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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 03:30:13 -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/t1208683882x1paf6k6kep7qt1.htm/, Retrieved Mon, 13 May 2024 19:40:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10307, Retrieved Mon, 13 May 2024 19:40:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid prijs...] [2008-04-20 09:30:13] [b64702de7eac3a2282df81a39c87ddc7] [Current]
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Dataseries X:
20.66
20.66
20.67
20.71
20.73
20.73
20.74
20.74
20.75
20.75
20.77
20.78
20.78
20.8
20.84
20.85
20.86
20.86
20.86
20.86
20.9
20.92
20.95
20.95
20.95
20.96
21.1
21.18
21.19
21.19
21.19
21.19
21.19
21.21
21.22
21.22
21.22
21.23
21.41
21.42
21.43
21.44
21.44
21.44
21.48
21.53
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.57
21.6
21.61
21.6
21.6
21.71
21.75
21.84
21.85
21.92
21.92
21.93
22
22
21.99
22.01
22.01




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10307&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10307&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10307&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean21.27753424657530.0485743404045292438.040621228721
Geometric Mean21.2735478112390
Harmonic Mean21.2695674936931
Quadratic Mean21.2815259134649
Winsorized Mean ( 1 / 24 )21.27753424657530.0485743404045292438.040621228721
Winsorized Mean ( 2 / 24 )21.27753424657530.0484692549626369438.990330323365
Winsorized Mean ( 3 / 24 )21.27917808219180.0481913176656412441.556261852602
Winsorized Mean ( 4 / 24 )21.27972602739730.0479007458572527444.246235555751
Winsorized Mean ( 5 / 24 )21.27561643835620.0470806758862811451.897005254245
Winsorized Mean ( 6 / 24 )21.27561643835620.0467912501664293454.692199133002
Winsorized Mean ( 7 / 24 )21.27561643835620.0467912501664293454.692199133002
Winsorized Mean ( 8 / 24 )21.26904109589040.0451975051773916470.579980297883
Winsorized Mean ( 9 / 24 )21.26780821917810.0449785364741226472.843491281982
Winsorized Mean ( 10 / 24 )21.25821917808220.0424570435905191500.699468929327
Winsorized Mean ( 11 / 24 )21.2536986301370.0412686500661754515.00833189494
Winsorized Mean ( 12 / 24 )21.23726027397260.0389078743864062545.834502883884
Winsorized Mean ( 13 / 24 )21.23904109589040.0380964311497229557.50736892962
Winsorized Mean ( 14 / 24 )21.24671232876710.0368948146951529575.87258546547
Winsorized Mean ( 15 / 24 )21.24876712328770.0365819617312276580.853680822398
Winsorized Mean ( 16 / 24 )21.24438356164380.035391905822787600.261078564628
Winsorized Mean ( 17 / 24 )21.2373972602740.0345199892443494615.22027454717
Winsorized Mean ( 18 / 24 )21.2373972602740.0345199892443494615.22027454717
Winsorized Mean ( 19 / 24 )21.23739726027400.0345199892443494615.22027454717
Winsorized Mean ( 20 / 24 )21.24835616438360.0328810721360861646.21847111439
Winsorized Mean ( 21 / 24 )21.25410958904110.0320410669326741663.33963328066
Winsorized Mean ( 22 / 24 )21.26315068493150.0307465932282243691.56119271818
Winsorized Mean ( 23 / 24 )21.26315068493150.0307465932282243691.56119271818
Winsorized Mean ( 24 / 24 )21.26315068493150.0307465932282243691.56119271818
Trimmed Mean ( 1 / 24 )21.27591549295770.0480679337617951442.621802684352
Trimmed Mean ( 2 / 24 )21.27420289855070.0474518672076898448.332260676628
Trimmed Mean ( 3 / 24 )21.27238805970150.0467699749214087454.830007829749
Trimmed Mean ( 4 / 24 )21.26984615384620.0460630276338074461.755278505302
Trimmed Mean ( 5 / 24 )21.26698412698410.045301874713604469.450420350876
Trimmed Mean ( 6 / 24 )21.26491803278690.0446232700148784476.543248078786
Trimmed Mean ( 7 / 24 )21.26271186440680.0438602201039528484.783519417188
Trimmed Mean ( 8 / 24 )21.2603508771930.0429102380363753495.46103331262
Trimmed Mean ( 9 / 24 )21.25890909090910.0421202964801284504.718885370112
Trimmed Mean ( 10 / 24 )21.25754716981130.041174612829776516.278009891537
Trimmed Mean ( 11 / 24 )21.25745098039220.040546118150072524.278326761458
Trimmed Mean ( 12 / 24 )21.25795918367350.0399797776176089531.717794606003
Trimmed Mean ( 13 / 24 )21.26063829787230.0396951895287376535.597349459197
Trimmed Mean ( 14 / 24 )21.26333333333330.0394341286838001539.211440522293
Trimmed Mean ( 15 / 24 )21.26534883720930.0392783023030034541.401934155979
Trimmed Mean ( 16 / 24 )21.26731707317070.0390559704536774544.534339465331
Trimmed Mean ( 17 / 24 )21.270.0389106037953576546.637623817539
