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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 02:52:53 -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/2007/Dec/13/t1197538646j7qpaq8g5gbc6qj.htm/, Retrieved Sun, 05 May 2024 14:43:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3365, Retrieved Sun, 05 May 2024 14:43:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendancy ...] [2007-12-13 09:52:53] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]
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Dataseries X:
1
1.04
1.02
1.07
1.12
1.08
1.02
1.01
1.04
0.98
0.95
0.94
0.94
0.96
0.97
1.03
1.01
0.99
1
1
1.02
1.01
0.99
0.98
1.01
1.03
1.03
1
0.96
0.97
0.98
1.02
1.04
1.01
1.01
1
1.01
1.02
1.03
1.06
1.12
1.12
1.13
1.13
1.13
1.17
1.14
1.08
1.07
1.12
1.14
1.21
1.2
1.23
1.29
1.31
1.37
1.35
1.26
1.26
1.28
1.28
1.27
1.35
1.37
1.37
1.4
1.4
1.28
1.23
1.23
1.25
1.21
1.22
1.29
1.32
1.36
1.36
1.37
1.32




Summary of compuational 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 compuational 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=3365&T=0

[TABLE]
[ROW][C]Summary of compuational 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=3365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3365&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 compuational 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 Mean1.129250.015788129453661471.5252559408246
Geometric Mean1.12079617882205
Harmonic Mean1.11265517825747
Quadratic Mean1.13793563086846
Winsorized Mean ( 1 / 26 )1.129250.015788129453661471.5252559408246
Winsorized Mean ( 2 / 26 )1.128750.015596144241121772.3736573956448
Winsorized Mean ( 3 / 26 )1.1291250.015543114546645072.6447068643475
Winsorized Mean ( 4 / 26 )1.1291250.015543114546645072.6447068643475
Winsorized Mean ( 5 / 26 )1.129750.015459189844002573.0795087841095
Winsorized Mean ( 6 / 26 )1.1290.015313806131326373.7243236800868
Winsorized Mean ( 7 / 26 )1.1298750.015201696430566274.3255863028649
Winsorized Mean ( 8 / 26 )1.1288750.015012646304054275.194937463833
Winsorized Mean ( 9 / 26 )1.1288750.015012646304054275.194937463833
Winsorized Mean ( 10 / 26 )1.1263750.014183744205376279.4130931642898
Winsorized Mean ( 11 / 26 )1.1263750.014183744205376279.4130931642898
Winsorized Mean ( 12 / 26 )1.1263750.013748698154711581.9259385379704
Winsorized Mean ( 13 / 26 )1.1231250.013213909230500284.9956648262434
Winsorized Mean ( 14 / 26 )1.1231250.013213909230500284.9956648262434
Winsorized Mean ( 15 / 26 )1.121250.012918163789649286.7963913647245
Winsorized Mean ( 16 / 26 )1.121250.012918163789649286.7963913647245
Winsorized Mean ( 17 / 26 )1.1233750.012671536615181088.6534154550878
Winsorized Mean ( 18 / 26 )1.1211250.012323428533601590.9750883808914
Winsorized Mean ( 19 / 26 )1.118750.011964312704080193.5072517469792
Winsorized Mean ( 20 / 26 )1.118750.011964312704080193.5072517469792
Winsorized Mean ( 21 / 26 )1.1161250.011575965047120396.4174473105937
Winsorized Mean ( 22 / 26 )1.1106250.010787568662967102.954153498248
Winsorized Mean ( 23 / 26 )1.1106250.010787568662967102.954153498248
Winsorized Mean ( 24 / 26 )1.1136250.0104400697018625106.668349139598
Winsorized Mean ( 25 / 26 )1.11050.0100030058773490111.016629762724
Winsorized Mean ( 26 / 26 )1.107250.00955658530986932115.862514077755
Trimmed Mean ( 1 / 26 )1.128205128205130.015624148157658672.2090648924182
Trimmed Mean ( 2 / 26 )1.127105263157890.015428176308043073.0549898221162
Trimmed Mean ( 3 / 26 )1.126216216216220.015310802886575573.556966578394
Trimmed Mean ( 4 / 26 )1.125138888888890.015187911467864774.0812119737144
Trimmed Mean ( 5 / 26 )1.1240.015035362044235774.7570957515403
Trimmed Mean ( 6 / 26 )1.122647058823530.014870848218462875.493142175287
Trimmed Mean ( 7 / 26 )1.121363636363640.014705954526579676.252353040864
Trimmed Mean ( 8 / 26 )1.119843750.014525381772945077.0956500493382
Trimmed Mean ( 9 / 26 )1.118387096774190.014342994775202177.9744477567401
Trimmed Mean ( 10 / 26 )1.116833333333330.014113125810771379.1343709613184
Trimmed Mean ( 11 / 26 )1.115517241379310.013996310147647179.7008089712015
Trimmed Mean ( 12 / 26 )1.114107142857140.013839940286153880.4994183372128
Trimmed Mean ( 13 / 26 )1.112592592592590.013716163334937881.1154377083423
Trimmed Mean ( 14 / 26 )1.111346153846150.013651084206450581.4108342633337
Trimmed Mean ( 15 / 26 )1.110.013549606515862181.9211981322524
Trimmed Mean ( 16 / 26 )1.108750.013460030797810882.3735113726735
Trimmed Mean ( 17 / 26 )1.107391304347830.013324035825786183.1123031210024
Trimmed Mean ( 18 / 26 )1.105681818181820.01316827875049883.9655538230465
