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 12:31:44 +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/t14762720568bw5mlbswt1umij.htm/, Retrieved Sun, 05 May 2024 18:18:18 +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 18:18:18 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
91,16
91,17
91,17
91,38
92,68
92,72
92,79
92,81
92,81
92,81
92,81
92,81
92,81
92,82
92,82
92,88
93,38
93,89
94,1
94,18
94,3
94,31
94,36
94,38
94,38
94,5
94,57
94,89
96,71
97,57
97,88
97,97
98,4
98,51
98,46
98,46
98,48
98,6
98,6
98,71
99,13
99,2
99,3
100,18
101,37
101,77
102,28
102,38
102,35
103,23
105,37
106,62
107
107,24
107,31
107,35
107,42
107,58
107,64
107,64
107,68
108,51
110,37
111,31
111,57
111,66
111,69
111,9
111,95
112,04
112,13
112,14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]'Gwilym Jenkins' @ jenkins.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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.0465277777780.816834876796757122.480724831576
Geometric Mean99.8140755609752
Harmonic Mean99.58631462406
Quadratic Mean100.283000975849
Winsorized Mean ( 1 / 24 )100.0465277777780.81678465564557122.488255730885
Winsorized Mean ( 2 / 24 )100.0440277777780.816265462907702122.563102720775
Winsorized Mean ( 3 / 24 )100.0490277777780.814165306982546122.885397989481
Winsorized Mean ( 4 / 24 )100.1184722222220.803463640000532124.608591151873
Winsorized Mean ( 5 / 24 )100.1066666666670.800109171932777125.116259353514
Winsorized Mean ( 6 / 24 )100.110.79884406413933125.318575293988
Winsorized Mean ( 7 / 24 )100.1031944444440.79681557201495125.629063939235
Winsorized Mean ( 8 / 24 )100.0743055555560.790997934170406126.516519490677
Winsorized Mean ( 9 / 24 )99.95680555555550.768017151709764130.149183951206
Winsorized Mean ( 10 / 24 )99.69847222222220.721041773161084138.270036401829
Winsorized Mean ( 11 / 24 )99.57166666666670.69977315796868142.291349036173
Winsorized Mean ( 12 / 24 )99.5650.698686561197596142.503098713304
Winsorized Mean ( 13 / 24 )99.56680555555550.698440802805105142.555825999385
Winsorized Mean ( 14 / 24 )99.55513888888890.696544567580989142.92716291598
Winsorized Mean ( 15 / 24 )99.53430555555560.689454344882377144.366782651194
Winsorized Mean ( 16 / 24 )99.62986111111110.67211149464256148.234127678617
Winsorized Mean ( 17 / 24 )99.74083333333330.655116158511153152.249081384298
Winsorized Mean ( 18 / 24 )99.77583333333330.645715527647243154.519798674938
Winsorized Mean ( 19 / 24 )99.73361111111110.63282671563157157.600190775093
Winsorized Mean ( 20 / 24 )99.66138888888890.61171640513497162.920902647526
Winsorized Mean ( 21 / 24 )99.29972222222220.553957308832273179.255189233884
Winsorized Mean ( 22 / 24 )98.66111111111110.454847158096331216.910470594203
Winsorized Mean ( 23 / 24 )98.39597222222220.416447250195874236.274755508512
Winsorized Mean ( 24 / 24 )98.38597222222220.415101033185007237.016929269777
Trimmed Mean ( 1 / 24 )100.0007142857140.812105010125638123.13766451243
Trimmed Mean ( 2 / 24 )99.95220588235290.80606161751904124.000701323546
Trimmed Mean ( 3 / 24 )99.90212121212120.798714979465129125.078562166221
Trimmed Mean ( 4 / 24 )99.847031250.790383442447784126.327331631313
Trimmed Mean ( 5 / 24 )99.76822580645160.783520966151798127.333192239201
Trimmed Mean ( 6 / 24 )99.6870.775614766193065128.526433927105
Trimmed Mean ( 7 / 24 )99.59948275862070.765685242938052130.07888512575
Trimmed Mean ( 8 / 24 )99.50696428571430.753423309364458132.07311620031
Trimmed Mean ( 9 / 24 )99.41240740740740.73916775377244134.492348861328
Trimmed Mean ( 10 / 24 )99.32865384615380.726487293761871136.72455760625
Trimmed Mean ( 11 / 24 )99.27540.720756643806935137.737752198358
Trimmed Mean ( 12 / 24 )99.2350.717138781488558138.376284425755
Trimmed Mean ( 13 / 24 )99.19195652173910.711609702744502139.390955658952
Trimmed Mean ( 14 / 24 )99.14477272727270.703417622656917140.947240350316
Trimmed Mean ( 15 / 24 )99.09452380952380.692121266084513143.175088911982
Trimmed Mean ( 16 / 24 )99.041750.67787733247588146.105711542617
Trimmed Mean ( 17 / 24 )98.97210526315790.661682857974232149.57634774787
Trimmed Mean ( 18 / 24 )98.88166666666670.642377837191077153.930694587855
Trimmed Mean ( 19 / 24 )98.77647058823530.616785248850982160.147264825557
Trimmed Mean ( 20 / 24 )98.6631250.583432805218943169.107948880206
