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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 computationSun, 20 Apr 2008 05:23:04 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/20/t12086906260kclu5ytv0tyh4f.htm/, Retrieved Mon, 13 May 2024 09:02:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10323, Retrieved Mon, 13 May 2024 09:02:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten verk...] [2008-04-20 11:23:04] [b410a83c5378683dfcb81b0901d2d85a] [Current]
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Dataseries X:
24,65
25,24
25,56
25,9
25,87
25,78
25,78
25,74
25,78
25,73
24,67
24,31
24,56
25
25,38
25,99
26,22
26,19
26,22
26,22
26,61
26,72
25,46
25,48
25,59
25,88
26
26,97
27,2
27,19
27,19
27,19
27,26
26,9
26,11
25,87
26,02
26,31
26,37
26,52
26,86
26,92
26,98
26,98
27,03
26,75
26,39
26,3
26,3
26,52
26,53
26,98
27,22
27,34
27,41
27,47
27,46
27,53
27,21
26,91
26,95
26,91
27,39
27,62
27,79
27,88
27,9
28,09
28,46
28,73
27,93
27,61




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10323&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10323&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10323&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26.55527777777780.110272633442371240.814760188490
Geometric Mean26.5389313795381
Harmonic Mean26.5224918923496
Quadratic Mean26.5715287792529
Winsorized Mean ( 1 / 24 )26.5550.108338389192243245.111637693624
Winsorized Mean ( 2 / 24 )26.54722222222220.105361591826283251.962994883301
Winsorized Mean ( 3 / 24 )26.54138888888890.103834410117243255.612651518126
Winsorized Mean ( 4 / 24 )26.55805555555560.099156189308999267.840623370399
Winsorized Mean ( 5 / 24 )26.57333333333330.0954013021436512278.542669085589
Winsorized Mean ( 6 / 24 )26.57750.0917574774257487289.649418724560
Winsorized Mean ( 7 / 24 )26.568750.0874060948149391303.969077399611
Winsorized Mean ( 8 / 24 )26.56986111111110.0868232814452528306.022309556049
Winsorized Mean ( 9 / 24 )26.56986111111110.083431513303962318.463132920895
Winsorized Mean ( 10 / 24 )26.56569444444440.081396945220758326.372130703372
Winsorized Mean ( 11 / 24 )26.58555555555560.0776886086217339342.206612104494
Winsorized Mean ( 12 / 24 )26.57888888888890.0761285862304934349.131518197598
Winsorized Mean ( 13 / 24 )26.58250.0744664774229378356.972706645203
Winsorized Mean ( 14 / 24 )26.57277777777780.0730042826316344363.989300625813
Winsorized Mean ( 15 / 24 )26.55611111111110.0705995328300398376.15137163927
Winsorized Mean ( 16 / 24 )26.56722222222220.0663281376165504400.542261201573
Winsorized Mean ( 17 / 24 )26.56486111111110.0660019659496275402.485906728677
Winsorized Mean ( 18 / 24 )26.56486111111110.065288571261629406.883786821717
Winsorized Mean ( 19 / 24 )26.56750.0641508120160309414.141289331785
Winsorized Mean ( 20 / 24 )26.59250.0605652010953863439.072264585046
Winsorized Mean ( 21 / 24 )26.59541666666670.0601575713607089442.095916858058
Winsorized Mean ( 22 / 24 )26.55263888888890.05276101115358503.262509727076
Winsorized Mean ( 23 / 24 )26.56541666666670.0467223584104052568.580387858813
Winsorized Mean ( 24 / 24 )26.59208333333330.0431383014006211616.437886285214
Trimmed Mean ( 1 / 24 )26.55628571428570.104149353544961254.982722507457
Trimmed Mean ( 2 / 24 )26.55764705882350.0991425304123803267.873403557059
Trimmed Mean ( 3 / 24 )26.56333333333330.0950924794217694279.342104600253
Trimmed Mean ( 4 / 24 )26.57156250.0909275447286299292.227867576342
Trimmed Mean ( 5 / 24 )26.57548387096770.087717901956238302.965338640066
Trimmed Mean ( 6 / 24 )26.5760.0850640171027075312.423524131382
Trimmed Mean ( 7 / 24 )26.57568965517240.0828829129413938320.641356728907
Trimmed Mean ( 8 / 24 )26.57696428571430.0813350133238652326.759204918162
Trimmed Mean ( 9 / 24 )26.57814814814810.079535722177593334.166176159218
Trimmed Mean ( 10 / 24 )26.57942307692310.0780659955277131340.473760659178
Trimmed Mean ( 11 / 24 )26.58140.0766380360619228346.843439183678
Trimmed Mean ( 12 / 24 )26.58083333333330.0755974040168698351.61039825391
Trimmed Mean ( 13 / 24 )26.58108695652170.0745305619386165356.646807230757
Trimmed Mean ( 14 / 24 )26.58090909090910.0734327569049504361.976183535023
Trimmed Mean ( 15 / 24 )26.58190476190480.0722327169649862368.003667573379
Trimmed Mean ( 16 / 24 )26.5850.0710786851818426374.022112704911
Trimmed Mean ( 17 / 24 )26.58710526315790.0703920214575795377.700550611125
Trimmed Mean ( 18 / 24 )26.58972222222220.0693753147982118383.273536121059
