Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Mar 2017 08:19:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/13/t1489393203wce4t4wzr9frmlm.htm/, Retrieved Tue, 14 May 2024 13:30:30 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 13:30:30 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
 93,65   
 92,68   
 92,70   
 92,73   
 92,80   
 92,86   
 93,02   
 93,02   
 93,04   
 93,09   
 93,11   
 93,11   
 93,20   
 93,21   
 93,22   
 93,23   
 93,29   
 93,42   
 93,43   
 93,45   
 93,45   
 93,49   
 93,50   
 93,56   
 93,68   
 93,70   
 94,01   
 94,07   
 94,33   
 94,43   
 94,47   
 95,35   
 95,37   
 95,46   
 95,83   
 96,00   
 96,85   
 97,84   
 98,38   
 98,90   
 99,51   
 99,93   
 99,95   
 101,40   
 101,56   
 101,65   
 101,70   
 101,91   
 101,91   
 102,29   
 102,33   
 102,44   
 102,57   
 102,59   
 102,84   
 102,88   
 103,04   
 103,16   
 103,20   
 103,23   
 103,27   
 103,31   
 103,59   
 104,35   
 104,55   
 104,60   
 104,67   
 104,93   
 105,08   
 105,15   
 109,25   
 109,82   




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.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]'Gertrude Mary Cox' @ cox.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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.16097222222220.579193835608305169.47862043305
Geometric Mean98.0410147828976
Harmonic Mean97.9225366595296
Quadratic Mean98.2822187277819
Winsorized Mean ( 1 / 24 )98.15333333333330.576962223101096170.120901167103
Winsorized Mean ( 2 / 24 )98.04027777777780.550958049216249177.945086594601
Winsorized Mean ( 3 / 24 )98.04027777777780.550036453914349178.243236571088
Winsorized Mean ( 4 / 24 )98.03527777777780.548101823789952178.863257742685
Winsorized Mean ( 5 / 24 )98.02833333333340.543488341608897180.368787751985
Winsorized Mean ( 6 / 24 )98.02250.542488244754115180.6905512661
Winsorized Mean ( 7 / 24 )98.01958333333330.541408043622135181.045672460944
Winsorized Mean ( 8 / 24 )98.00291666666670.536952597753246182.516887108354
Winsorized Mean ( 9 / 24 )97.91041666666670.521425023062064187.774679649413
Winsorized Mean ( 10 / 24 )97.87152777777780.515552473453751189.838149979427
Winsorized Mean ( 11 / 24 )97.87916666666670.51286835497086190.846570504877
Winsorized Mean ( 12 / 24 )97.87416666666670.511669371542452191.284005082462
Winsorized Mean ( 13 / 24 )97.87055555555560.510640262470616191.662433906076
Winsorized Mean ( 14 / 24 )97.86472222222220.509249730906261192.17432289667
Winsorized Mean ( 15 / 24 )97.85222222222220.504008820680004194.147836718812
Winsorized Mean ( 16 / 24 )97.84555555555560.495225991664794197.577585188188
Winsorized Mean ( 17 / 24 )97.83847222222220.493578785996727198.222603965137
Winsorized Mean ( 18 / 24 )97.78097222222220.484116217169206201.978303461886
Winsorized Mean ( 19 / 24 )97.77569444444450.483378370347446202.275692174982
Winsorized Mean ( 20 / 24 )97.75069444444440.476956489847557204.946775073104
Winsorized Mean ( 21 / 24 )97.72152777777780.472162667410475206.965807597032
Winsorized Mean ( 22 / 24 )97.72763888888890.468180161954303208.739384601323
Winsorized Mean ( 23 / 24 )97.6350.448087223232724217.892845271536
Winsorized Mean ( 24 / 24 )97.6450.446836034037715218.525348364717
Trimmed Mean ( 1 / 24 )98.07271428571430.566194002900453173.21397574562
Trimmed Mean ( 2 / 24 )97.98735294117650.553162970620123177.140116286757
Trimmed Mean ( 3 / 24 )97.95848484848480.5536673343528176.926610566599
Trimmed Mean ( 4 / 24 )97.92781250.554048656820413176.749480924636
Trimmed Mean ( 5 / 24 )97.89661290322580.554518239773577176.543539745779
Trimmed Mean ( 6 / 24 )97.8650.555712221789595176.107337867861
Trimmed Mean ( 7 / 24 )97.83241379310350.556627848772706175.759107290107
Trimmed Mean ( 8 / 24 )97.79803571428570.557170986115588175.526073954607
Trimmed Mean ( 9 / 24 )97.76388888888890.557960272541798175.216576699133
Trimmed Mean ( 10 / 24 )97.74134615384620.561244646035336174.151053100099
Trimmed Mean ( 11 / 24 )97.72260.565285321491614172.873054163409
Trimmed Mean ( 12 / 24 )97.701250.569481662495325171.561713808128
Trimmed Mean ( 13 / 24 )97.67869565217390.573522096386057170.31374426143
Trimmed Mean ( 14 / 24 )97.65454545454550.577269256369516169.166371458444
Trimmed Mean ( 15 / 24 )97.62880952380950.580647662178714168.137781107196
Trimmed Mean ( 16 / 24 )97.6020.584215581916339167.06504075062
