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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 computationTue, 16 Oct 2012 16:56:05 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/16/t1350421013o6fy2sq2a0t60ma.htm/, Retrieved Tue, 30 Apr 2024 19:00:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179256, Retrieved Tue, 30 Apr 2024 19:00:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact44
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-16 20:56:05] [c9eeded7548c00546c4c5f04921b1379] [Current]
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Dataseries X:
102,89
102,64
103,33
103,56
103,6
104,24
105,31
105,4
105,89
105,89
105,54
106,15
106,14
105,85
106,27
106,51
106,82
106,53
107,14
107,39
107,33
107,53
107,42
108,25
108,26
108,93
109,43
109,61
109,74
110,12
110,16
110,44
111,23
112,86
112,77
113,04
112,79
113,87
114,28
115,51
116,76
116,91
116,47
116,94
117,24
116,82
117,48
117,11
117,31
117,77
118,37
117,91
118,12
118,02
117,77
117,85
118,68
118,9
118,6
118,21
118,37
117,43
117,5
116,71
116,98
117,74
117,44
117,85
118,54
118,73
118,68
118,19




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179256&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179256&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112.3341666666670.645907507477628173.916799799014
Geometric Mean112.201072294977
Harmonic Mean112.066886315757
Quadratic Mean112.465932409676
Winsorized Mean ( 1 / 24 )112.3352777777780.644848430354576174.204157891815
Winsorized Mean ( 2 / 24 )112.3461111111110.642185710308228174.943336962744
Winsorized Mean ( 3 / 24 )112.3556944444440.640311104769849175.470476159912
Winsorized Mean ( 4 / 24 )112.3534722222220.639266872733463175.753628123738
Winsorized Mean ( 5 / 24 )112.393750.630358079345701178.30143482362
Winsorized Mean ( 6 / 24 )112.468750.612957565587117183.485376988981
Winsorized Mean ( 7 / 24 )112.47750.611524741756953183.92959813342
Winsorized Mean ( 8 / 24 )112.4752777777780.606614427025921185.414775459951
Winsorized Mean ( 9 / 24 )112.5115277777780.600131984039922187.477972795886
Winsorized Mean ( 10 / 24 )112.5073611111110.597974279685111188.14749218036
Winsorized Mean ( 11 / 24 )112.4920833333330.595966454399214188.755730298168
Winsorized Mean ( 12 / 24 )112.5154166666670.587145422500709191.631259232939
Winsorized Mean ( 13 / 24 )112.5063888888890.585472045333341192.163553812092
Winsorized Mean ( 14 / 24 )112.5297222222220.581920420732107193.376479348585
Winsorized Mean ( 15 / 24 )112.5630555555560.572266744511322196.696831740025
Winsorized Mean ( 16 / 24 )112.56750.571605094960926196.932289429112
Winsorized Mean ( 17 / 24 )112.6288888888890.560605758735607200.9056937676
Winsorized Mean ( 18 / 24 )112.6488888888890.54139413713089208.071866987459
Winsorized Mean ( 19 / 24 )112.693750.533585197186442211.201042671773
Winsorized Mean ( 20 / 24 )112.6993055555560.529827175530576212.709560325397
Winsorized Mean ( 21 / 24 )112.7051388888890.528225651896443213.36551620364
Winsorized Mean ( 22 / 24 )112.7020833333330.518895161355443217.196250277101
Winsorized Mean ( 23 / 24 )112.9097222222220.484342477845935233.119594887438
Winsorized Mean ( 24 / 24 )112.8697222222220.478457516564808235.903331674242
Trimmed Mean ( 1 / 24 )112.3788571428570.642762172879171174.837384470636
Trimmed Mean ( 2 / 24 )112.4250.639798293911456175.719443252468
Trimmed Mean ( 3 / 24 )112.468030303030.637410854672926176.445113035831
Trimmed Mean ( 4 / 24 )112.510156250.634831424169027177.22839791252
Trimmed Mean ( 5 / 24 )112.555645161290.631521444445633178.229331958941
Trimmed Mean ( 6 / 24 )112.59450.629608811604251178.832471726544
Trimmed Mean ( 7 / 24 )112.6205172413790.631120266054474178.445414129133
Trimmed Mean ( 8 / 24 )112.6467857142860.632350547362407178.139777349993
Trimmed Mean ( 9 / 24 )112.675370370370.63391541787566177.745117397462
Trimmed Mean ( 10 / 24 )112.7005769230770.636100157021922177.174263642247
Trimmed Mean ( 11 / 24 )112.72840.638003413719995176.689336727395
Trimmed Mean ( 12 / 24 )112.7606250.639444393016118176.341565007917
Trimmed Mean ( 13 / 24 )112.7926086956520.64157794867826175.804995991556
Trimmed Mean ( 14 / 24 )112.8286363636360.643022197601083175.466160864376
Trimmed Mean ( 15 / 24 )112.8652380952380.643926980056005175.276454615121
Trimmed Mean ( 16 / 24 )112.90150.645256413949981174.971526914186
Trimmed Mean ( 17 / 24 )112.9410526315790.645124706975015175.06855869954