Trimmed Mean ( 19 / 24 )26.59264705882350.0679982552249807391.078373567652
Trimmed Mean ( 20 / 24 )26.5956250.0662274573637776401.580040343602
Trimmed Mean ( 21 / 24 )26.5960.064602409122012411.687433355143
Trimmed Mean ( 22 / 24 )26.59607142857140.0621789942365027427.734024249591
Trimmed Mean ( 23 / 24 )26.60153846153850.0607888965258328437.605220391423
Trimmed Mean ( 24 / 24 )26.606250.0604416490078043440.197288405625
Median26.57
Midrange26.52
Midmean - Weighted Average at Xnp26.5518421052632
Midmean - Weighted Average at X(n+1)p26.5897222222222
Midmean - Empirical Distribution Function26.5518421052632
Midmean - Empirical Distribution Function - Averaging26.5897222222222
Midmean - Empirical Distribution Function - Interpolation26.5897222222222
Midmean - Closest Observation26.5518421052632
Midmean - True Basic - Statistics Graphics Toolkit26.5897222222222
Midmean - MS Excel (old versions)26.5687179487180
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26.5552777777778 & 0.110272633442371 & 240.814760188490 \tabularnewline
Geometric Mean & 26.5389313795381 &  &  \tabularnewline
Harmonic Mean & 26.5224918923496 &  &  \tabularnewline
Quadratic Mean & 26.5715287792529 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 26.555 & 0.108338389192243 & 245.111637693624 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 26.5472222222222 & 0.105361591826283 & 251.962994883301 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 26.5413888888889 & 0.103834410117243 & 255.612651518126 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 26.5580555555556 & 0.099156189308999 & 267.840623370399 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 26.5733333333333 & 0.0954013021436512 & 278.542669085589 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 26.5775 & 0.0917574774257487 & 289.649418724560 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 26.56875 & 0.0874060948149391 & 303.969077399611 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 26.5698611111111 & 0.0868232814452528 & 306.022309556049 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 26.5698611111111 & 0.083431513303962 & 318.463132920895 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 26.5656944444444 & 0.081396945220758 & 326.372130703372 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 26.5855555555556 & 0.0776886086217339 & 342.206612104494 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 26.5788888888889 & 0.0761285862304934 & 349.131518197598 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 26.5825 & 0.0744664774229378 & 356.972706645203 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 26.5727777777778 & 0.0730042826316344 & 363.989300625813 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 26.5561111111111 & 0.0705995328300398 & 376.15137163927 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 26.5672222222222 & 0.0663281376165504 & 400.542261201573 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 26.5648611111111 & 0.0660019659496275 & 402.485906728677 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 26.5648611111111 & 0.065288571261629 & 406.883786821717 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 26.5675 & 0.0641508120160309 & 414.141289331785 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 26.5925 & 0.0605652010953863 & 439.072264585046 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 26.5954166666667 & 0.0601575713607089 & 442.095916858058 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 26.5526388888889 & 0.05276101115358 & 503.262509727076 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 26.5654166666667 & 0.0467223584104052 & 568.580387858813 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 26.5920833333333 & 0.0431383014006211 & 616.437886285214 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 26.5562857142857 & 0.104149353544961 & 254.982722507457 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 26.5576470588235 & 0.0991425304123803 & 267.873403557059 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 26.5633333333333 & 0.0950924794217694 & 279.342104600253 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 26.5715625 & 0.0909275447286299 & 292.227867576342 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 26.5754838709677 & 0.087717901956238 & 302.965338640066 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 26.576 & 0.0850640171027075 & 312.423524131382 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 26.5756896551724 & 0.0828829129413938 & 320.641356728907 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 26.5769642857143 & 0.0813350133238652 & 326.759204918162 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 26.5781481481481 & 0.079535722177593 & 334.166176159218 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 26.5794230769231 & 0.0780659955277131 & 340.473760659178 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 26.5814 & 0.0766380360619228 & 346.843439183678 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 26.5808333333333 & 0.0755974040168698 & 351.61039825391 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 26.5810869565217 & 0.0745305619386165 & 356.646807230757 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 26.5809090909091 & 0.0734327569049504 & 361.976183535023 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 26.5819047619048 & 0.0722327169649862 & 368.003667573379 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 26.585 & 0.0710786851818426 & 374.022112704911 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 26.5871052631579 & 0.0703920214575795 & 377.700550611125 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 26.5897222222222 & 0.0693753147982118 & 383.273536121059 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 26.5926470588235 & 0.0679982552249807 & 391.078373567652 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 26.595625 & 0.0662274573637776 & 401.580040343602 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 26.596 & 0.064602409122012 & 411.687433355143 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 26.5960714285714 & 0.0621789942365027 & 427.734024249591 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 26.6015384615385 & 0.0607888965258328 & 437.605220391423 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 26.60625 & 0.0604416490078043 & 440.197288405625 \tabularnewline
Median & 26.57 &  &  \tabularnewline
Midrange & 26.52 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.5518421052632 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26.5897222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26.5518421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26.5897222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26.5897222222222 &  &  \tabularnewline
Midmean - Closest Observation & 26.5518421052632 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26.5897222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26.5687179487180 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10323&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]26.5552777777778[/C][C]0.110272633442371[/C][C]240.814760188490[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26.5389313795381[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]26.5224918923496[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26.5715287792529[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]26.555[/C][C]0.108338389192243[/C][C]245.111637693624[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]26.5472222222222[/C][C]0.105361591826283[/C][C]251.962994883301[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]26.5413888888889[/C][C]0.103834410117243[/C][C]255.612651518126[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]26.5580555555556[/C][C]0.099156189308999[/C][C]267.840623370399[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]26.5733333333333[/C][C]0.0954013021436512[/C][C]278.542669085589[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]26.5775[/C][C]0.0917574774257487[/C][C]289.649418724560[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]26.56875[/C][C]0.0874060948149391[/C][C]303.969077399611[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]26.5698611111111[/C][C]0.0868232814452528[/C][C]306.022309556049[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]26.5698611111111[/C][C]0.083431513303962[/C][C]318.463132920895[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]26.5656944444444[/C][C]0.081396945220758[/C][C]326.372130703372[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]26.5855555555556[/C][C]0.0776886086217339[/C][C]342.206612104494[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]26.5788888888889[/C][C]0.0761285862304934[/C][C]349.131518197598[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]26.5825[/C][C]0.0744664774229378[/C][C]356.972706645203[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]26.5727777777778[/C][C]0.0730042826316344[/C][C]363.989300