Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 12:23:18 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476271553yx954ngey5k3j8k.htm/, Retrieved Sun, 05 May 2024 21:55:34 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 21:55:34 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
95,77
97,63
100,87
100,39
98,62
97,42
95,62
97,22
97,56
97,06
97,68
98,18
98,54
98,24
98,1
96,32
96,15
96,67
94,7
93,94
96,69
96,54
95,94
95,6
99,15
100,33
99,86
96,09
94,42
93,85
93,73
94,63
95,54
95,48
95,84
96,29
97,63
98,8
99,84
100,73
100,44
100,54
100,25
100,29
100,7
100,62
100,43
99,73
99,17
98,9
98,94
98,91
99,5
99,52
99,1
99,12
99
98,66
98,3
98,18
97,95
97,84
98,61
99,54
99,64
99,69
99,77
99,85
99,87
100,23
100,46
100,36




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.16347222222220.231191727820453424.597684128462
Geometric Mean98.1439872433923
Harmonic Mean98.124347557882
Quadratic Mean98.1827999264071
Winsorized Mean ( 1 / 24 )98.16319444444440.230434103024728425.992477484595
Winsorized Mean ( 2 / 24 )98.16486111111110.229650512955589427.453262993995
Winsorized Mean ( 3 / 24 )98.18152777777780.224178875500669437.960657793936
Winsorized Mean ( 4 / 24 )98.188750.220801901164603444.691596775711
Winsorized Mean ( 5 / 24 )98.18805555555560.218881836095396448.589327041107
Winsorized Mean ( 6 / 24 )98.25138888888890.205119655292482478.995485580314
Winsorized Mean ( 7 / 24 )98.256250.203871223191357481.952521115622
Winsorized Mean ( 8 / 24 )98.25847222222220.201963625279218486.515688586885
Winsorized Mean ( 9 / 24 )98.25722222222220.200945751193256488.973872991845
Winsorized Mean ( 10 / 24 )98.27388888888890.196536476717624500.028750541228
Winsorized Mean ( 11 / 24 )98.27847222222220.19373184802871507.291254495534
Winsorized Mean ( 12 / 24 )98.28847222222220.189829597802779517.772114358782
Winsorized Mean ( 13 / 24 )98.31194444444440.184647089571861532.431595171088
Winsorized Mean ( 14 / 24 )98.25361111111110.172913597241331568.223741097591
Winsorized Mean ( 15 / 24 )98.28069444444450.167700353907381586.049415845145
Winsorized Mean ( 16 / 24 )98.28513888888890.166293595723646591.033818597702
Winsorized Mean ( 17 / 24 )98.33472222222220.157482389931651624.417258748109
Winsorized Mean ( 18 / 24 )98.34972222222220.149963998316818655.822219506616
Winsorized Mean ( 19 / 24 )98.34444444444440.147730204021779665.703030031326
Winsorized Mean ( 20 / 24 )98.43611111111110.130476818397393754.433717193384
Winsorized Mean ( 21 / 24 )98.46819444444450.121659644531564809.374339564976
Winsorized Mean ( 22 / 24 )98.498750.108838464369409904.999446387676
Winsorized Mean ( 23 / 24 )98.53708333333330.101826903184031967.692036703188
Winsorized Mean ( 24 / 24 )98.553750.09779002398547541007.80985609164
Trimmed Mean ( 1 / 24 )98.18814285714290.225777175634657434.889587847563
Trimmed Mean ( 2 / 24 )98.21455882352940.220185733895368446.053234630546
Trimmed Mean ( 3 / 24 )98.24166666666670.213956576137347459.166380581831
Trimmed Mean ( 4 / 24 )98.264218750.208981705914939470.204883818855
Trimmed Mean ( 5 / 24 )98.28612903225810.204183163854994481.362552997065
Trimmed Mean ( 6 / 24 )98.30966666666670.198906042985048494.251784366635
Trimmed Mean ( 7 / 24 )98.3217241379310.196383998866893500.660566569746
Trimmed Mean ( 8 / 24 )98.333750.193490253202624508.210353608997
Trimmed Mean ( 9 / 24 )98.34629629629630.190259357408518516.906488258187
Trimmed Mean ( 10 / 24 )98.360.186358895706778527.798791825651
Trimmed Mean ( 11 / 24 )98.37240.182394853131824539.337587168112
Trimmed Mean ( 12 / 24 )98.38520833333330.177911691573439553.000241092765
Trimmed Mean ( 13 / 24 )98.39782608695650.172987925926286568.813260001084
Trimmed Mean ( 14 / 24 )98.40863636363640.16777413303471586.554283330892
Trimmed Mean ( 15 / 24 )98.4276190476190.163448894691337602.192013800358
Trimmed Mean ( 16 / 24 )98.445250.15886334536324619.685112225893
Trimmed Mean ( 17 / 24 )98.46421052631580.152892747567505644.008379029504
Trimmed Mean ( 18 / 24 )98.47944444444440.147096741973159669.487597913039
Trimmed Mean ( 19 / 24 )98.49470588235290.141028963343085698.400552252108
Trimmed Mean ( 20 / 24 )98.51250.132905648075327741.221320738501
Trimmed Mean ( 21 / 24 )98.52166666666670.126961921464334775.993821851092
Trimmed Mean ( 22 / 24 )98.52821428571430.121049263629506813.951372618658
Trimmed Mean ( 23 / 24 )98.53192307692310.116522720439828845.602666201095
Trimmed Mean ( 24 / 24 )98.531250.111839546847841881.005447331192
Median98.615
Midrange97.3
Midmean - Weighted Average at Xnp98.427027027027
Midmean - Weighted Average at X(n+1)p98.4794444444444
Midmean - Empirical Distribution Function98.427027027027
Midmean - Empirical Distribution Function - Averaging98.4794444444444
Midmean - Empirical Distribution Function - Interpolation98.4794444444444
Midmean - Closest Observation98.427027027027
Midmean - True Basic - Statistics Graphics Toolkit98.4794444444444
Midmean - MS Excel (old versions)98.4642105263158
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.1634722222222 & 0.231191727820453 & 424.597684128462 \tabularnewline
Geometric Mean & 98.1439872433923 &  &  \tabularnewline
Harmonic Mean & 98.124347557882 &  &  \tabularnewline
