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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, 05 Mar 2013 11:05:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t13624997294v5wufjjsc30rp3.htm/, Retrieved Sat, 04 May 2024 17:28:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207412, Retrieved Sat, 04 May 2024 17:28:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 16:05:12] [d4c272cfec48e7f4e5af64cbab0d9d0c] [Current]
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Dataseries X:
108,56
108,71
116,73
118,88
119,6
119,62
119,64
119,74
119,74
119,74
119,9
119,9
119,9
119,9
119,9
121,02
122,95
123,62
123,67
123,81
123,83
123,83
123,83
123,83
123,89
123,89
124,44
125,51
125,89
126,12
126,25
126,25
126,3
126,31
126,38
125,51
126,82
126,86
126,86
127,28
128,72
128,77
128,84
128,88
128,88
128,88
128,88
128,88
128,89
128,9
128,92
129,05
129,83
130,54
130,82
130,91
131,04
131,07
131,15
131,2
131,2
131,42
131,45
131,7
134,24
135,17
135,51
135,65
136,02
136,07
136,13
136,07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207412&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207412&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean126.376250.68328067006216184.955107816094
Geometric Mean126.242242729687
Harmonic Mean126.105145921254
Quadratic Mean126.507329865594
Winsorized Mean ( 1 / 24 )126.37750.682351113329703185.208901299083
Winsorized Mean ( 2 / 24 )126.6002777777780.615790011697451205.590015058541
Winsorized Mean ( 3 / 24 )126.6877777777780.596942693982553212.227704694013
Winsorized Mean ( 4 / 24 )126.7072222222220.585360469115985216.460162425345
Winsorized Mean ( 5 / 24 )126.6988888888890.583042266603501217.306525008848
Winsorized Mean ( 6 / 24 )126.6722222222220.576801295793209219.61154239091
Winsorized Mean ( 7 / 24 )126.5915277777780.556989015062174227.278320315971
Winsorized Mean ( 8 / 24 )126.3093055555560.508337078658906248.475491673329
Winsorized Mean ( 9 / 24 )126.2780555555560.503743522770012250.679264045264
Winsorized Mean ( 10 / 24 )126.2961111111110.499104266344926253.045545044148
Winsorized Mean ( 11 / 24 )126.26250.494309668246601255.431985475571
Winsorized Mean ( 12 / 24 )126.26250.494309668246601255.431985475571
Winsorized Mean ( 13 / 24 )126.2534722222220.493043237243905256.0697778312
Winsorized Mean ( 14 / 24 )126.2379166666670.490876939465226257.16815461772
Winsorized Mean ( 15 / 24 )126.4650.448786008097582281.793544625175
Winsorized Mean ( 16 / 24 )126.8650.375979628106595337.42519678229
Winsorized Mean ( 17 / 24 )127.0019444444440.350355600647236362.494403428473
Winsorized Mean ( 18 / 24 )126.9444444444440.338035432165636375.535912407673
Winsorized Mean ( 19 / 24 )126.7940277777780.305796547001673414.635250204718
Winsorized Mean ( 20 / 24 )126.5829166666670.276168908356607458.353249900292
Winsorized Mean ( 21 / 24 )126.5450.271446885376485466.186966280669
Winsorized Mean ( 22 / 24 )126.5388888888890.270694966861841467.45933386147
Winsorized Mean ( 23 / 24 )126.5356944444440.270302808404162468.12571127728
Winsorized Mean ( 24 / 24 )126.5523611111110.267079894989005473.837093264999
Trimmed Mean ( 1 / 24 )126.4914285714290.639158520490255197.903062411506
Trimmed Mean ( 2 / 24 )126.6120588235290.585951143616223216.079548957167
Trimmed Mean ( 3 / 24 )126.6184848484850.566579079029283223.478927364243
Trimmed Mean ( 4 / 24 )126.59250.552058063213218229.310118691459
Trimmed Mean ( 5 / 24 )126.5591935483870.538772440746398234.902871744991
Trimmed Mean ( 6 / 24 )126.5256666666670.523322197513679241.773934428531
Trimmed Mean ( 7 / 24 )126.4953448275860.506251255472127249.866728151849
Trimmed Mean ( 8 / 24 )126.4776785714290.490713765264662257.742267538009
Trimmed Mean ( 9 / 24 )126.5057407407410.483462543406558261.666063826496
Trimmed Mean ( 10 / 24 )126.5407692307690.475123136072017266.332577017653
Trimmed Mean ( 11 / 24 )126.5760.465415767604293271.963282747261
Trimmed Mean ( 12 / 24 )126.618750.453835567220627278.996974114296
Trimmed Mean ( 13 / 24 )126.6652173913040.438724627148635288.712348368791
Trimmed Mean ( 14 / 24 )126.7170454545450.419170955091765302.30397386862
Trimmed Mean ( 15 / 24 )126.7757142857140.393669142885321322.036198612207
Trimmed Mean ( 16 / 24 )126.8130.371672967636597341.195112483917
Trimmed Mean ( 17 / 24 )126.8068421052630.361549948004834350.731186119733
Trimmed Mean ( 18 / 24 )126.7838888888890.353564227742754358.587998843408
Trimmed Mean ( 19 / 24 )126.7650.345189567903871367.232998290672