Trimmed Mean ( 17 / 24 )97.57315789473680.58857195178431165.779489829468
Trimmed Mean ( 18 / 24 )97.54194444444440.592359931798822164.66668187404
Trimmed Mean ( 19 / 24 )97.51382352941180.59698290965632163.344413972504
Trimmed Mean ( 20 / 24 )97.48281250.600535418762714162.326499743919
Trimmed Mean ( 21 / 24 )97.45066666666670.603829147894289161.387814759362
Trimmed Mean ( 22 / 24 )97.41750.606145691402941160.716311906011
Trimmed Mean ( 23 / 24 )97.37846153846150.606506691524426160.556285527049
Trimmed Mean ( 24 / 24 )97.3450.608871015111968159.877868356238
Median96.425
Midrange101.25
Midmean - Weighted Average at Xnp97.4308108108108
Midmean - Weighted Average at X(n+1)p97.5419444444444
Midmean - Empirical Distribution Function97.4308108108108
Midmean - Empirical Distribution Function - Averaging97.5419444444444
Midmean - Empirical Distribution Function - Interpolation97.5419444444444
Midmean - Closest Observation97.4308108108108
Midmean - True Basic - Statistics Graphics Toolkit97.5419444444444
Midmean - MS Excel (old versions)97.5731578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.1609722222222 & 0.579193835608305 & 169.47862043305 \tabularnewline
Geometric Mean & 98.0410147828976 &  &  \tabularnewline
Harmonic Mean & 97.9225366595296 &  &  \tabularnewline
Quadratic Mean & 98.2822187277819 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.1533333333333 & 0.576962223101096 & 170.120901167103 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.0402777777778 & 0.550958049216249 & 177.945086594601 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.0402777777778 & 0.550036453914349 & 178.243236571088 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.0352777777778 & 0.548101823789952 & 178.863257742685 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.0283333333334 & 0.543488341608897 & 180.368787751985 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.0225 & 0.542488244754115 & 180.6905512661 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.0195833333333 & 0.541408043622135 & 181.045672460944 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.0029166666667 & 0.536952597753246 & 182.516887108354 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.9104166666667 & 0.521425023062064 & 187.774679649413 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 97.8715277777778 & 0.515552473453751 & 189.838149979427 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 97.8791666666667 & 0.51286835497086 & 190.846570504877 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 97.8741666666667 & 0.511669371542452 & 191.284005082462 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.8705555555556 & 0.510640262470616 & 191.662433906076 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.8647222222222 & 0.509249730906261 & 192.17432289667 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.8522222222222 & 0.504008820680004 & 194.147836718812 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.8455555555556 & 0.495225991664794 & 197.577585188188 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.8384722222222 & 0.493578785996727 & 198.222603965137 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.7809722222222 & 0.484116217169206 & 201.978303461886 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.7756944444445 & 0.483378370347446 & 202.275692174982 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.7506944444444 & 0.476956489847557 & 204.946775073104 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.7215277777778 & 0.472162667410475 & 206.965807597032 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.7276388888889 & 0.468180161954303 & 208.739384601323 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.635 & 0.448087223232724 & 217.892845271536 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.645 & 0.446836034037715 & 218.525348364717 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.0727142857143 & 0.566194002900453 & 173.21397574562 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.9873529411765 & 0.553162970620123 & 177.140116286757 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.9584848484848 & 0.5536673343528 & 176.926610566599 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.9278125 & 0.554048656820413 & 176.749480924636 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 97.8966129032258 & 0.554518239773577 & 176.543539745779 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.865 & 0.555712221789595 & 176.107337867861 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.8324137931035 & 0.556627848772706 & 175.759107290107 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.7980357142857 & 0.557170986115588 & 175.526073954607 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.7638888888889 & 0.557960272541798 & 175.216576699133 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.7413461538462 & 0.561244646035336 & 174.151053100099 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.7226 & 0.565285321491614 & 172.873054163409 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.70125 & 0.569481662495325 & 171.561713808128 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.6786956521739 & 0.573522096386057 & 170.31374426143 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.6545454545455 & 0.577269256369516 & 169.166371458444 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.6288095238095 & 0.580647662178714 & 168.137781107196 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.602 & 0.584215581916339 & 167.06504075062 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.5731578947368 & 0.58857195178431 & 165.779489829468 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.5419444444444 & 0.592359931798822 & 164.66668187404 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.5138235294118 & 0.59698290965632 & 163.344413972504 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.4828125 & 0.600535418762714 & 162.326499743919 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.4506666666667 & 0.603829147894289 & 161.387814759362 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.4175 & 0.606145691402941 & 160.716311906011 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.3784615384615 & 0.606506691524426 & 160.556285527049 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.345 & 0.608871015111968 & 159.877868356238 \tabularnewline
Median & 96.425 &  &  \tabularnewline
Midrange & 101.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.4308108108108 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.5419444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.4308108108108 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.5419444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.5419444444444 &  &  \tabularnewline
Midmean - Closest Observation & 97.4308108108108 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.5419444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.5731578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]98.1609722222222[/C][C]0.579193835608305[/C][C]169.47862043305[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.0410147828976[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.9225366595296[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.2822187277819[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.1533333333333[/C][C]0.576962223101096[/C][C]170.120901167103[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.0402777777778[/C][C]0.550958049216249[/C][C]177.945086594601[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.0402777777778[/C][C]0.550036453914349[/C][C]178.243236571088[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.0352777777778[/C][C]0.548101823789952[/C][C]178.863257742685[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.0283333333334[/C][C]0.543488341608897[/C][C]180.368787751985[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.0225[/C][C]0.542488244754115[/C][C]180.6905512661[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.0195833333333[/C][C]0.541408043622135[/C][C]181.045672460944[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.0029166666667[/C][C]0.536952597753246[/C][C]182.516887108354[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.9104166666667[/C][C]0.521425023062064[/C][C]187.774679649413[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]97.8715277777778[/C][C]0.515552473453751[/C][C]189.838149979427[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]97.8791666666667[/C][C]0.51286835497086[/C][C]190.846570504877[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]97.8741666666667[/C][C]0.511669371542452[/C][C]191.284005082462[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.8705555555556[/C][