Quadratic Mean & 98.1827999264071 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.1631944444444 & 0.230434103024728 & 425.992477484595 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.1648611111111 & 0.229650512955589 & 427.453262993995 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.1815277777778 & 0.224178875500669 & 437.960657793936 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.18875 & 0.220801901164603 & 444.691596775711 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.1880555555556 & 0.218881836095396 & 448.589327041107 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.2513888888889 & 0.205119655292482 & 478.995485580314 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.25625 & 0.203871223191357 & 481.952521115622 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.2584722222222 & 0.201963625279218 & 486.515688586885 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.2572222222222 & 0.200945751193256 & 488.973872991845 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.2738888888889 & 0.196536476717624 & 500.028750541228 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.2784722222222 & 0.19373184802871 & 507.291254495534 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.2884722222222 & 0.189829597802779 & 517.772114358782 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.3119444444444 & 0.184647089571861 & 532.431595171088 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.2536111111111 & 0.172913597241331 & 568.223741097591 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.2806944444445 & 0.167700353907381 & 586.049415845145 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.2851388888889 & 0.166293595723646 & 591.033818597702 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.3347222222222 & 0.157482389931651 & 624.417258748109 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.3497222222222 & 0.149963998316818 & 655.822219506616 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.3444444444444 & 0.147730204021779 & 665.703030031326 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.4361111111111 & 0.130476818397393 & 754.433717193384 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.4681944444445 & 0.121659644531564 & 809.374339564976 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.49875 & 0.108838464369409 & 904.999446387676 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.5370833333333 & 0.101826903184031 & 967.692036703188 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.55375 & 0.0977900239854754 & 1007.80985609164 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.1881428571429 & 0.225777175634657 & 434.889587847563 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 98.2145588235294 & 0.220185733895368 & 446.053234630546 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.2416666666667 & 0.213956576137347 & 459.166380581831 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.26421875 & 0.208981705914939 & 470.204883818855 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.2861290322581 & 0.204183163854994 & 481.362552997065 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.3096666666667 & 0.198906042985048 & 494.251784366635 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.321724137931 & 0.196383998866893 & 500.660566569746 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.33375 & 0.193490253202624 & 508.210353608997 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.3462962962963 & 0.190259357408518 & 516.906488258187 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.36 & 0.186358895706778 & 527.798791825651 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.3724 & 0.182394853131824 & 539.337587168112 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.3852083333333 & 0.177911691573439 & 553.000241092765 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.3978260869565 & 0.172987925926286 & 568.813260001084 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.4086363636364 & 0.16777413303471 & 586.554283330892 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.427619047619 & 0.163448894691337 & 602.192013800358 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 98.44525 & 0.15886334536324 & 619.685112225893 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.4642105263158 & 0.152892747567505 & 644.008379029504 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.4794444444444 & 0.147096741973159 & 669.487597913039 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.4947058823529 & 0.141028963343085 & 698.400552252108 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.5125 & 0.132905648075327 & 741.221320738501 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.5216666666667 & 0.126961921464334 & 775.993821851092 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.5282142857143 & 0.121049263629506 & 813.951372618658 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.5319230769231 & 0.116522720439828 & 845.602666201095 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.53125 & 0.111839546847841 & 881.005447331192 \tabularnewline
Median & 98.615 &  &  \tabularnewline
Midrange & 97.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.427027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.4794444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.427027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.4794444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.4794444444444 &  &  \tabularnewline