Trimmed Mean ( 20 / 24 )126.76156250.341318337531522371.388081334168
Trimmed Mean ( 21 / 24 )126.7830.341937397644724370.778396493878
Trimmed Mean ( 22 / 24 )126.8121428571430.341972707357583370.825332340168
Trimmed Mean ( 23 / 24 )126.8465384615380.339971918436573373.108870417495
Trimmed Mean ( 24 / 24 )126.8870833333330.334633954876128379.181734203582
Median126.6
Midrange122.345
Midmean - Weighted Average at Xnp126.698378378378
Midmean - Weighted Average at X(n+1)p126.783888888889
Midmean - Empirical Distribution Function126.698378378378
Midmean - Empirical Distribution Function - Averaging126.783888888889
Midmean - Empirical Distribution Function - Interpolation126.783888888889
Midmean - Closest Observation126.698378378378
Midmean - True Basic - Statistics Graphics Toolkit126.783888888889
Midmean - MS Excel (old versions)126.806842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 126.37625 & 0.68328067006216 & 184.955107816094 \tabularnewline
Geometric Mean & 126.242242729687 &  &  \tabularnewline
Harmonic Mean & 126.105145921254 &  &  \tabularnewline
Quadratic Mean & 126.507329865594 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 126.3775 & 0.682351113329703 & 185.208901299083 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 126.600277777778 & 0.615790011697451 & 205.590015058541 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 126.687777777778 & 0.596942693982553 & 212.227704694013 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 126.707222222222 & 0.585360469115985 & 216.460162425345 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 126.698888888889 & 0.583042266603501 & 217.306525008848 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 126.672222222222 & 0.576801295793209 & 219.61154239091 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 126.591527777778 & 0.556989015062174 & 227.278320315971 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 126.309305555556 & 0.508337078658906 & 248.475491673329 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 126.278055555556 & 0.503743522770012 & 250.679264045264 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 126.296111111111 & 0.499104266344926 & 253.045545044148 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 126.2625 & 0.494309668246601 & 255.431985475571 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 126.2625 & 0.494309668246601 & 255.431985475571 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 126.253472222222 & 0.493043237243905 & 256.0697778312 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 126.237916666667 & 0.490876939465226 & 257.16815461772 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 126.465 & 0.448786008097582 & 281.793544625175 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 126.865 & 0.375979628106595 & 337.42519678229 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 127.001944444444 & 0.350355600647236 & 362.494403428473 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 126.944444444444 & 0.338035432165636 & 375.535912407673 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 126.794027777778 & 0.305796547001673 & 414.635250204718 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 126.582916666667 & 0.276168908356607 & 458.353249900292 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 126.545 & 0.271446885376485 & 466.186966280669 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 126.538888888889 & 0.270694966861841 & 467.45933386147 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 126.535694444444 & 0.270302808404162 & 468.12571127728 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 126.552361111111 & 0.267079894989005 & 473.837093264999 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 126.491428571429 & 0.639158520490255 & 197.903062411506 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 126.612058823529 & 0.585951143616223 & 216.079548957167 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 126.618484848485 & 0.566579079029283 & 223.478927364243 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 126.5925 & 0.552058063213218 & 229.310118691459 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 126.559193548387 & 0.538772440746398 & 234.902871744991 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 126.525666666667 & 0.523322197513679 & 241.773934428531 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 126.495344827586 & 0.506251255472127 & 