Trimmed Mean ( 19 / 26 )1.104047619047620.013017720094052584.8111352119201
Trimmed Mean ( 20 / 26 )1.10250.012873895272495485.6384160865011
Trimmed Mean ( 21 / 26 )1.100789473684210.012652380335633387.002559556641
Trimmed Mean ( 22 / 26 )1.099166666666670.012423575898075388.4742585938523
Trimmed Mean ( 23 / 26 )1.097941176470590.012285807731517489.3666253342047
Trimmed Mean ( 24 / 26 )1.09656250.012053387415390190.9754629308506
Trimmed Mean ( 25 / 26 )1.094666666666670.011761356295755593.073165980161
Trimmed Mean ( 26 / 26 )1.092857142857140.011441791295835095.5145146944747
Median1.08
Midrange1.17
Midmean - Weighted Average at Xnp1.09977272727273
Midmean - Weighted Average at X(n+1)p1.09977272727273
Midmean - Empirical Distribution Function1.09977272727273
Midmean - Empirical Distribution Function - Averaging1.09977272727273
Midmean - Empirical Distribution Function - Interpolation1.09977272727273
Midmean - Closest Observation1.09977272727273
Midmean - True Basic - Statistics Graphics Toolkit1.09977272727273
Midmean - MS Excel (old versions)1.09977272727273
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.12925 & 0.0157881294536614 & 71.5252559408246 \tabularnewline
Geometric Mean & 1.12079617882205 &  &  \tabularnewline
Harmonic Mean & 1.11265517825747 &  &  \tabularnewline
Quadratic Mean & 1.13793563086846 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 1.12925 & 0.0157881294536614 & 71.5252559408246 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 1.12875 & 0.0155961442411217 & 72.3736573956448 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 1.129125 & 0.0155431145466450 & 72.6447068643475 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 1.129125 & 0.0155431145466450 & 72.6447068643475 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 1.12975 & 0.0154591898440025 & 73.0795087841095 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 1.129 & 0.0153138061313263 & 73.7243236800868 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 1.129875 & 0.0152016964305662 & 74.3255863028649 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 1.128875 & 0.0150126463040542 & 75.194937463833 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 1.128875 & 0.0150126463040542 & 75.194937463833 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 1.126375 & 0.0141837442053762 & 79.4130931642898 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 1.126375 & 0.0141837442053762 & 79.4130931642898 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 1.126375 & 0.0137486981547115 & 81.9259385379704 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 1.123125 & 0.0132139092305002 & 84.9956648262434 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 1.123125 & 0.0132139092305002 & 84.9956648262434 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 1.12125 & 0.0129181637896492 & 86.7963913647245 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 1.12125 & 0.0129181637896492 & 86.7963913647245 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 1.123375 & 0.0126715366151810 & 88.6534154550878 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 1.121125 & 0.0123234285336015 & 90.9750883808914 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 1.11875 & 0.0119643127040801 & 93.5072517469792 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 1.11875 & 0.0119643127040801 & 93.5072517469792 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 1.116125 & 0.0115759650471203 & 96.4174473105937 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 1.110625 & 0.010787568662967 & 102.954153498248 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 1.110625 & 0.010787568662967 & 102.954153498248 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 1.113625 & 0.0104400697018625 & 106.668349139598 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 1.1105 & 0.0100030058773490 & 111.016629762724 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 1.10725 & 0.00955658530986932 & 115.862514077755 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 1.12820512820513 & 0.0156241481576586 & 72.2090648924182 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 1.12710526315789 & 0.0154281763080430 & 73.0549898221162 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 1.12621621621622 & 0.0153108028865755 & 73.556966578394 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 1.12513888888889 & 0.0151879114678647 & 74.0812119737144 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 1.124 & 0.0150353620442357 & 74.7570957515403 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 