Trimmed Mean ( 18 / 24 )112.9777777777780.645258421359301175.089195333211
Trimmed Mean ( 19 / 24 )113.0164705882350.647241904094485174.612412875754
Trimmed Mean ( 20 / 24 )113.05468750.648917209847986174.22051038912
Trimmed Mean ( 21 / 24 )113.0973333333330.648916503375041174.28641858407
Trimmed Mean ( 22 / 24 )113.1453571428570.645785990511128175.205654513045
Trimmed Mean ( 23 / 24 )113.2011538461540.6401015128443176.8487522286
Trimmed Mean ( 24 / 24 )113.2391666666670.639099773534149177.185427621836
Median112.95
Midrange110.77
Midmean - Weighted Average at Xnp112.811351351351
Midmean - Weighted Average at X(n+1)p112.977777777778
Midmean - Empirical Distribution Function112.811351351351
Midmean - Empirical Distribution Function - Averaging112.977777777778
Midmean - Empirical Distribution Function - Interpolation112.977777777778
Midmean - Closest Observation112.811351351351
Midmean - True Basic - Statistics Graphics Toolkit112.977777777778
Midmean - MS Excel (old versions)112.941052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.334166666667 & 0.645907507477628 & 173.916799799014 \tabularnewline
Geometric Mean & 112.201072294977 &  &  \tabularnewline
Harmonic Mean & 112.066886315757 &  &  \tabularnewline
Quadratic Mean & 112.465932409676 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 112.335277777778 & 0.644848430354576 & 174.204157891815 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 112.346111111111 & 0.642185710308228 & 174.943336962744 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 112.355694444444 & 0.640311104769849 & 175.470476159912 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 112.353472222222 & 0.639266872733463 & 175.753628123738 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 112.39375 & 0.630358079345701 & 178.30143482362 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 112.46875 & 0.612957565587117 & 183.485376988981 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 112.4775 & 0.611524741756953 & 183.92959813342 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 112.475277777778 & 0.606614427025921 & 185.414775459951 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 112.511527777778 & 0.600131984039922 & 187.477972795886 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 112.507361111111 & 0.597974279685111 & 188.14749218036 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 112.492083333333 & 0.595966454399214 & 188.755730298168 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 112.515416666667 & 0.587145422500709 & 191.631259232939 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 112.506388888889 & 0.585472045333341 & 192.163553812092 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 112.529722222222 & 0.581920420732107 & 193.376479348585 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 112.563055555556 & 0.572266744511322 & 196.696831740025 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 112.5675 & 0.571605094960926 & 196.932289429112 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 112.628888888889 & 0.560605758735607 & 200.9056937676 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 112.648888888889 & 0.54139413713089 & 208.071866987459 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 112.69375 & 0.533585197186442 & 211.201042671773 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 112.699305555556 & 0.529827175530576 & 212.709560325397 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 112.705138888889 & 0.528225651896443 & 213.36551620364 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 112.702083333333 & 0.518895161355443 & 217.196250277101 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 112.909722222222 & 0.484342477845935 & 233.119594887438 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 112.869722222222 & 0.478457516564808 & 235.903331674242 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 112.378857142857 & 0.642762172879171 & 174.837384470636 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 112.425 & 0.639798293911456 & 175.719443252468 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 112.46803030303 & 0.637410854672926 & 176.445113035831 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 112.51015625 & 0.634831424169027 & 177.22839791252 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 112.55564516129 & 0.631521444445633 & 178.229331958941 