249.866728151849 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 126.477678571429 & 0.490713765264662 & 257.742267538009 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 126.505740740741 & 0.483462543406558 & 261.666063826496 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 126.540769230769 & 0.475123136072017 & 266.332577017653 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 126.576 & 0.465415767604293 & 271.963282747261 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 126.61875 & 0.453835567220627 & 278.996974114296 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 126.665217391304 & 0.438724627148635 & 288.712348368791 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 126.717045454545 & 0.419170955091765 & 302.30397386862 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 126.775714285714 & 0.393669142885321 & 322.036198612207 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 126.813 & 0.371672967636597 & 341.195112483917 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 126.806842105263 & 0.361549948004834 & 350.731186119733 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 126.783888888889 & 0.353564227742754 & 358.587998843408 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 126.765 & 0.345189567903871 & 367.232998290672 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 126.7615625 & 0.341318337531522 & 371.388081334168 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 126.783 & 0.341937397644724 & 370.778396493878 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 126.812142857143 & 0.341972707357583 & 370.825332340168 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 126.846538461538 & 0.339971918436573 & 373.108870417495 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 126.887083333333 & 0.334633954876128 & 379.181734203582 \tabularnewline
Median & 126.6 &  &  \tabularnewline
Midrange & 122.345 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 126.698378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 126.783888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 126.698378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 126.783888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 126.783888888889 &  &  \tabularnewline
Midmean - Closest Observation & 126.698378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 126.783888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 126.806842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207412&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]126.37625[/C][C]0.68328067006216[/C][C]184.955107816094[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]126.242242729687[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]126.105145921254[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]126.507329865594[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]126.3775[/C][C]0.682351113329703[/C][C]185.208901299083[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]126.600277777778[/C][C]0.615790011697451[/C][C]205.590015058541[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]126.687777777778[/C][C]0.596942693982553[/C][C]212.227704694013[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]126.707222222222[/C][C]0.585360469115985[/C][C]216.460162425345[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]126.698888888889[/C][C]0.583042266603501[/C][C]217.306525008848[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]126.672222222222[/C][C]0.576801295793209[/C][C]219.61154239091[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]126.591527777778[/C][C]0.556989015062174[/C][C]227.278320315971[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]126.309305555556[/C][C]0.508337078658906[/C][C]248.475491673329[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]126.278055555556[/C][C]0.503743522770012[/C][C]250.679264045264[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]126.296111111111[/C][C]0.499104266344926[/C][C]253.045545044148[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]126.2625[/C][C]0.494309668246601[/C][C]255.431985475571[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]126.2625[/C][C]0.494309668246601[/C][C]255.431985475571[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]126.253472222222[/C][C]0.493043237243905[/C][C]256.0697778312[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]126.237916666667[/C][C]0.490876939465226[/C][C]257.16815461772[