026589
Trimmed Mean ( 8 / 20 )0.1217039908863640.0016395153181635974.2316888034224
Trimmed Mean ( 9 / 20 )0.1216837523333330.0015965256298949776.2178508473667
Trimmed Mean ( 10 / 20 )0.12171384580.0015615570704626477.9438984986567
Trimmed Mean ( 11 / 20 )0.1217443833947370.0015148733214926780.3660488751475
Trimmed Mean ( 12 / 20 )0.1217918412777780.0014737386140620082.6414128772053
Trimmed Mean ( 13 / 20 )0.1218791659411760.0014336236912889085.0147543471475
Trimmed Mean ( 14 / 20 )0.121966864656250.0013925169532032387.587346334052
Trimmed Mean ( 15 / 20 )0.1220497180.0013377356371609691.2360518846779
Trimmed Mean ( 16 / 20 )0.1221287940.0012636569450548796.6471117639425
Trimmed Mean ( 17 / 20 )0.1221405680384620.00121822719549656100.260910682326
Trimmed Mean ( 18 / 20 )0.1221396180833330.00116642038475464104.713206044513
Trimmed Mean ( 19 / 20 )0.1221424206363640.00108365219078357112.713674807453
Trimmed Mean ( 20 / 20 )0.12205293170.00100706023227211121.197250957499
Median0.1215113705
Midrange0.1287970165
Midmean - Weighted Average at Xnp0.121572129483871
Midmean - Weighted Average at X(n+1)p0.122049718
Midmean - Empirical Distribution Function0.121572129483871
Midmean - Empirical Distribution Function - Averaging0.122049718
Midmean - Empirical Distribution Function - Interpolation0.122049718
Midmean - Closest Observation0.121572129483871
Midmean - True Basic - Statistics Graphics Toolkit0.122049718
Midmean - MS Excel (old versions)0.12196686465625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.122200032083333 & 0.00209092166689041 & 58.443142092964 \tabularnewline
Geometric Mean & 0.121147916978902 &  &  \tabularnewline
Harmonic Mean & 0.120102151470360 &  &  \tabularnewline
Quadratic Mean & 0.123250935464097 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.122020476433333 & 0.00203679951819951 & 59.9079464341178 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.122020891366667 & 0.00200236617612194 & 60.9383502486989 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.122000947516667 & 0.00199513137580766 & 61.1493303127866 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.122016144583333 & 0.00197747810256742 & 61.7029055466738 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.121732597583333 & 0.00187712442996487 & 64.8505744425326 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.121846907583333 & 0.00182003279702388 & 66.9476439010207 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.121918867583333 & 0.00179109057356378 & 68.0696271773393 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.121817326783333 & 0.00173506289956485 & 70.209170407531 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.121503191533333 & 0.00165137238104452 & 73.5771004335684 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.121520441033333 & 0.00164470698937558 & 73.8857692089393 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.121431161366667 & 0.00155947729115061 & 77.866578792611 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.121198033566667 & 0.00149190815610955 & 81.236926730607 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.121271121516667 & 0.00143131132951934 & 84.727284005634 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.12138689125 & 0.00140963572966686 & 86.1122406983025 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.121496186 & 0.00138405981793654 & 87.7824675100644 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.122047160666667 & 0.00119882018166706 & 101.806061103300 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.122147027733333 & 0.00113948511879291 & 107.194930165238 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.122121121233333 & 0.00112794339386845 & 108.268838575756 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.1227091839 & 0.000995175524002767 & 123.304061384511 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.122809771566667 & 0.000810887529653717 & 151.45105464763 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.121972549862069 & 0.00199128921606701 & 61.253055999056 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.121921199964286 & 0.00193497863588042 & 63.0090677506687 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.121865815851852 & 0.00188790620295811 & 64.5507788792175 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.121813842134615 & 0.00183227667216970 & 66.4822316328291 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.1217531514 & 0.00176909106938928 & 68.8224328903719 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.121758289854167 & 0.00172417061067478 & 70.6184695994294 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.121739025130435 & 0.00168394429796254 & 72.2939739026589 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.121703990886364 & 0.00163951531816359 & 74.2316888034224 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.121683752333333 & 0.00159652562989497 & 76.2178508473667 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.1217138458 & 0.00156155707046264 & 77.9438984986567 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.121744383394737 & 0.00151487332149267 & 80.3660488751475 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.121791841277778 & 0.00147373861406200 & 82.6414128772053 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.121879165941176 & 0.00143362369128890 & 85.0147543471475 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.12196686465625 & 0.00139251695320323 & 87.587346334052 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.122049718 & 0.00133773563716096 & 91.2360518846779 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.122128794 & 0.00126365694505487 & 96.6471117639425 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.122140568038462 & 0.00121822719549656 & 100.260910682326 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.122139618083333 & 0.00116642038475464 & 104.713206044513 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.122142420636364 & 0.00108365219078357 & 112.713674807453 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.1220529317 & 0.00100706023227211 & 121.197250957499 \tabularnewline