Trimmed Mean ( 21 / 24 )98.54333333333330.541275066226044182.057773361724
Trimmed Mean ( 22 / 24 )98.45071428571430.501488242428503196.317093714815
Trimmed Mean ( 23 / 24 )98.42423076923080.481237242972392204.523303643973
Trimmed Mean ( 24 / 24 )98.42791666666670.463385454463358212.410458115598
Median98.495
Midrange101.65
Midmean - Weighted Average at Xnp98.7467567567568
Midmean - Weighted Average at X(n+1)p98.8816666666666
Midmean - Empirical Distribution Function98.7467567567568
Midmean - Empirical Distribution Function - Averaging98.8816666666666
Midmean - Empirical Distribution Function - Interpolation98.8816666666666
Midmean - Closest Observation98.7467567567568
Midmean - True Basic - Statistics Graphics Toolkit98.8816666666666
Midmean - MS Excel (old versions)98.9721052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.046527777778 & 0.816834876796757 & 122.480724831576 \tabularnewline
Geometric Mean & 99.8140755609752 &  &  \tabularnewline
Harmonic Mean & 99.58631462406 &  &  \tabularnewline
Quadratic Mean & 100.283000975849 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 100.046527777778 & 0.81678465564557 & 122.488255730885 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 100.044027777778 & 0.816265462907702 & 122.563102720775 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 100.049027777778 & 0.814165306982546 & 122.885397989481 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 100.118472222222 & 0.803463640000532 & 124.608591151873 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 100.106666666667 & 0.800109171932777 & 125.116259353514 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 100.11 & 0.79884406413933 & 125.318575293988 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 100.103194444444 & 0.79681557201495 & 125.629063939235 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 100.074305555556 & 0.790997934170406 & 126.516519490677 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.9568055555555 & 0.768017151709764 & 130.149183951206 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.6984722222222 & 0.721041773161084 & 138.270036401829 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.5716666666667 & 0.69977315796868 & 142.291349036173 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.565 & 0.698686561197596 & 142.503098713304 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.5668055555555 & 0.698440802805105 & 142.555825999385 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.5551388888889 & 0.696544567580989 & 142.92716291598 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.5343055555556 & 0.689454344882377 & 144.366782651194 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.6298611111111 & 0.67211149464256 & 148.234127678617 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.7408333333333 & 0.655116158511153 & 152.249081384298 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.7758333333333 & 0.645715527647243 & 154.519798674938 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.7336111111111 & 0.63282671563157 & 157.600190775093 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.6613888888889 & 0.61171640513497 & 162.920902647526 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.2997222222222 & 0.553957308832273 & 179.255189233884 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.6611111111111 & 0.454847158096331 & 216.910470594203 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.3959722222222 & 0.416447250195874 & 236.274755508512 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.3859722222222 & 0.415101033185007 & 237.016929269777 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 100.000714285714 & 0.812105010125638 & 123.13766451243 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.9522058823529 & 0.80606161751904 & 124.000701323546 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.9021212121212 & 0.798714979465129 & 125.078562166221 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.84703125 & 0.790383442447784 & 126.327331631313 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.7682258064516 & 0.783520966151798 & 127.333192239201 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.687 & 0.775614766193065 & 128.526433927105 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.5994827586207 & 0.765685242938052 & 