1.12264705882353 & 0.0148708482184628 & 75.493142175287 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 1.12136363636364 & 0.0147059545265796 & 76.252353040864 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 1.11984375 & 0.0145253817729450 & 77.0956500493382 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 1.11838709677419 & 0.0143429947752021 & 77.9744477567401 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 1.11683333333333 & 0.0141131258107713 & 79.1343709613184 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 1.11551724137931 & 0.0139963101476471 & 79.7008089712015 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 1.11410714285714 & 0.0138399402861538 & 80.4994183372128 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 1.11259259259259 & 0.0137161633349378 & 81.1154377083423 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 1.11134615384615 & 0.0136510842064505 & 81.4108342633337 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 1.11 & 0.0135496065158621 & 81.9211981322524 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 1.10875 & 0.0134600307978108 & 82.3735113726735 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 1.10739130434783 & 0.0133240358257861 & 83.1123031210024 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 1.10568181818182 & 0.013168278750498 & 83.9655538230465 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 1.10404761904762 & 0.0130177200940525 & 84.8111352119201 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 1.1025 & 0.0128738952724954 & 85.6384160865011 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 1.10078947368421 & 0.0126523803356333 & 87.002559556641 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 1.09916666666667 & 0.0124235758980753 & 88.4742585938523 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 1.09794117647059 & 0.0122858077315174 & 89.3666253342047 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 1.0965625 & 0.0120533874153901 & 90.9754629308506 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 1.09466666666667 & 0.0117613562957555 & 93.073165980161 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 1.09285714285714 & 0.0114417912958350 & 95.5145146944747 \tabularnewline
Median & 1.08 &  &  \tabularnewline
Midrange & 1.17 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.09977272727273 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.09977272727273 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.09977272727273 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.09977272727273 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.09977272727273 &  &  \tabularnewline
Midmean - Closest Observation & 1.09977272727273 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.09977272727273 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.09977272727273 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3365&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]1.12925[/C][C]0.0157881294536614[/C][C]71.5252559408246[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.12079617882205[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.11265517825747[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.13793563086846[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]1.12925[/C][C]0.0157881294536614[/C][C]71.5252559408246[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]1.12875[/C][C]0.0155961442411217[/C][C]72.3736573956448[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]1.129125[/C][C]0.0155431145466450[/C][C]72.6447068643475[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]1.129125[/C][C]0.0155431145466450[/C][C]72.6447068643475[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]1.12975[/C][C]0.0154591898440025[/C][C]73.0795087841095[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]1.129[/C][C]0.0153138061313263[/C][C]73.7243236800868[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]1.129875[/C][C]0.0152016964305662[/C][C]74.3255863028649[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]1.128875[/C][C]0.0150126463040542[/C][C]75.194937463833[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]1.128875[/C][C]0.0150126463040542[/C][C]75.194937463833[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]1.126375[/C][C]0.0141837442053762[/C][C]79.4130931642898[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]1.126375[/C][C]0.0141837442053762[/C][C]79.4130931642898[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]1.126375[/C][C]0.0137486981547115[/C][C]81.9259385379704[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