Midmean - Closest Observation & 98.427027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.4794444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.4642105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]98.1634722222222[/C][C]0.231191727820453[/C][C]424.597684128462[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.1439872433923[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.124347557882[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.1827999264071[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.1631944444444[/C][C]0.230434103024728[/C][C]425.992477484595[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.1648611111111[/C][C]0.229650512955589[/C][C]427.453262993995[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.1815277777778[/C][C]0.224178875500669[/C][C]437.960657793936[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.18875[/C][C]0.220801901164603[/C][C]444.691596775711[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.1880555555556[/C][C]0.218881836095396[/C][C]448.589327041107[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.2513888888889[/C][C]0.205119655292482[/C][C]478.995485580314[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.25625[/C][C]0.203871223191357[/C][C]481.952521115622[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.2584722222222[/C][C]0.201963625279218[/C][C]486.515688586885[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.2572222222222[/C][C]0.200945751193256[/C][C]488.973872991845[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.2738888888889[/C][C]0.196536476717624[/C][C]500.028750541228[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.2784722222222[/C][C]0.19373184802871[/C][C]507.291254495534[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.2884722222222[/C][C]0.189829597802779[/C][C]517.772114358782[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.3119444444444[/C][C]0.184647089571861[/C][C]532.431595171088[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.2536111111111[/C][C]0.172913597241331[/C][C]568.223741097591[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.2806944444445[/C][C]0.167700353907381[/C][C]586.049415845145[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.2851388888889[/C][C]0.166293595723646[/C][C]591.033818597702[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.3347222222222[/C][C]0.157482389931651[/C][C]624.417258748109[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.3497222222222[/C][C]0.149963998316818[/C][C]655.822219506616[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.3444444444444[/C][C]0.147730204021779[/C][C]665.703030031326[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.4361111111111[/C][C]0.130476818397393[/C][C]754.433717193384[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.4681944444445[/C][C]0.121659644531564[/C][C]809.374339564976[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.49875[/C][C]0.108838464369409[/C][C]904.999446387676[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.5370833333333[/C][C]0.101826903184031[/C][C]967.692036703188[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.55375[/C][C]0.0977900239854754[/C][C]1007.80985609164[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.1881428571429[/C][C]0.225777175634657[/C][C]434.889587847563[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]98.2145588235294[/C][C]0.220185733895368[/C][C]446.053234630546[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.2416666666667[/C][C]0.213956576137347[/C][C]459.166380581831[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.26421875[/C][C]0.208981705914939[/C][C]470.204883818855[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.2861290322581[/C][C]0.204183163854994[/C][C]481.362552997065[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.3096666666667[/C][C]0.198906042985048[/C][C]494.251784366635[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.321724137931[/C][C]0.196383998866893[/C][C]500.660566569746[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.33375[/C][C]0.193490253202624[/C][C]508.210353608997[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.3462962962963[/C][C]0.190259357408518[/C][C]516.906488258187[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.36[/C][C]0.186358895706778[/C][C]527.798791825651[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.3724[/C][C]0.182394853131824[/C][C]539.337587168112[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.3852083333333[/C][C]0.177911691573439[/C][C]553.000241092765[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.3978260869565[/C][C]0.172987925926286[/C][C]568.813260001084[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.4086363636364[/C][C]0.16777413303471[/C][C]586.554283330892[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.427619047619[/C][C]0.163448894691337[/C][C]602.192013800358[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]98.44525[/C][C]0.15886334536324[/C][C]619.685112225893[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.4642105263158[/C][C]0.152892747567505[/C][C]644.008379029504[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.4794444444444[/C][C]0.147096741973159[/C][C]669.487597913039[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.4947058823529[/C][C]0.141028963343085[/C][C]698.400552252108[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.5125[/C][C]0.132905648075327[/C][C]741.221320738501[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.5216666666667[/C][C]0.126961921464334[/C][C]775.993821851092[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.5282142857143[/C][C]0.121049263629506[/C][C]813.951372618658[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.5319230769231[/C][C]0.116522720439828[/C][C]845.602666201095[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.53125[/C][C]0.111839546847841[/C][C]881.005447331192[/C][/ROW]