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]126.465[/C][C]0.448786008097582[/C][C]281.793544625175[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]126.865[/C][C]0.375979628106595[/C][C]337.42519678229[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]127.001944444444[/C][C]0.350355600647236[/C][C]362.494403428473[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]126.944444444444[/C][C]0.338035432165636[/C][C]375.535912407673[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]126.794027777778[/C][C]0.305796547001673[/C][C]414.635250204718[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]126.582916666667[/C][C]0.276168908356607[/C][C]458.353249900292[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]126.545[/C][C]0.271446885376485[/C][C]466.186966280669[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]126.538888888889[/C][C]0.270694966861841[/C][C]467.45933386147[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]126.535694444444[/C][C]0.270302808404162[/C][C]468.12571127728[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]126.552361111111[/C][C]0.267079894989005[/C][C]473.837093264999[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]126.491428571429[/C][C]0.639158520490255[/C][C]197.903062411506[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]126.612058823529[/C][C]0.585951143616223[/C][C]216.079548957167[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]126.618484848485[/C][C]0.566579079029283[/C][C]223.478927364243[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]126.5925[/C][C]0.552058063213218[/C][C]229.310118691459[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]126.559193548387[/C][C]0.538772440746398[/C][C]234.902871744991[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]126.525666666667[/C][C]0.523322197513679[/C][C]241.773934428531[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]126.495344827586[/C][C]0.506251255472127[/C][C]249.866728151849[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]126.477678571429[/C][C]0.490713765264662[/C][C]257.742267538009[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]126.505740740741[/C][C]0.483462543406558[/C][C]261.666063826496[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]126.540769230769[/C][C]0.475123136072017[/C][C]266.332577017653[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]126.576[/C][C]0.465415767604293[/C][C]271.963282747261[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]126.61875[/C][C]0.453835567220627[/C][C]278.996974114296[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]126.665217391304[/C][C]0.438724627148635[/C][C]288.712348368791[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]126.717045454545[/C][C]0.419170955091765[/C][C]302.30397386862[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]126.775714285714[/C][C]0.393669142885321[/C][C]322.036198612207[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]126.813[/C][C]0.371672967636597[/C][C]341.195112483917[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]126.806842105263[/C][C]0.361549948004834[/C][C]350.731186119733[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]126.783888888889[/C][C]0.353564227742754[/C][C]358.587998843408[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]126.765[/C][C]0.345189567903871[/C][C]367.232998290672[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]126.7615625[/C][C]0.341318337531522[/C][C]371.388081334168[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]126.783[/C][C]0.341937397644724[/C][C]370.778396493878[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]126.812142857143[/C][C]0.341972707357583[/C][C]370.825332340168[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]126.846538461538[/C][C]0.339971918436573[/C][C]373.108870417495[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]126.887083333333[/C][C]0.334633954876128[/C][C]379.181734203582[/C][/ROW]
[ROW][C]Median[/C][C]126.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]122.345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]126.698378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]126.783888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]126.698378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]126.783888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]126.783888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]126.698378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]126.783888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]126.806842105263[/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=207412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207412&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 Mean126.376250.68328067006216184.955107816094