Trimmed Mean ( 18 / 24 )21.27378378378380.0387711994734663548.700686919497
Trimmed Mean ( 19 / 24 )21.2780.0384528522835367553.352969582181
Trimmed Mean ( 20 / 24 )21.28272727272730.0378825755682007561.807822026556
Trimmed Mean ( 21 / 24 )21.28677419354840.0374205598619468568.85237078441
Trimmed Mean ( 22 / 24 )21.29068965517240.0368592417593549577.621476702484
Trimmed Mean ( 23 / 24 )21.29407407407410.0362928075537129586.729864934232
Trimmed Mean ( 24 / 24 )21.2980.0352467492590924604.254305650779
Median21.22
Midrange21.335
Midmean - Weighted Average at Xnp21.25975
Midmean - Weighted Average at X(n+1)p21.25975
Midmean - Empirical Distribution Function21.25975
Midmean - Empirical Distribution Function - Averaging21.25975
Midmean - Empirical Distribution Function - Interpolation21.25975
Midmean - Closest Observation21.25975
Midmean - True Basic - Statistics Graphics Toolkit21.25975
Midmean - MS Excel (old versions)21.25975
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.2775342465753 & 0.0485743404045292 & 438.040621228721 \tabularnewline
Geometric Mean & 21.2735478112390 &  &  \tabularnewline
Harmonic Mean & 21.2695674936931 &  &  \tabularnewline
Quadratic Mean & 21.2815259134649 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 21.2775342465753 & 0.0485743404045292 & 438.040621228721 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 21.2775342465753 & 0.0484692549626369 & 438.990330323365 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 21.2791780821918 & 0.0481913176656412 & 441.556261852602 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 21.2797260273973 & 0.0479007458572527 & 444.246235555751 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 21.2756164383562 & 0.0470806758862811 & 451.897005254245 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 21.2756164383562 & 0.0467912501664293 & 454.692199133002 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 21.2756164383562 & 0.0467912501664293 & 454.692199133002 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 21.2690410958904 & 0.0451975051773916 & 470.579980297883 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 21.2678082191781 & 0.0449785364741226 & 472.843491281982 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 21.2582191780822 & 0.0424570435905191 & 500.699468929327 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 21.253698630137 & 0.0412686500661754 & 515.00833189494 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 21.2372602739726 & 0.0389078743864062 & 545.834502883884 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 21.2390410958904 & 0.0380964311497229 & 557.50736892962 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 21.2467123287671 & 0.0368948146951529 & 575.87258546547 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 21.2487671232877 & 0.0365819617312276 & 580.853680822398 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 21.2443835616438 & 0.035391905822787 & 600.261078564628 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 21.237397260274 & 0.0345199892443494 & 615.22027454717 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 21.237397260274 & 0.0345199892443494 & 615.22027454717 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 21.2373972602740 & 0.0345199892443494 & 615.22027454717 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 21.2483561643836 & 0.0328810721360861 & 646.21847111439 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 21.2541095890411 & 0.0320410669326741 & 663.33963328066 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 21.2631506849315 & 0.0307465932282243 & 691.56119271818 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 21.2631506849315 & 0.0307465932282243 & 691.56119271818 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 21.2631506849315 & 0.0307465932282243 & 691.56119271818 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 21.2759154929577 & 0.0480679337617951 & 442.621802684352 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 21.2742028985507 & 0.0474518672076898 & 448.332260676628 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 21.2723880597015 & 0.0467699749214087 & 454.830007829749 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 21.2698461538462 & 0.0460630276338074 & 461.755278505302 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 21.2669841269841 & 0.045301874713604 & 469.450420350876 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 21.2649180327869 & 0.0446232700148784 & 476.543248078786 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 21.2627118644068 & 0.0438602201039528 & 484.783519417188 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 21.260350877193 & 0.0429102380363753 & 495.46103331262 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 21.2589090909091 & 0.0421202964801284 & 504.718885370112 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 21.2575471698113 & 0.041174612829776 & 516.278009891537 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 21.2574509803922 & 0.040546118150072 & 524.278326761458 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 21.2579591836735 & 0.0399797776176089 & 531.717794606003 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 21.2606382978723 & 0.0396951895287376 & 535.597349459197 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 21.2633333333333 & 0.0394341286838001 & 539.211440522293 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 21.2653488372093 & 0.0392783023030034 & 541.401934155979 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 21.2673170731707 & 0.0390559704536774 & 544.534339465331 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 21.27 & 0.0389106037953576 & 546.637623817539 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 21.2737837837838 & 0.0387711994734663 & 548.700686919497 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 21.278 & 0.0384528522835367 & 553.352969582181 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 21.2827272727273 & 0.0378825755682007 & 561.807822026556 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 21.2867741935484 & 0.0374205598619468 & 568.85237078441 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 21.2906896551724 & 0.0368592417593549 & 577.621476702484 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 21.2940740740741 & 0.0362928075537129 & 586.729864934232 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 21.298 & 0.0352467492590924 & 604.254305650779 \tabularnewline
Median & 21.22 &  &  \tabularnewline
Midrange & 21.335 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.25975 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.25975 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.25975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.25975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.25975 &  &  \tabularnewline
Midmean - Closest Observation & 21.25975 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.25975 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.25975 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10307&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]21.2775342465753[/C][C]0.0485743404045292[/C][C]438.040621228721[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.2735478112390[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.2695674936931[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.2815259134649[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]21.2775342465753[/C][C]0.0485743404045292[/C][C]438.040621228721[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]21.2775342465753[/C][C]0.0484692549626369[/C][C]438.990330323365[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]21.2791780821918[/C][C]0.0481913176656412[/C][C]441.556261852602[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]21.2797260273973[/C][C]0.0479007458572527[/C][C]444.246235555751[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]21.2756164383562[/C][C]0.0470806758862811[/C][C]451.897005254245[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]21.2756164383562[/C][C]0.0467912501664293[/C][C]454.692199133002[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]21.2756164383562[/C][C]0.0467912501664293[/C][C]454.692199133002[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]21.2690410958904[/C][C]0.0451975051773916[/C][C]470.579980297883[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]21.2678082191781[/C][C]0.0449785364741226[/C][C]472.843491281982[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]21.2582191780822[/C][C]0.0424570435905191[/C][C]500.699468929327[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]21.253698630137[/C][C]0.0412686500661754[/C][C]515.00833189494[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]21.2372602739726[