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 112.5945 & 0.629608811604251 & 178.832471726544 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 112.620517241379 & 0.631120266054474 & 178.445414129133 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 112.646785714286 & 0.632350547362407 & 178.139777349993 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 112.67537037037 & 0.63391541787566 & 177.745117397462 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 112.700576923077 & 0.636100157021922 & 177.174263642247 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 112.7284 & 0.638003413719995 & 176.689336727395 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 112.760625 & 0.639444393016118 & 176.341565007917 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 112.792608695652 & 0.64157794867826 & 175.804995991556 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 112.828636363636 & 0.643022197601083 & 175.466160864376 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 112.865238095238 & 0.643926980056005 & 175.276454615121 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 112.9015 & 0.645256413949981 & 174.971526914186 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 112.941052631579 & 0.645124706975015 & 175.06855869954 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 112.977777777778 & 0.645258421359301 & 175.089195333211 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 113.016470588235 & 0.647241904094485 & 174.612412875754 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 113.0546875 & 0.648917209847986 & 174.22051038912 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 113.097333333333 & 0.648916503375041 & 174.28641858407 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 113.145357142857 & 0.645785990511128 & 175.205654513045 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 113.201153846154 & 0.6401015128443 & 176.8487522286 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 113.239166666667 & 0.639099773534149 & 177.185427621836 \tabularnewline
Median & 112.95 &  &  \tabularnewline
Midrange & 110.77 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.811351351351 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.977777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.811351351351 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.977777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.977777777778 &  &  \tabularnewline
Midmean - Closest Observation & 112.811351351351 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.977777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.941052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179256&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]112.334166666667[/C][C]0.645907507477628[/C][C]173.916799799014[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.201072294977[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112.066886315757[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112.465932409676[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]112.335277777778[/C][C]0.644848430354576[/C][C]174.204157891815[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]112.346111111111[/C][C]0.642185710308228[/C][C]174.943336962744[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]112.355694444444[/C][C]0.640311104769849[/C][C]175.470476159912[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]112.353472222222[/C][C]0.639266872733463[/C][C]175.753628123738[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]112.39375[/C][C]0.630358079345701[/C][C]178.30143482362[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]112.46875[/C][C]0.612957565587117[/C][C]183.485376988981[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]112.4775[/C][C]0.611524741756953[/C][C]183.92959813342[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]112.475277777778[/C][C]0.606614427025921[/C][C]185.414775459951[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]112.511527777778[/C][C]0.600131984039922[/C][C]187.477972795886[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]112.507361111111[/C][C]0.597974279685111[/C][C]188.14749218036[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]112.492083333333[/C][C]0.595966454399214[/C][C]188.755730298168[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]112.515416666667[/C][C]0.587145422500709[/C][C]191.631259232939[