Geometric Mean126.242242729687
Harmonic Mean126.105145921254
Quadratic Mean126.507329865594
Winsorized Mean ( 1 / 24 )126.37750.682351113329703185.208901299083
Winsorized Mean ( 2 / 24 )126.6002777777780.615790011697451205.590015058541
Winsorized Mean ( 3 / 24 )126.6877777777780.596942693982553212.227704694013
Winsorized Mean ( 4 / 24 )126.7072222222220.585360469115985216.460162425345
Winsorized Mean ( 5 / 24 )126.6988888888890.583042266603501217.306525008848
Winsorized Mean ( 6 / 24 )126.6722222222220.576801295793209219.61154239091
Winsorized Mean ( 7 / 24 )126.5915277777780.556989015062174227.278320315971
Winsorized Mean ( 8 / 24 )126.3093055555560.508337078658906248.475491673329
Winsorized Mean ( 9 / 24 )126.2780555555560.503743522770012250.679264045264
Winsorized Mean ( 10 / 24 )126.2961111111110.499104266344926253.045545044148
Winsorized Mean ( 11 / 24 )126.26250.494309668246601255.431985475571
Winsorized Mean ( 12 / 24 )126.26250.494309668246601255.431985475571
Winsorized Mean ( 13 / 24 )126.2534722222220.493043237243905256.0697778312
Winsorized Mean ( 14 / 24 )126.2379166666670.490876939465226257.16815461772
Winsorized Mean ( 15 / 24 )126.4650.448786008097582281.793544625175
Winsorized Mean ( 16 / 24 )126.8650.375979628106595337.42519678229
Winsorized Mean ( 17 / 24 )127.0019444444440.350355600647236362.494403428473
Winsorized Mean ( 18 / 24 )126.9444444444440.338035432165636375.535912407673
Winsorized Mean ( 19 / 24 )126.7940277777780.305796547001673414.635250204718
Winsorized Mean ( 20 / 24 )126.5829166666670.276168908356607458.353249900292
Winsorized Mean ( 21 / 24 )126.5450.271446885376485466.186966280669
Winsorized Mean ( 22 / 24 )126.5388888888890.270694966861841467.45933386147
Winsorized Mean ( 23 / 24 )126.5356944444440.270302808404162468.12571127728
Winsorized Mean ( 24 / 24 )126.5523611111110.267079894989005473.837093264999
Trimmed Mean ( 1 / 24 )126.4914285714290.639158520490255197.903062411506
Trimmed Mean ( 2 / 24 )126.6120588235290.585951143616223216.079548957167
Trimmed Mean ( 3 / 24 )126.6184848484850.566579079029283223.478927364243
Trimmed Mean ( 4 / 24 )126.59250.552058063213218229.310118691459
Trimmed Mean ( 5 / 24 )126.5591935483870.538772440746398234.902871744991
Trimmed Mean ( 6 / 24 )126.5256666666670.523322197513679241.773934428531
Trimmed Mean ( 7 / 24 )126.4953448275860.506251255472127249.866728151849
Trimmed Mean ( 8 / 24 )126.4776785714290.490713765264662257.742267538009
Trimmed Mean ( 9 / 24 )126.5057407407410.483462543406558261.666063826496
Trimmed Mean ( 10 / 24 )126.5407692307690.475123136072017266.332577017653
Trimmed Mean ( 11 / 24 )126.5760.465415767604293271.963282747261
Trimmed Mean ( 12 / 24 )126.618750.453835567220627278.996974114296
Trimmed Mean ( 13 / 24 )126.6652173913040.438724627148635288.712348368791
Trimmed Mean ( 14 / 24 )126.7170454545450.419170955091765302.30397386862
Trimmed Mean ( 15 / 24 )126.7757142857140.393669142885321322.036198612207
Trimmed Mean ( 16 / 24 )126.8130.371672967636597341.195112483917
Trimmed Mean ( 17 / 24 )126.8068421052630.361549948004834350.731186119733
Trimmed Mean ( 18 / 24 )126.7838888888890.353564227742754358.587998843408
Trimmed Mean ( 19 / 24 )126.7650.345189567903871367.232998290672
Trimmed Mean ( 20 / 24 )126.76156250.341318337531522371.388081334168
Trimmed Mean ( 21 / 24 )126.7830.341937397644724370.778396493878
Trimmed Mean ( 22 / 24 )126.8121428571430.341972707357583370.825332340168
Trimmed Mean ( 23 / 24 )126.8465384615380.339971918436573373.108870417495
Trimmed Mean ( 24 / 24 )126.8870833333330.334633954876128379.181734203582
Median126.6
Midrange122.345
Midmean - Weighted Average at Xnp126.698378378378
Midmean - Weighted Average at X(n+1)p126.783888888889
Midmean - Empirical Distribution Function126.698378378378
Midmean - Empirical Distribution Function - Averaging126.783888888889
Midmean - Empirical Distribution Function - Interpolation126.783888888889
Midmean - Closest Observation126.698378378378
Midmean - True Basic - Statistics Graphics Toolkit126.783888888889
Midmean - MS Excel (old versions)126.806842105263
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')