]1.123125[/C][C]0.0132139092305002[/C][C]84.9956648262434[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]1.123125[/C][C]0.0132139092305002[/C][C]84.9956648262434[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]1.12125[/C][C]0.0129181637896492[/C][C]86.7963913647245[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]1.12125[/C][C]0.0129181637896492[/C][C]86.7963913647245[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]1.123375[/C][C]0.0126715366151810[/C][C]88.6534154550878[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]1.121125[/C][C]0.0123234285336015[/C][C]90.9750883808914[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]1.11875[/C][C]0.0119643127040801[/C][C]93.5072517469792[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]1.11875[/C][C]0.0119643127040801[/C][C]93.5072517469792[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]1.116125[/C][C]0.0115759650471203[/C][C]96.4174473105937[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]1.110625[/C][C]0.010787568662967[/C][C]102.954153498248[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]1.110625[/C][C]0.010787568662967[/C][C]102.954153498248[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]1.113625[/C][C]0.0104400697018625[/C][C]106.668349139598[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]1.1105[/C][C]0.0100030058773490[/C][C]111.016629762724[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]1.10725[/C][C]0.00955658530986932[/C][C]115.862514077755[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]1.12820512820513[/C][C]0.0156241481576586[/C][C]72.2090648924182[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]1.12710526315789[/C][C]0.0154281763080430[/C][C]73.0549898221162[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]1.12621621621622[/C][C]0.0153108028865755[/C][C]73.556966578394[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]1.12513888888889[/C][C]0.0151879114678647[/C][C]74.0812119737144[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]1.124[/C][C]0.0150353620442357[/C][C]74.7570957515403[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]1.12264705882353[/C][C]0.0148708482184628[/C][C]75.493142175287[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]1.12136363636364[/C][C]0.0147059545265796[/C][C]76.252353040864[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]1.11984375[/C][C]0.0145253817729450[/C][C]77.0956500493382[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]1.11838709677419[/C][C]0.0143429947752021[/C][C]77.9744477567401[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]1.11683333333333[/C][C]0.0141131258107713[/C][C]79.1343709613184[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]1.11551724137931[/C][C]0.0139963101476471[/C][C]79.7008089712015[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]1.11410714285714[/C][C]0.0138399402861538[/C][C]80.4994183372128[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]1.11259259259259[/C][C]0.0137161633349378[/C][C]81.1154377083423[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]1.11134615384615[/C][C]0.0136510842064505[/C][C]81.4108342633337[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]1.11[/C][C]0.0135496065158621[/C][C]81.9211981322524[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]1.10875[/C][C]0.0134600307978108[/C][C]82.3735113726735[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]1.10739130434783[/C][C]0.0133240358257861[/C][C]83.1123031210024[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]1.10568181818182[/C][C]0.013168278750498[/C][C]83.9655538230465[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]1.10404761904762[/C][C]0.0130177200940525[/C][C]84.8111352119201[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]1.1025[/C][C]0.0128738952724954[/C][C]85.6384160865011[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]1.10078947368421[/C][C]0.0126523803356333[/C][C]87.002559556641[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]1.09916666666667[/C][C]0.0124235758980753[/C][C]88.4742585938523[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]1.09794117647059[/C][C]0.0122858077315174[/C][C]89.3666253342047[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]1.0965625[/C][C]0.0120533874153901[/C][C]90.9754629308506[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]1.09466666666667[/C][C]0.0117613562957555[/C][C]93.073165980161[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]1.09285714285714[/C][C]0.0114417912958350[/C][C]95.5145146944747[/C][/ROW]