/C][C]0.0389078743864062[/C][C]545.834502883884[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]21.2390410958904[/C][C]0.0380964311497229[/C][C]557.50736892962[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]21.2467123287671[/C][C]0.0368948146951529[/C][C]575.87258546547[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]21.2487671232877[/C][C]0.0365819617312276[/C][C]580.853680822398[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]21.2443835616438[/C][C]0.035391905822787[/C][C]600.261078564628[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]21.237397260274[/C][C]0.0345199892443494[/C][C]615.22027454717[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]21.237397260274[/C][C]0.0345199892443494[/C][C]615.22027454717[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]21.2373972602740[/C][C]0.0345199892443494[/C][C]615.22027454717[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]21.2483561643836[/C][C]0.0328810721360861[/C][C]646.21847111439[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]21.2541095890411[/C][C]0.0320410669326741[/C][C]663.33963328066[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]21.2631506849315[/C][C]0.0307465932282243[/C][C]691.56119271818[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]21.2631506849315[/C][C]0.0307465932282243[/C][C]691.56119271818[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]21.2631506849315[/C][C]0.0307465932282243[/C][C]691.56119271818[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]21.2759154929577[/C][C]0.0480679337617951[/C][C]442.621802684352[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]21.2742028985507[/C][C]0.0474518672076898[/C][C]448.332260676628[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]21.2723880597015[/C][C]0.0467699749214087[/C][C]454.830007829749[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]21.2698461538462[/C][C]0.0460630276338074[/C][C]461.755278505302[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]21.2669841269841[/C][C]0.045301874713604[/C][C]469.450420350876[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]21.2649180327869[/C][C]0.0446232700148784[/C][C]476.543248078786[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]21.2627118644068[/C][C]0.0438602201039528[/C][C]484.783519417188[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]21.260350877193[/C][C]0.0429102380363753[/C][C]495.46103331262[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]21.2589090909091[/C][C]0.0421202964801284[/C][C]504.718885370112[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]21.2575471698113[/C][C]0.041174612829776[/C][C]516.278009891537[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]21.2574509803922[/C][C]0.040546118150072[/C][C]524.278326761458[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]21.2579591836735[/C][C]0.0399797776176089[/C][C]531.717794606003[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]21.2606382978723[/C][C]0.0396951895287376[/C][C]535.597349459197[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]21.2633333333333[/C][C]0.0394341286838001[/C][C]539.211440522293[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]21.2653488372093[/C][C]0.0392783023030034[/C][C]541.401934155979[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]21.2673170731707[/C][C]0.0390559704536774[/C][C]544.534339465331[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]21.27[/C][C]0.0389106037953576[/C][C]546.637623817539[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]21.2737837837838[/C][C]0.0387711994734663[/C][C]548.700686919497[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]21.278[/C][C]0.0384528522835367[/C][C]553.352969582181[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]21.2827272727273[/C][C]0.0378825755682007[/C][C]561.807822026556[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]21.2867741935484[/C][C]0.0374205598619468[/C][C]568.85237078441[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]21.2906896551724[/C][C]0.0368592417593549[/C][C]577.621476702484[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]21.2940740740741[/C][C]0.0362928075537129[/C][C]586.729864934232[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]21.298[/C][C]0.0352467492590924[/C][C]604.254305650779[/C][/ROW]