625813[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]26.5561111111111[/C][C]0.0705995328300398[/C][C]376.15137163927[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]26.5672222222222[/C][C]0.0663281376165504[/C][C]400.542261201573[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]26.5648611111111[/C][C]0.0660019659496275[/C][C]402.485906728677[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]26.5648611111111[/C][C]0.065288571261629[/C][C]406.883786821717[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]26.5675[/C][C]0.0641508120160309[/C][C]414.141289331785[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]26.5925[/C][C]0.0605652010953863[/C][C]439.072264585046[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]26.5954166666667[/C][C]0.0601575713607089[/C][C]442.095916858058[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]26.5526388888889[/C][C]0.05276101115358[/C][C]503.262509727076[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]26.5654166666667[/C][C]0.0467223584104052[/C][C]568.580387858813[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]26.5920833333333[/C][C]0.0431383014006211[/C][C]616.437886285214[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]26.5562857142857[/C][C]0.104149353544961[/C][C]254.982722507457[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]26.5576470588235[/C][C]0.0991425304123803[/C][C]267.873403557059[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]26.5633333333333[/C][C]0.0950924794217694[/C][C]279.342104600253[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]26.5715625[/C][C]0.0909275447286299[/C][C]292.227867576342[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]26.5754838709677[/C][C]0.087717901956238[/C][C]302.965338640066[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]26.576[/C][C]0.0850640171027075[/C][C]312.423524131382[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]26.5756896551724[/C][C]0.0828829129413938[/C][C]320.641356728907[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]26.5769642857143[/C][C]0.0813350133238652[/C][C]326.759204918162[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]26.5781481481481[/C][C]0.079535722177593[/C][C]334.166176159218[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]26.5794230769231[/C][C]0.0780659955277131[/C][C]340.473760659178[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]26.5814[/C][C]0.0766380360619228[/C][C]346.843439183678[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]26.5808333333333[/C][C]0.0755974040168698[/C][C]351.61039825391[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]26.5810869565217[/C][C]0.0745305619386165[/C][C]356.646807230757[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]26.5809090909091[/C][C]0.0734327569049504[/C][C]361.976183535023[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]26.5819047619048[/C][C]0.0722327169649862[/C][C]368.003667573379[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]26.585[/C][C]0.0710786851818426[/C][C]374.022112704911[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]26.5871052631579[/C][C]0.0703920214575795[/C][C]377.700550611125[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]26.5897222222222[/C][C]0.0693753147982118[/C][C]383.273536121059[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]26.5926470588235[/C][C]0.0679982552249807[/C][C]391.078373567652[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]26.595625[/C][C]0.0662274573637776[/C][C]401.580040343602[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]26.596[/C][C]0.064602409122012[/C][C]411.687433355143[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]26.5960714285714[/C][C]0.0621789942365027[/C][C]427.734024249591[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]26.6015384615385[/C][C]0.0607888965258328[/C][C]437.605220391423[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]26.60625[/C][C]0.0604416490078043[/C][C]440.197288405625[/C][/ROW]
[ROW][C]Median[/C][C]26.57[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]26.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.5518421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26.5897222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26.5518421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26.5897222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26.5897222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26.5518421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26.5897222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26.5687179487180[/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=10323&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10323&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 Mean26.55527777777780.110272633442371240.814760188490