130.07888512575 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.5069642857143 & 0.753423309364458 & 132.07311620031 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 99.4124074074074 & 0.73916775377244 & 134.492348861328 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.3286538461538 & 0.726487293761871 & 136.72455760625 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.2754 & 0.720756643806935 & 137.737752198358 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.235 & 0.717138781488558 & 138.376284425755 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.1919565217391 & 0.711609702744502 & 139.390955658952 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.1447727272727 & 0.703417622656917 & 140.947240350316 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.0945238095238 & 0.692121266084513 & 143.175088911982 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.04175 & 0.67787733247588 & 146.105711542617 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.9721052631579 & 0.661682857974232 & 149.57634774787 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.8816666666667 & 0.642377837191077 & 153.930694587855 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.7764705882353 & 0.616785248850982 & 160.147264825557 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.663125 & 0.583432805218943 & 169.107948880206 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.5433333333333 & 0.541275066226044 & 182.057773361724 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.4507142857143 & 0.501488242428503 & 196.317093714815 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.4242307692308 & 0.481237242972392 & 204.523303643973 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.4279166666667 & 0.463385454463358 & 212.410458115598 \tabularnewline
Median & 98.495 &  &  \tabularnewline
Midrange & 101.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.7467567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.8816666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.7467567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.8816666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.8816666666666 &  &  \tabularnewline
Midmean - Closest Observation & 98.7467567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.8816666666666 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.9721052631579 &  &  \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]100.046527777778[/C][C]0.816834876796757[/C][C]122.480724831576[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.8140755609752[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.58631462406[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.283000975849[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]100.046527777778[/C][C]0.81678465564557[/C][C]122.488255730885[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]100.044027777778[/C][C]0.816265462907702[/C][C]122.563102720775[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]100.049027777778[/C][C]0.814165306982546[/C][C]122.885397989481[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]100.118472222222[/C][C]0.803463640000532[/C][C]124.608591151873[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]100.106666666667[/C][C]0.800109171932777[/C][C]125.116259353514[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]100.11[/C][C]0.79884406413933[/C][C]125.318575293988[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]100.103194444444[/C][C]0.79681557201495[/C][C]125.629063939235[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]100.074305555556[/C][C]0.790997934170406[/C][C]126.516519490677[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.9568055555555[/C][C]0.768017151709764[/C][C]130.149183951206[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.6984722222222[/C][C]0.721041773161084[/C][C]138.270036401829[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.5716666666667[/C][C]0.69977315796868[/C][C]142.291349036173[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.565[/C][C]0.698686561197596[/C][C]142.503098713304[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.5668055555555[/C][C]0.698440802805105[/C][C]142.555825999385[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.5551388888889[/C][C]0.696544567580989[/C][C]142.92716291598[