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]112.506388888889[/C][C]0.585472045333341[/C][C]192.163553812092[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]112.529722222222[/C][C]0.581920420732107[/C][C]193.376479348585[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]112.563055555556[/C][C]0.572266744511322[/C][C]196.696831740025[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]112.5675[/C][C]0.571605094960926[/C][C]196.932289429112[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]112.628888888889[/C][C]0.560605758735607[/C][C]200.9056937676[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]112.648888888889[/C][C]0.54139413713089[/C][C]208.071866987459[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]112.69375[/C][C]0.533585197186442[/C][C]211.201042671773[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]112.699305555556[/C][C]0.529827175530576[/C][C]212.709560325397[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]112.705138888889[/C][C]0.528225651896443[/C][C]213.36551620364[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]112.702083333333[/C][C]0.518895161355443[/C][C]217.196250277101[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]112.909722222222[/C][C]0.484342477845935[/C][C]233.119594887438[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]112.869722222222[/C][C]0.478457516564808[/C][C]235.903331674242[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]112.378857142857[/C][C]0.642762172879171[/C][C]174.837384470636[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]112.425[/C][C]0.639798293911456[/C][C]175.719443252468[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]112.46803030303[/C][C]0.637410854672926[/C][C]176.445113035831[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]112.51015625[/C][C]0.634831424169027[/C][C]177.22839791252[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]112.55564516129[/C][C]0.631521444445633[/C][C]178.229331958941[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]112.5945[/C][C]0.629608811604251[/C][C]178.832471726544[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]112.620517241379[/C][C]0.631120266054474[/C][C]178.445414129133[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]112.646785714286[/C][C]0.632350547362407[/C][C]178.139777349993[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]112.67537037037[/C][C]0.63391541787566[/C][C]177.745117397462[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]112.700576923077[/C][C]0.636100157021922[/C][C]177.174263642247[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]112.7284[/C][C]0.638003413719995[/C][C]176.689336727395[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]112.760625[/C][C]0.639444393016118[/C][C]176.341565007917[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]112.792608695652[/C][C]0.64157794867826[/C][C]175.804995991556[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]112.828636363636[/C][C]0.643022197601083[/C][C]175.466160864376[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]112.865238095238[/C][C]0.643926980056005[/C][C]175.276454615121[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]112.9015[/C][C]0.645256413949981[/C][C]174.971526914186[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]112.941052631579[/C][C]0.645124706975015[/C][C]175.06855869954[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]112.977777777778[/C][C]0.645258421359301[/C][C]175.089195333211[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]113.016470588235[/C][C]0.647241904094485[/C][C]174.612412875754[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]113.0546875[/C][C]0.648917209847986[/C][C]174.22051038912[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]113.097333333333[/C][C]0.648916503375041[/C][C]174.28641858407[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]113.145357142857[/C][C]0.645785990511128[/C][C]175.205654513045[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]113.201153846154[/C][C]0.6401015128443[/C][C]176.8487522286[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]113.239166666667[/C][C]0.639099773534149[/C][C]177.185427621836[/C][/ROW]