C]0.510640262470616[/C][C]191.662433906076[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.8647222222222[/C][C]0.509249730906261[/C][C]192.17432289667[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.8522222222222[/C][C]0.504008820680004[/C][C]194.147836718812[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.8455555555556[/C][C]0.495225991664794[/C][C]197.577585188188[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.8384722222222[/C][C]0.493578785996727[/C][C]198.222603965137[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.7809722222222[/C][C]0.484116217169206[/C][C]201.978303461886[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.7756944444445[/C][C]0.483378370347446[/C][C]202.275692174982[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.7506944444444[/C][C]0.476956489847557[/C][C]204.946775073104[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.7215277777778[/C][C]0.472162667410475[/C][C]206.965807597032[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.7276388888889[/C][C]0.468180161954303[/C][C]208.739384601323[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.635[/C][C]0.448087223232724[/C][C]217.892845271536[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.645[/C][C]0.446836034037715[/C][C]218.525348364717[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.0727142857143[/C][C]0.566194002900453[/C][C]173.21397574562[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.9873529411765[/C][C]0.553162970620123[/C][C]177.140116286757[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.9584848484848[/C][C]0.5536673343528[/C][C]176.926610566599[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.9278125[/C][C]0.554048656820413[/C][C]176.749480924636[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]97.8966129032258[/C][C]0.554518239773577[/C][C]176.543539745779[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.865[/C][C]0.555712221789595[/C][C]176.107337867861[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.8324137931035[/C][C]0.556627848772706[/C][C]175.759107290107[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.7980357142857[/C][C]0.557170986115588[/C][C]175.526073954607[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.7638888888889[/C][C]0.557960272541798[/C][C]175.216576699133[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.7413461538462[/C][C]0.561244646035336[/C][C]174.151053100099[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.7226[/C][C]0.565285321491614[/C][C]172.873054163409[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.70125[/C][C]0.569481662495325[/C][C]171.561713808128[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.6786956521739[/C][C]0.573522096386057[/C][C]170.31374426143[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.6545454545455[/C][C]0.577269256369516[/C][C]169.166371458444[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.6288095238095[/C][C]0.580647662178714[/C][C]168.137781107196[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.602[/C][C]0.584215581916339[/C][C]167.06504075062[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.5731578947368[/C][C]0.58857195178431[/C][C]165.779489829468[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.5419444444444[/C][C]0.592359931798822[/C][C]164.66668187404[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.5138235294118[/C][C]0.59698290965632[/C][C]163.344413972504[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.4828125[/C][C]0.600535418762714[/C][C]162.326499743919[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.4506666666667[/C][C]0.603829147894289[/C][C]161.387814759362[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.4175[/C][C]0.606145691402941[/C][C]160.716311906011[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.3784615384615[/C][C]0.606506691524426[/C][C]160.556285527049[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.345[/C][C]0.608871015111968[/C][C]159.877868356238[/C][/ROW]
[ROW][C]Median[/C][C]96.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.4308108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.5419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.4308108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.5419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.5419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.4308108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.5419444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.5731578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.16097222222220.579193835608305169.47862043305