[ROW][C]Median[/C][C]98.615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.427027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.4794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.427027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.4794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.4794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.427027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.4794444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.4642105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean98.16347222222220.231191727820453424.597684128462
Geometric Mean98.1439872433923
Harmonic Mean98.124347557882
Quadratic Mean98.1827999264071
Winsorized Mean ( 1 / 24 )98.16319444444440.230434103024728425.992477484595
Winsorized Mean ( 2 / 24 )98.16486111111110.229650512955589427.453262993995
Winsorized Mean ( 3 / 24 )98.18152777777780.224178875500669437.960657793936
Winsorized Mean ( 4 / 24 )98.188750.220801901164603444.691596775711
Winsorized Mean ( 5 / 24 )98.18805555555560.218881836095396448.589327041107
Winsorized Mean ( 6 / 24 )98.25138888888890.205119655292482478.995485580314
Winsorized Mean ( 7 / 24 )98.256250.203871223191357481.952521115622
Winsorized Mean ( 8 / 24 )98.25847222222220.201963625279218486.515688586885
Winsorized Mean ( 9 / 24 )98.25722222222220.200945751193256488.973872991845
Winsorized Mean ( 10 / 24 )98.27388888888890.196536476717624500.028750541228
Winsorized Mean ( 11 / 24 )98.27847222222220.19373184802871507.291254495534
Winsorized Mean ( 12 / 24 )98.28847222222220.189829597802779517.772114358782
Winsorized Mean ( 13 / 24 )98.31194444444440.184647089571861532.431595171088
Winsorized Mean ( 14 / 24 )98.25361111111110.172913597241331568.223741097591
Winsorized Mean ( 15 / 24 )98.28069444444450.167700353907381586.049415845145
Winsorized Mean ( 16 / 24 )98.28513888888890.166293595723646591.033818597702
Winsorized Mean ( 17 / 24 )98.33472222222220.157482389931651624.417258748109
Winsorized Mean ( 18 / 24 )98.34972222222220.149963998316818655.822219506616
Winsorized Mean ( 19 / 24 )98.34444444444440.147730204021779665.703030031326
Winsorized Mean ( 20 / 24 )98.43611111111110.130476818397393754.433717193384
Winsorized Mean ( 21 / 24 )98.46819444444450.121659644531564809.374339564976
Winsorized Mean ( 22 / 24 )98.498750.108838464369409904.999446387676
Winsorized Mean ( 23 / 24 )98.53708333333330.101826903184031967.692036703188
Winsorized Mean ( 24 / 24 )98.553750.09779002398547541007.80985609164
Trimmed Mean ( 1 / 24 )98.18814285714290.225777175634657434.889587847563
Trimmed Mean ( 2 / 24 )98.21455882352940.220185733895368446.053234630546
Trimmed Mean ( 3 / 24 )98.24166666666670.213956576137347459.166380581831
Trimmed Mean ( 4 / 24 )98.264218750.208981705914939470.204883818855
Trimmed Mean ( 5 / 24 )98.28612903225810.204183163854994481.362552997065
Trimmed Mean ( 6 / 24 )98.30966666666670.198906042985048494.251784366635
Trimmed Mean ( 7 / 24 )98.3217241379310.196383998866893500.660566569746
Trimmed Mean ( 8 / 24 )98.333750.193490253202624508.210353608997
Trimmed Mean ( 9 / 24 )98.34629629629630.190259357408518516.906488258187
Trimmed Mean ( 10 / 24 )98.360.186358895706778527.798791825651
Trimmed Mean ( 11 / 24 )98.37240.182394853131824539.337587168112
Trimmed Mean ( 12 / 24 )98.38520833333330.177911691573439553.000241092765
Trimmed Mean ( 13 / 24 )98.39782608695650.172987925926286568.813260001084
Trimmed Mean ( 14 / 24 )98.40863636363640.16777413303471586.554283330892
Trimmed Mean ( 15 / 24 )98.4276190476190.163448894691337602.192013800358
Trimmed Mean ( 16 / 24 )98.445250.15886334536324619.685112225893
Trimmed Mean ( 17 / 24 )98.46421052631580.152892747567505644.008379029504
Trimmed Mean ( 18 / 24 )98.47944444444440.147096741973159669.487597913039
Trimmed Mean ( 19 / 24 )98.49470588235290.141028963343085698.400552252108
Trimmed Mean ( 20 / 24 )98.51250.132905648075327741.221320738501
Trimmed Mean ( 21 / 24 )98.52166666666670.126961921464334775.993821851092
Trimmed Mean ( 22 / 24 )98.52821428571430.121049263629506813.951372618658
Trimmed Mean ( 23 / 24 )98.53192307692310.116522720439828845.602666201095
Trimmed Mean ( 24 / 24 )98.531250.111839546847841881.005447331192
Median98.615
Midrange97.3
Midmean - Weighted Average at Xnp98.427027027027
Midmean - Weighted Average at X(n+1)p98.4794444444444
Midmean - Empirical Distribution Function98.427027027027
Midmean - Empirical Distribution Function - Averaging98.4794444444444
Midmean - Empirical Distribution Function - Interpolation98.4794444444444
Midmean - Closest Observation98.427027027027
Midmean - True Basic - Statistics Graphics Toolkit98.4794444444444
Midmean - MS Excel (old versions)98.4642105263158
Number of observations72



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')