Median & 0.1215113705 &  &  \tabularnewline
Midrange & 0.1287970165 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.121572129483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.122049718 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.121572129483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.122049718 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.122049718 &  &  \tabularnewline
Midmean - Closest Observation & 0.121572129483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.122049718 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.12196686465625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49099&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]0.122200032083333[/C][C]0.00209092166689041[/C][C]58.443142092964[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.121147916978902[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.120102151470360[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.123250935464097[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.122020476433333[/C][C]0.00203679951819951[/C][C]59.9079464341178[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.122020891366667[/C][C]0.00200236617612194[/C][C]60.9383502486989[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.122000947516667[/C][C]0.00199513137580766[/C][C]61.1493303127866[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.122016144583333[/C][C]0.00197747810256742[/C][C]61.7029055466738[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.121732597583333[/C][C]0.00187712442996487[/C][C]64.8505744425326[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.121846907583333[/C][C]0.00182003279702388[/C][C]66.9476439010207[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.121918867583333[/C][C]0.00179109057356378[/C][C]68.0696271773393[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.121817326783333[/C][C]0.00173506289956485[/C][C]70.209170407531[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.121503191533333[/C][C]0.00165137238104452[/C][C]73.5771004335684[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.121520441033333[/C][C]0.00164470698937558[/C][C]73.8857692089393[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.121431161366667[/C][C]0.00155947729115061[/C][C]77.866578792611[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.121198033566667[/C][C]0.00149190815610955[/C][C]81.236926730607[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.121271121516667[/C][C]0.00143131132951934[/C][C]84.727284005634[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.12138689125[/C][C]0.00140963572966686[/C][C]86.1122406983025[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.121496186[/C][C]0.00138405981793654[/C][C]87.7824675100644[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.122047160666667[/C][C]0.00119882018166706[/C][C]101.806061103300[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.122147027733333[/C][C]0.00113948511879291[/C][C]107.194930165238[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.122121121233333[/C][C]0.00112794339386845[/C][C]108.268838575756[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.1227091839[/C][C]0.000995175524002767[/C][C]123.304061384511[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.122809771566667[/C][C]0.000810887529653717[/C][C]151.45105464763[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.121972549862069[/C][C]0.00199128921606701[/C][C]61.253055999056[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.121921199964286[/C][C]0.00193497863588042[/C][C]63.0090677506687[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.121865815851852[/C][C]0.00188790620295811[/C][C]64.5507788792175[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.121813842134615[/C][C]0.00183227667216970[/C][C]66.4822316328291[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.1217531514[/C][C]0.00176909106938928[/C][C]68.8224328903719[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.121758289854167[/C][C]0.00172417061067478[/C][C]70.6184695994294[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.121739025130435[/C][C]0.00168394429796254[/C][C]72.2939739026589[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.121703990886364[/C][C]0.00163951531816359[/C][C]74.2316888034224[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.121683752333333[/C][C]0.00159652562989497[/C][C]76.2178508473667[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.1217138458[/C][C]0.00156155707046264[/C][C]77.9438984986567[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.121744383394737[/C][C]0.00151487332149267[/C][C]80.3660488751475[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.121791841277778[/C][C]0.00147373861406200[/C][C]82.6414128772053[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