Geometric Mean98.0410147828976
Harmonic Mean97.9225366595296
Quadratic Mean98.2822187277819
Winsorized Mean ( 1 / 24 )98.15333333333330.576962223101096170.120901167103
Winsorized Mean ( 2 / 24 )98.04027777777780.550958049216249177.945086594601
Winsorized Mean ( 3 / 24 )98.04027777777780.550036453914349178.243236571088
Winsorized Mean ( 4 / 24 )98.03527777777780.548101823789952178.863257742685
Winsorized Mean ( 5 / 24 )98.02833333333340.543488341608897180.368787751985
Winsorized Mean ( 6 / 24 )98.02250.542488244754115180.6905512661
Winsorized Mean ( 7 / 24 )98.01958333333330.541408043622135181.045672460944
Winsorized Mean ( 8 / 24 )98.00291666666670.536952597753246182.516887108354
Winsorized Mean ( 9 / 24 )97.91041666666670.521425023062064187.774679649413
Winsorized Mean ( 10 / 24 )97.87152777777780.515552473453751189.838149979427
Winsorized Mean ( 11 / 24 )97.87916666666670.51286835497086190.846570504877
Winsorized Mean ( 12 / 24 )97.87416666666670.511669371542452191.284005082462
Winsorized Mean ( 13 / 24 )97.87055555555560.510640262470616191.662433906076
Winsorized Mean ( 14 / 24 )97.86472222222220.509249730906261192.17432289667
Winsorized Mean ( 15 / 24 )97.85222222222220.504008820680004194.147836718812
Winsorized Mean ( 16 / 24 )97.84555555555560.495225991664794197.577585188188
Winsorized Mean ( 17 / 24 )97.83847222222220.493578785996727198.222603965137
Winsorized Mean ( 18 / 24 )97.78097222222220.484116217169206201.978303461886
Winsorized Mean ( 19 / 24 )97.77569444444450.483378370347446202.275692174982
Winsorized Mean ( 20 / 24 )97.75069444444440.476956489847557204.946775073104
Winsorized Mean ( 21 / 24 )97.72152777777780.472162667410475206.965807597032
Winsorized Mean ( 22 / 24 )97.72763888888890.468180161954303208.739384601323
Winsorized Mean ( 23 / 24 )97.6350.448087223232724217.892845271536
Winsorized Mean ( 24 / 24 )97.6450.446836034037715218.525348364717
Trimmed Mean ( 1 / 24 )98.07271428571430.566194002900453173.21397574562
Trimmed Mean ( 2 / 24 )97.98735294117650.553162970620123177.140116286757
Trimmed Mean ( 3 / 24 )97.95848484848480.5536673343528176.926610566599
Trimmed Mean ( 4 / 24 )97.92781250.554048656820413176.749480924636
Trimmed Mean ( 5 / 24 )97.89661290322580.554518239773577176.543539745779
Trimmed Mean ( 6 / 24 )97.8650.555712221789595176.107337867861
Trimmed Mean ( 7 / 24 )97.83241379310350.556627848772706175.759107290107
Trimmed Mean ( 8 / 24 )97.79803571428570.557170986115588175.526073954607
Trimmed Mean ( 9 / 24 )97.76388888888890.557960272541798175.216576699133
Trimmed Mean ( 10 / 24 )97.74134615384620.561244646035336174.151053100099
Trimmed Mean ( 11 / 24 )97.72260.565285321491614172.873054163409
Trimmed Mean ( 12 / 24 )97.701250.569481662495325171.561713808128
Trimmed Mean ( 13 / 24 )97.67869565217390.573522096386057170.31374426143
Trimmed Mean ( 14 / 24 )97.65454545454550.577269256369516169.166371458444
Trimmed Mean ( 15 / 24 )97.62880952380950.580647662178714168.137781107196
Trimmed Mean ( 16 / 24 )97.6020.584215581916339167.06504075062
Trimmed Mean ( 17 / 24 )97.57315789473680.58857195178431165.779489829468
Trimmed Mean ( 18 / 24 )97.54194444444440.592359931798822164.66668187404
Trimmed Mean ( 19 / 24 )97.51382352941180.59698290965632163.344413972504
Trimmed Mean ( 20 / 24 )97.48281250.600535418762714162.326499743919
Trimmed Mean ( 21 / 24 )97.45066666666670.603829147894289161.387814759362
Trimmed Mean ( 22 / 24 )97.41750.606145691402941160.716311906011
Trimmed Mean ( 23 / 24 )97.37846153846150.606506691524426160.556285527049
Trimmed Mean ( 24 / 24 )97.3450.608871015111968159.877868356238
Median96.425
Midrange101.25
Midmean - Weighted Average at Xnp97.4308108108108
Midmean - Weighted Average at X(n+1)p97.5419444444444
Midmean - Empirical Distribution Function97.4308108108108
Midmean - Empirical Distribution Function - Averaging97.5419444444444
Midmean - Empirical Distribution Function - Interpolation97.5419444444444
Midmean - Closest Observation97.4308108108108
Midmean - True Basic - Statistics Graphics Toolkit97.5419444444444
Midmean - MS Excel (old versions)97.5731578947368
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')