[ROW][C]Median[/C][C]112.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.811351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.811351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.811351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.941052631579[/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=179256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179256&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 Mean112.3341666666670.645907507477628173.916799799014
Geometric Mean112.201072294977
Harmonic Mean112.066886315757
Quadratic Mean112.465932409676
Winsorized Mean ( 1 / 24 )112.3352777777780.644848430354576174.204157891815
Winsorized Mean ( 2 / 24 )112.3461111111110.642185710308228174.943336962744
Winsorized Mean ( 3 / 24 )112.3556944444440.640311104769849175.470476159912
Winsorized Mean ( 4 / 24 )112.3534722222220.639266872733463175.753628123738
Winsorized Mean ( 5 / 24 )112.393750.630358079345701178.30143482362
Winsorized Mean ( 6 / 24 )112.468750.612957565587117183.485376988981
Winsorized Mean ( 7 / 24 )112.47750.611524741756953183.92959813342
Winsorized Mean ( 8 / 24 )112.4752777777780.606614427025921185.414775459951
Winsorized Mean ( 9 / 24 )112.5115277777780.600131984039922187.477972795886
Winsorized Mean ( 10 / 24 )112.5073611111110.597974279685111188.14749218036
Winsorized Mean ( 11 / 24 )112.4920833333330.595966454399214188.755730298168
Winsorized Mean ( 12 / 24 )112.5154166666670.587145422500709191.631259232939
Winsorized Mean ( 13 / 24 )112.5063888888890.585472045333341192.163553812092
Winsorized Mean ( 14 / 24 )112.5297222222220.581920420732107193.376479348585
Winsorized Mean ( 15 / 24 )112.5630555555560.572266744511322196.696831740025
Winsorized Mean ( 16 / 24 )112.56750.571605094960926196.932289429112
Winsorized Mean ( 17 / 24 )112.6288888888890.560605758735607200.9056937676
Winsorized Mean ( 18 / 24 )112.6488888888890.54139413713089208.071866987459
Winsorized Mean ( 19 / 24 )112.693750.533585197186442211.201042671773
Winsorized Mean ( 20 / 24 )112.6993055555560.529827175530576212.709560325397
Winsorized Mean ( 21 / 24 )112.7051388888890.528225651896443213.36551620364
Winsorized Mean ( 22 / 24 )112.7020833333330.518895161355443217.196250277101
Winsorized Mean ( 23 / 24 )112.9097222222220.484342477845935233.119594887438
Winsorized Mean ( 24 / 24 )112.8697222222220.478457516564808235.903331674242
Trimmed Mean ( 1 / 24 )112.3788571428570.642762172879171174.837384470636
Trimmed Mean ( 2 / 24 )112.4250.639798293911456175.719443252468
Trimmed Mean ( 3 / 24 )112.468030303030.637410854672926176.445113035831
Trimmed Mean ( 4 / 24 )112.510156250.634831424169027177.22839791252
Trimmed Mean ( 5 / 24 )112.555645161290.631521444445633178.229331958941
Trimmed Mean ( 6 / 24 )112.59450.629608811604251178.832471726544
Trimmed Mean ( 7 / 24 )112.6205172413790.631120266054474178.445414129133
Trimmed Mean ( 8 / 24 )112.6467857142860.632350547362407178.139777349993
Trimmed Mean ( 9 / 24 )112.675370370370.63391541787566177.745117397462
Trimmed Mean ( 10 / 24 )112.7005769230770.636100157021922177.174263642247
Trimmed Mean ( 11 / 24 )112.72840.638003413719995176.689336727395
Trimmed Mean ( 12 / 24 )112.7606250.639444393016118176.341565007917
Trimmed Mean ( 13 / 24 )112.7926086956520.64157794867826175.804995991556
Trimmed Mean ( 14 / 24 )112.8286363636360.643022197601083175.466160864376
Trimmed Mean ( 15 / 24 )112.8652380952380.643926980056005175.276454615121
Trimmed Mean ( 16 / 24 )112.90150.645256413949981174.971526914186
Trimmed Mean ( 17 / 24 )112.9410526315790.645124706975015175.06855869954
Trimmed Mean ( 18 / 24 )112.9777777777780.645258421359301175.089195333211
Trimmed Mean ( 19 / 24 )113.0164705882350.647241904094485174.612412875754
Trimmed Mean ( 20 / 24 )113.05468750.648917209847986174.22051038912
Trimmed Mean ( 21 / 24 )113.0973333333330.648916503375041174.28641858407
Trimmed Mean ( 22 / 24 )113.1453571428570.645785990511128175.205654513045
Trimmed Mean ( 23 / 24 )113.2011538461540.6401015128443176.8487522286
Trimmed Mean ( 24 / 24 )113.2391666666670.639099773534149177.185427621836
Median112.95
Midrange110.77
Midmean - Weighted Average at Xnp112.811351351351
Midmean - Weighted Average at X(n+1)p112.977777777778
Midmean - Empirical Distribution Function112.811351351351
Midmean - Empirical Distribution Function - Averaging112.977777777778
Midmean - Empirical Distribution Function - Interpolation112.977777777778
Midmean - Closest Observation112.811351351351
Midmean - True Basic - Statistics Graphics Toolkit112.977777777778
Midmean - MS Excel (old versions)112.941052631579
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')