.121879165941176[/C][C]0.00143362369128890[/C][C]85.0147543471475[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.12196686465625[/C][C]0.00139251695320323[/C][C]87.587346334052[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.122049718[/C][C]0.00133773563716096[/C][C]91.2360518846779[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.122128794[/C][C]0.00126365694505487[/C][C]96.6471117639425[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.122140568038462[/C][C]0.00121822719549656[/C][C]100.260910682326[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.122139618083333[/C][C]0.00116642038475464[/C][C]104.713206044513[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.122142420636364[/C][C]0.00108365219078357[/C][C]112.713674807453[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.1220529317[/C][C]0.00100706023227211[/C][C]121.197250957499[/C][/ROW]
[ROW][C]Median[/C][C]0.1215113705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.1287970165[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.121572129483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.122049718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.121572129483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.122049718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.122049718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.121572129483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.122049718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.12196686465625[/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=49099&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49099&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 Mean0.1222000320833330.0020909216668904158.443142092964
Geometric Mean0.121147916978902
Harmonic Mean0.120102151470360
Quadratic Mean0.123250935464097
Winsorized Mean ( 1 / 20 )0.1220204764333330.0020367995181995159.9079464341178
Winsorized Mean ( 2 / 20 )0.1220208913666670.0020023661761219460.9383502486989
Winsorized Mean ( 3 / 20 )0.1220009475166670.0019951313758076661.1493303127866
Winsorized Mean ( 4 / 20 )0.1220161445833330.0019774781025674261.7029055466738
Winsorized Mean ( 5 / 20 )0.1217325975833330.0018771244299648764.8505744425326
Winsorized Mean ( 6 / 20 )0.1218469075833330.0018200327970238866.9476439010207
Winsorized Mean ( 7 / 20 )0.1219188675833330.0017910905735637868.0696271773393
Winsorized Mean ( 8 / 20 )0.1218173267833330.0017350628995648570.209170407531
Winsorized Mean ( 9 / 20 )0.1215031915333330.0016513723810445273.5771004335684
Winsorized Mean ( 10 / 20 )0.1215204410333330.0016447069893755873.8857692089393
Winsorized Mean ( 11 / 20 )0.1214311613666670.0015594772911506177.866578792611
Winsorized Mean ( 12 / 20 )0.1211980335666670.0014919081561095581.236926730607
Winsorized Mean ( 13 / 20 )0.1212711215166670.0014313113295193484.727284005634
Winsorized Mean ( 14 / 20 )0.121386891250.0014096357296668686.1122406983025
Winsorized Mean ( 15 / 20 )0.1214961860.0013840598179365487.7824675100644
Winsorized Mean ( 16 / 20 )0.1220471606666670.00119882018166706101.806061103300
Winsorized Mean ( 17 / 20 )0.1221470277333330.00113948511879291107.194930165238
Winsorized Mean ( 18 / 20 )0.1221211212333330.00112794339386845108.268838575756
Winsorized Mean ( 19 / 20 )0.12270918390.000995175524002767123.304061384511
Winsorized Mean ( 20 / 20 )0.1228097715666670.000810887529653717151.45105464763
Trimmed Mean ( 1 / 20 )0.1219725498620690.0019912892160670161.253055999056
Trimmed Mean ( 2 / 20 )0.1219211999642860.0019349786358804263.0090677506687
Trimmed Mean ( 3 / 20 )0.1218658158518520.0018879062029581164.5507788792175
Trimmed Mean ( 4 / 20 )0.1218138421346150.0018322766721697066.4822316328291
Trimmed Mean ( 5 / 20 )0.12175315140.0017690910693892868.8224328903719
Trimmed Mean ( 6 / 20 )0.1217582898541670.0017241706106747870.6184695994294
Trimmed Mean ( 7 / 20 )0.1217390251304350.0016839442979625472.2939739026589
Trimmed Mean ( 8 / 20 )0.1217039908863640.0016395153181635974.2316888034224
Trimmed Mean ( 9 / 20 )0.1216837523333330.0015965256298949776.2178508473667
Trimmed Mean ( 10 / 20 )0.12171384580.0015615570704626477.9438984986567
Trimmed Mean ( 11 / 20 )0.1217443833947370.0015148733214926780.3660488751475
Trimmed Mean ( 12 / 20 )0.1217918412777780.0014737386140620082.6414128772053
Trimmed Mean ( 13 / 20 )0.1218791659411760.0014336236912889085.0147543471475
Trimmed Mean ( 14 / 20 )0.121966864656250.0013925169532032387.587346334052
Trimmed Mean ( 15 / 20 )0.1220497180.0013377356371609691.2360518846779
Trimmed Mean ( 16 / 20 )0.1221287940.0012636569450548796.6471117639425
Trimmed Mean ( 17 / 20 )0.1221405680384620.00121822719549656100.260910682326
Trimmed Mean ( 18 / 20 )0.1221396180833330.00116642038475464104.713206044513
Trimmed Mean ( 19 / 20 )0.1221424206363640.00108365219078357112.713674807453
Trimmed Mean ( 20 / 20 )0.12205293170.00100706023227211121.197250957499
Median0.1215113705
Midrange0.1287970165
Midmean - Weighted Average at Xnp0.121572129483871
Midmean - Weighted Average at X(n+1)p0.122049718
Midmean - Empirical Distribution Function0.121572129483871
Midmean - Empirical Distribution Function - Averaging0.122049718
Midmean - Empirical Distribution Function - Interpolation0.122049718
Midmean - Closest Observation0.121572129483871
Midmean - True Basic - Statistics Graphics Toolkit0.122049718
Midmean - MS Excel (old versions)0.12196686465625
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')