[ROW][C]Median[/C][C]21.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.25975[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10307&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10307&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 Mean21.27753424657530.0485743404045292438.040621228721
Geometric Mean21.2735478112390
Harmonic Mean21.2695674936931
Quadratic Mean21.2815259134649
Winsorized Mean ( 1 / 24 )21.27753424657530.0485743404045292438.040621228721
Winsorized Mean ( 2 / 24 )21.27753424657530.0484692549626369438.990330323365
Winsorized Mean ( 3 / 24 )21.27917808219180.0481913176656412441.556261852602
Winsorized Mean ( 4 / 24 )21.27972602739730.0479007458572527444.246235555751
Winsorized Mean ( 5 / 24 )21.27561643835620.0470806758862811451.897005254245
Winsorized Mean ( 6 / 24 )21.27561643835620.0467912501664293454.692199133002
Winsorized Mean ( 7 / 24 )21.27561643835620.0467912501664293454.692199133002
Winsorized Mean ( 8 / 24 )21.26904109589040.0451975051773916470.579980297883
Winsorized Mean ( 9 / 24 )21.26780821917810.0449785364741226472.843491281982
Winsorized Mean ( 10 / 24 )21.25821917808220.0424570435905191500.699468929327
Winsorized Mean ( 11 / 24 )21.2536986301370.0412686500661754515.00833189494
Winsorized Mean ( 12 / 24 )21.23726027397260.0389078743864062545.834502883884
Winsorized Mean ( 13 / 24 )21.23904109589040.0380964311497229557.50736892962
Winsorized Mean ( 14 / 24 )21.24671232876710.0368948146951529575.87258546547
Winsorized Mean ( 15 / 24 )21.24876712328770.0365819617312276580.853680822398
Winsorized Mean ( 16 / 24 )21.24438356164380.035391905822787600.261078564628
Winsorized Mean ( 17 / 24 )21.2373972602740.0345199892443494615.22027454717
Winsorized Mean ( 18 / 24 )21.2373972602740.0345199892443494615.22027454717
Winsorized Mean ( 19 / 24 )21.23739726027400.0345199892443494615.22027454717
Winsorized Mean ( 20 / 24 )21.24835616438360.0328810721360861646.21847111439
Winsorized Mean ( 21 / 24 )21.25410958904110.0320410669326741663.33963328066
Winsorized Mean ( 22 / 24 )21.26315068493150.0307465932282243691.56119271818
Winsorized Mean ( 23 / 24 )21.26315068493150.0307465932282243691.56119271818
Winsorized Mean ( 24 / 24 )21.26315068493150.0307465932282243691.56119271818
Trimmed Mean ( 1 / 24 )21.27591549295770.0480679337617951442.621802684352
Trimmed Mean ( 2 / 24 )21.27420289855070.0474518672076898448.332260676628
Trimmed Mean ( 3 / 24 )21.27238805970150.0467699749214087454.830007829749
Trimmed Mean ( 4 / 24 )21.26984615384620.0460630276338074461.755278505302
Trimmed Mean ( 5 / 24 )21.26698412698410.045301874713604469.450420350876
Trimmed Mean ( 6 / 24 )21.26491803278690.0446232700148784476.543248078786
Trimmed Mean ( 7 / 24 )21.26271186440680.0438602201039528484.783519417188
Trimmed Mean ( 8 / 24 )21.2603508771930.0429102380363753495.46103331262
Trimmed Mean ( 9 / 24 )21.25890909090910.0421202964801284504.718885370112
Trimmed Mean ( 10 / 24 )21.25754716981130.041174612829776516.278009891537
Trimmed Mean ( 11 / 24 )21.25745098039220.040546118150072524.278326761458
Trimmed Mean ( 12 / 24 )21.25795918367350.0399797776176089531.717794606003
Trimmed Mean ( 13 / 24 )21.26063829787230.0396951895287376535.597349459197
Trimmed Mean ( 14 / 24 )21.26333333333330.0394341286838001539.211440522293
Trimmed Mean ( 15 / 24 )21.26534883720930.0392783023030034541.401934155979
Trimmed Mean ( 16 / 24 )21.26731707317070.0390559704536774544.534339465331
Trimmed Mean ( 17 / 24 )21.270.0389106037953576546.637623817539
Trimmed Mean ( 18 / 24 )21.27378378378380.0387711994734663548.700686919497
Trimmed Mean ( 19 / 24 )21.2780.0384528522835367553.352969582181
Trimmed Mean ( 20 / 24 )21.28272727272730.0378825755682007561.807822026556
Trimmed Mean ( 21 / 24 )21.28677419354840.0374205598619468568.85237078441
Trimmed Mean ( 22 / 24 )21.29068965517240.0368592417593549577.621476702484
Trimmed Mean ( 23 / 24 )21.29407407407410.0362928075537129586.729864934232
Trimmed Mean ( 24 / 24 )21.2980.0352467492590924604.254305650779
Median21.22
Midrange21.335
Midmean - Weighted Average at Xnp21.25975
Midmean - Weighted Average at X(n+1)p21.25975
Midmean - Empirical Distribution Function21.25975
Midmean - Empirical Distribution Function - Averaging21.25975
Midmean - Empirical Distribution Function - Interpolation21.25975
Midmean - Closest Observation21.25975
Midmean - True Basic - Statistics Graphics Toolkit21.25975
Midmean - MS Excel (old versions)21.25975
Number of observations73



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')