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.5343055555556[/C][C]0.689454344882377[/C][C]144.366782651194[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.6298611111111[/C][C]0.67211149464256[/C][C]148.234127678617[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.7408333333333[/C][C]0.655116158511153[/C][C]152.249081384298[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.7758333333333[/C][C]0.645715527647243[/C][C]154.519798674938[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.7336111111111[/C][C]0.63282671563157[/C][C]157.600190775093[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.6613888888889[/C][C]0.61171640513497[/C][C]162.920902647526[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.2997222222222[/C][C]0.553957308832273[/C][C]179.255189233884[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.6611111111111[/C][C]0.454847158096331[/C][C]216.910470594203[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.3959722222222[/C][C]0.416447250195874[/C][C]236.274755508512[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.3859722222222[/C][C]0.415101033185007[/C][C]237.016929269777[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]100.000714285714[/C][C]0.812105010125638[/C][C]123.13766451243[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.9522058823529[/C][C]0.80606161751904[/C][C]124.000701323546[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.9021212121212[/C][C]0.798714979465129[/C][C]125.078562166221[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.84703125[/C][C]0.790383442447784[/C][C]126.327331631313[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.7682258064516[/C][C]0.783520966151798[/C][C]127.333192239201[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.687[/C][C]0.775614766193065[/C][C]128.526433927105[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.5994827586207[/C][C]0.765685242938052[/C][C]130.07888512575[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.5069642857143[/C][C]0.753423309364458[/C][C]132.07311620031[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]99.4124074074074[/C][C]0.73916775377244[/C][C]134.492348861328[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.3286538461538[/C][C]0.726487293761871[/C][C]136.72455760625[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.2754[/C][C]0.720756643806935[/C][C]137.737752198358[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.235[/C][C]0.717138781488558[/C][C]138.376284425755[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.1919565217391[/C][C]0.711609702744502[/C][C]139.390955658952[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.1447727272727[/C][C]0.703417622656917[/C][C]140.947240350316[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.0945238095238[/C][C]0.692121266084513[/C][C]143.175088911982[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.04175[/C][C]0.67787733247588[/C][C]146.105711542617[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.9721052631579[/C][C]0.661682857974232[/C][C]149.57634774787[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.8816666666667[/C][C]0.642377837191077[/C][C]153.930694587855[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.7764705882353[/C][C]0.616785248850982[/C][C]160.147264825557[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.663125[/C][C]0.583432805218943[/C][C]169.107948880206[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.5433333333333[/C][C]0.541275066226044[/C][C]182.057773361724[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.4507142857143[/C][C]0.501488242428503[/C][C]196.317093714815[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.4242307692308[/C][C]0.481237242972392[/C][C]204.523303643973[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.4279166666667[/C][C]0.463385454463358[/C][C]212.410458115598[/C][/ROW]
[ROW][C]Median[/C][C]98.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.7467567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.8816666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.7467567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.8816666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.8816666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.7467567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.8816666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.9721052631579[/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 Mean100.0465277777780.816834876796757122.480724831576