[ROW][C]Median[/C][C]1.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.17[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.09977272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3365&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 Mean1.129250.015788129453661471.5252559408246
Geometric Mean1.12079617882205
Harmonic Mean1.11265517825747
Quadratic Mean1.13793563086846
Winsorized Mean ( 1 / 26 )1.129250.015788129453661471.5252559408246
Winsorized Mean ( 2 / 26 )1.128750.015596144241121772.3736573956448
Winsorized Mean ( 3 / 26 )1.1291250.015543114546645072.6447068643475
Winsorized Mean ( 4 / 26 )1.1291250.015543114546645072.6447068643475
Winsorized Mean ( 5 / 26 )1.129750.015459189844002573.0795087841095
Winsorized Mean ( 6 / 26 )1.1290.015313806131326373.7243236800868
Winsorized Mean ( 7 / 26 )1.1298750.015201696430566274.3255863028649
Winsorized Mean ( 8 / 26 )1.1288750.015012646304054275.194937463833
Winsorized Mean ( 9 / 26 )1.1288750.015012646304054275.194937463833
Winsorized Mean ( 10 / 26 )1.1263750.014183744205376279.4130931642898
Winsorized Mean ( 11 / 26 )1.1263750.014183744205376279.4130931642898
Winsorized Mean ( 12 / 26 )1.1263750.013748698154711581.9259385379704
Winsorized Mean ( 13 / 26 )1.1231250.013213909230500284.9956648262434
Winsorized Mean ( 14 / 26 )1.1231250.013213909230500284.9956648262434
Winsorized Mean ( 15 / 26 )1.121250.012918163789649286.7963913647245
Winsorized Mean ( 16 / 26 )1.121250.012918163789649286.7963913647245
Winsorized Mean ( 17 / 26 )1.1233750.012671536615181088.6534154550878
Winsorized Mean ( 18 / 26 )1.1211250.012323428533601590.9750883808914
Winsorized Mean ( 19 / 26 )1.118750.011964312704080193.5072517469792
Winsorized Mean ( 20 / 26 )1.118750.011964312704080193.5072517469792
Winsorized Mean ( 21 / 26 )1.1161250.011575965047120396.4174473105937
Winsorized Mean ( 22 / 26 )1.1106250.010787568662967102.954153498248
Winsorized Mean ( 23 / 26 )1.1106250.010787568662967102.954153498248
Winsorized Mean ( 24 / 26 )1.1136250.0104400697018625106.668349139598
Winsorized Mean ( 25 / 26 )1.11050.0100030058773490111.016629762724
Winsorized Mean ( 26 / 26 )1.107250.00955658530986932115.862514077755
Trimmed Mean ( 1 / 26 )1.128205128205130.015624148157658672.2090648924182
Trimmed Mean ( 2 / 26 )1.127105263157890.015428176308043073.0549898221162
Trimmed Mean ( 3 / 26 )1.126216216216220.015310802886575573.556966578394
Trimmed Mean ( 4 / 26 )1.125138888888890.015187911467864774.0812119737144
Trimmed Mean ( 5 / 26 )1.1240.015035362044235774.7570957515403
Trimmed Mean ( 6 / 26 )1.122647058823530.014870848218462875.493142175287
Trimmed Mean ( 7 / 26 )1.121363636363640.014705954526579676.252353040864
Trimmed Mean ( 8 / 26 )1.119843750.014525381772945077.0956500493382
Trimmed Mean ( 9 / 26 )1.118387096774190.014342994775202177.9744477567401
Trimmed Mean ( 10 / 26 )1.116833333333330.014113125810771379.1343709613184
Trimmed Mean ( 11 / 26 )1.115517241379310.013996310147647179.7008089712015
Trimmed Mean ( 12 / 26 )1.114107142857140.013839940286153880.4994183372128
Trimmed Mean ( 13 / 26 )1.112592592592590.013716163334937881.1154377083423
Trimmed Mean ( 14 / 26 )1.111346153846150.013651084206450581.4108342633337
Trimmed Mean ( 15 / 26 )1.110.013549606515862181.9211981322524
Trimmed Mean ( 16 / 26 )1.108750.013460030797810882.3735113726735
Trimmed Mean ( 17 / 26 )1.107391304347830.013324035825786183.1123031210024
Trimmed Mean ( 18 / 26 )1.105681818181820.01316827875049883.9655538230465
Trimmed Mean ( 19 / 26 )1.104047619047620.013017720094052584.8111352119201
Trimmed Mean ( 20 / 26 )1.10250.012873895272495485.6384160865011
Trimmed Mean ( 21 / 26 )1.100789473684210.012652380335633387.002559556641
Trimmed Mean ( 22 / 26 )1.099166666666670.012423575898075388.4742585938523
Trimmed Mean ( 23 / 26 )1.097941176470590.012285807731517489.3666253342047
Trimmed Mean ( 24 / 26 )1.09656250.012053387415390190.9754629308506
Trimmed Mean ( 25 / 26 )1.094666666666670.011761356295755593.073165980161
Trimmed Mean ( 26 / 26 )1.092857142857140.011441791295835095.5145146944747
Median1.08
Midrange1.17
Midmean - Weighted Average at Xnp1.09977272727273
Midmean - Weighted Average at X(n+1)p1.09977272727273
Midmean - Empirical Distribution Function1.09977272727273
Midmean - Empirical Distribution Function - Averaging1.09977272727273
Midmean - Empirical Distribution Function - Interpolation1.09977272727273
Midmean - Closest Observation1.09977272727273
Midmean - True Basic - Statistics Graphics Toolkit1.09977272727273
Midmean - MS Excel (old versions)1.09977272727273
Number of observations80



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')