Geometric Mean26.5389313795381
Harmonic Mean26.5224918923496
Quadratic Mean26.5715287792529
Winsorized Mean ( 1 / 24 )26.5550.108338389192243245.111637693624
Winsorized Mean ( 2 / 24 )26.54722222222220.105361591826283251.962994883301
Winsorized Mean ( 3 / 24 )26.54138888888890.103834410117243255.612651518126
Winsorized Mean ( 4 / 24 )26.55805555555560.099156189308999267.840623370399
Winsorized Mean ( 5 / 24 )26.57333333333330.0954013021436512278.542669085589
Winsorized Mean ( 6 / 24 )26.57750.0917574774257487289.649418724560
Winsorized Mean ( 7 / 24 )26.568750.0874060948149391303.969077399611
Winsorized Mean ( 8 / 24 )26.56986111111110.0868232814452528306.022309556049
Winsorized Mean ( 9 / 24 )26.56986111111110.083431513303962318.463132920895
Winsorized Mean ( 10 / 24 )26.56569444444440.081396945220758326.372130703372
Winsorized Mean ( 11 / 24 )26.58555555555560.0776886086217339342.206612104494
Winsorized Mean ( 12 / 24 )26.57888888888890.0761285862304934349.131518197598
Winsorized Mean ( 13 / 24 )26.58250.0744664774229378356.972706645203
Winsorized Mean ( 14 / 24 )26.57277777777780.0730042826316344363.989300625813
Winsorized Mean ( 15 / 24 )26.55611111111110.0705995328300398376.15137163927
Winsorized Mean ( 16 / 24 )26.56722222222220.0663281376165504400.542261201573
Winsorized Mean ( 17 / 24 )26.56486111111110.0660019659496275402.485906728677
Winsorized Mean ( 18 / 24 )26.56486111111110.065288571261629406.883786821717
Winsorized Mean ( 19 / 24 )26.56750.0641508120160309414.141289331785
Winsorized Mean ( 20 / 24 )26.59250.0605652010953863439.072264585046
Winsorized Mean ( 21 / 24 )26.59541666666670.0601575713607089442.095916858058
Winsorized Mean ( 22 / 24 )26.55263888888890.05276101115358503.262509727076
Winsorized Mean ( 23 / 24 )26.56541666666670.0467223584104052568.580387858813
Winsorized Mean ( 24 / 24 )26.59208333333330.0431383014006211616.437886285214
Trimmed Mean ( 1 / 24 )26.55628571428570.104149353544961254.982722507457
Trimmed Mean ( 2 / 24 )26.55764705882350.0991425304123803267.873403557059
Trimmed Mean ( 3 / 24 )26.56333333333330.0950924794217694279.342104600253
Trimmed Mean ( 4 / 24 )26.57156250.0909275447286299292.227867576342
Trimmed Mean ( 5 / 24 )26.57548387096770.087717901956238302.965338640066
Trimmed Mean ( 6 / 24 )26.5760.0850640171027075312.423524131382
Trimmed Mean ( 7 / 24 )26.57568965517240.0828829129413938320.641356728907
Trimmed Mean ( 8 / 24 )26.57696428571430.0813350133238652326.759204918162
Trimmed Mean ( 9 / 24 )26.57814814814810.079535722177593334.166176159218
Trimmed Mean ( 10 / 24 )26.57942307692310.0780659955277131340.473760659178
Trimmed Mean ( 11 / 24 )26.58140.0766380360619228346.843439183678
Trimmed Mean ( 12 / 24 )26.58083333333330.0755974040168698351.61039825391
Trimmed Mean ( 13 / 24 )26.58108695652170.0745305619386165356.646807230757
Trimmed Mean ( 14 / 24 )26.58090909090910.0734327569049504361.976183535023
Trimmed Mean ( 15 / 24 )26.58190476190480.0722327169649862368.003667573379
Trimmed Mean ( 16 / 24 )26.5850.0710786851818426374.022112704911
Trimmed Mean ( 17 / 24 )26.58710526315790.0703920214575795377.700550611125
Trimmed Mean ( 18 / 24 )26.58972222222220.0693753147982118383.273536121059
Trimmed Mean ( 19 / 24 )26.59264705882350.0679982552249807391.078373567652
Trimmed Mean ( 20 / 24 )26.5956250.0662274573637776401.580040343602
Trimmed Mean ( 21 / 24 )26.5960.064602409122012411.687433355143
Trimmed Mean ( 22 / 24 )26.59607142857140.0621789942365027427.734024249591
Trimmed Mean ( 23 / 24 )26.60153846153850.0607888965258328437.605220391423
Trimmed Mean ( 24 / 24 )26.606250.0604416490078043440.197288405625
Median26.57
Midrange26.52
Midmean - Weighted Average at Xnp26.5518421052632
Midmean - Weighted Average at X(n+1)p26.5897222222222
Midmean - Empirical Distribution Function26.5518421052632
Midmean - Empirical Distribution Function - Averaging26.5897222222222
Midmean - Empirical Distribution Function - Interpolation26.5897222222222
Midmean - Closest Observation26.5518421052632
Midmean - True Basic - Statistics Graphics Toolkit26.5897222222222
Midmean - MS Excel (old versions)26.5687179487180
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')