Geometric Mean99.8140755609752
Harmonic Mean99.58631462406
Quadratic Mean100.283000975849
Winsorized Mean ( 1 / 24 )100.0465277777780.81678465564557122.488255730885
Winsorized Mean ( 2 / 24 )100.0440277777780.816265462907702122.563102720775
Winsorized Mean ( 3 / 24 )100.0490277777780.814165306982546122.885397989481
Winsorized Mean ( 4 / 24 )100.1184722222220.803463640000532124.608591151873
Winsorized Mean ( 5 / 24 )100.1066666666670.800109171932777125.116259353514
Winsorized Mean ( 6 / 24 )100.110.79884406413933125.318575293988
Winsorized Mean ( 7 / 24 )100.1031944444440.79681557201495125.629063939235
Winsorized Mean ( 8 / 24 )100.0743055555560.790997934170406126.516519490677
Winsorized Mean ( 9 / 24 )99.95680555555550.768017151709764130.149183951206
Winsorized Mean ( 10 / 24 )99.69847222222220.721041773161084138.270036401829
Winsorized Mean ( 11 / 24 )99.57166666666670.69977315796868142.291349036173
Winsorized Mean ( 12 / 24 )99.5650.698686561197596142.503098713304
Winsorized Mean ( 13 / 24 )99.56680555555550.698440802805105142.555825999385
Winsorized Mean ( 14 / 24 )99.55513888888890.696544567580989142.92716291598
Winsorized Mean ( 15 / 24 )99.53430555555560.689454344882377144.366782651194
Winsorized Mean ( 16 / 24 )99.62986111111110.67211149464256148.234127678617
Winsorized Mean ( 17 / 24 )99.74083333333330.655116158511153152.249081384298
Winsorized Mean ( 18 / 24 )99.77583333333330.645715527647243154.519798674938
Winsorized Mean ( 19 / 24 )99.73361111111110.63282671563157157.600190775093
Winsorized Mean ( 20 / 24 )99.66138888888890.61171640513497162.920902647526
Winsorized Mean ( 21 / 24 )99.29972222222220.553957308832273179.255189233884
Winsorized Mean ( 22 / 24 )98.66111111111110.454847158096331216.910470594203
Winsorized Mean ( 23 / 24 )98.39597222222220.416447250195874236.274755508512
Winsorized Mean ( 24 / 24 )98.38597222222220.415101033185007237.016929269777
Trimmed Mean ( 1 / 24 )100.0007142857140.812105010125638123.13766451243
Trimmed Mean ( 2 / 24 )99.95220588235290.80606161751904124.000701323546
Trimmed Mean ( 3 / 24 )99.90212121212120.798714979465129125.078562166221
Trimmed Mean ( 4 / 24 )99.847031250.790383442447784126.327331631313
Trimmed Mean ( 5 / 24 )99.76822580645160.783520966151798127.333192239201
Trimmed Mean ( 6 / 24 )99.6870.775614766193065128.526433927105
Trimmed Mean ( 7 / 24 )99.59948275862070.765685242938052130.07888512575
Trimmed Mean ( 8 / 24 )99.50696428571430.753423309364458132.07311620031
Trimmed Mean ( 9 / 24 )99.41240740740740.73916775377244134.492348861328
Trimmed Mean ( 10 / 24 )99.32865384615380.726487293761871136.72455760625
Trimmed Mean ( 11 / 24 )99.27540.720756643806935137.737752198358
Trimmed Mean ( 12 / 24 )99.2350.717138781488558138.376284425755
Trimmed Mean ( 13 / 24 )99.19195652173910.711609702744502139.390955658952
Trimmed Mean ( 14 / 24 )99.14477272727270.703417622656917140.947240350316
Trimmed Mean ( 15 / 24 )99.09452380952380.692121266084513143.175088911982
Trimmed Mean ( 16 / 24 )99.041750.67787733247588146.105711542617
Trimmed Mean ( 17 / 24 )98.97210526315790.661682857974232149.57634774787
Trimmed Mean ( 18 / 24 )98.88166666666670.642377837191077153.930694587855
Trimmed Mean ( 19 / 24 )98.77647058823530.616785248850982160.147264825557
Trimmed Mean ( 20 / 24 )98.6631250.583432805218943169.107948880206
Trimmed Mean ( 21 / 24 )98.54333333333330.541275066226044182.057773361724
Trimmed Mean ( 22 / 24 )98.45071428571430.501488242428503196.317093714815
Trimmed Mean ( 23 / 24 )98.42423076923080.481237242972392204.523303643973
Trimmed Mean ( 24 / 24 )98.42791666666670.463385454463358212.410458115598
Median98.495
Midrange101.65
Midmean - Weighted Average at Xnp98.7467567567568
Midmean - Weighted Average at X(n+1)p98.8816666666666
Midmean - Empirical Distribution Function98.7467567567568
Midmean - Empirical Distribution Function - Averaging98.8816666666666
Midmean - Empirical Distribution Function - Interpolation98.8816666666666
Midmean - Closest Observation98.7467567567568
Midmean - True Basic - Statistics Graphics Toolkit98.8816666666666
Midmean - MS Excel (old versions)98.9721052631579
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')