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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Oct 2014 13:20:45 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/11/t1413030083lhjdqeby4jnorl6.htm/, Retrieved Sun, 19 May 2024 02:39:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240415, Retrieved Sun, 19 May 2024 02:39:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-11 12:20:45] [5cac5f97919544233533b60e31cabb24] [Current]
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Dataseries X:
8378669,00
7557530,00
8656721,00
7729873,00
7067002,00
7222189,00
6758161,00
6745665,00
8203660,00
8799755,00
7995151,00
6844694,00
7400186,00
6146183,00
6793027,00
5815146,00
5993505,00
5838016,00
5926815,00
5642890,00
7120621,00
7781743,00
7638921,00
5886070,00
7358890,00
6981189,00
8423532,00
6819313,00
6727221,00
6923349,00
7578240,00
7228898,00
8988846,00
8404694,00
9601659,00
8213138,00
8434646,00
8466539,00
9106270,00
8438555,00
7723821,00
7538413,00
7199881,00
8168314,00
9045790,00
8544483,00
9020709,00
7932021,00
8435986,00
7920357,00
8333659,00
7415547,00
7770392,00
8188878,00
8092465,00
7188528,00
8152373,00
9025069,00
9233973,00
6916290,00
8171721,00
7012501,00
8779456,00
7308709,00
8084547,00
8255978,00
7658071,00
7371877,00
8780827,00
10116778,00
9567175,00
7455902,00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240415&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240415&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7750661.98611111115513.48291121767.0974659474882
Geometric Mean7687854.36750296
Harmonic Mean7623221.67017239
Quadratic Mean7811538.90850463
Winsorized Mean ( 1 / 24 )7745900113056.87434939968.5133039859349
Winsorized Mean ( 2 / 24 )7745577.38888889112684.96156489668.7365668082353
Winsorized Mean ( 3 / 24 )7733696.22222222109281.46559571170.7685990489292
Winsorized Mean ( 4 / 24 )7728865.22222222107417.55237436971.9516042898259
Winsorized Mean ( 5 / 24 )7729296.47222222105586.00175268673.2037992150377
Winsorized Mean ( 6 / 24 )7740292.88888889102413.00224480975.5792010704504
Winsorized Mean ( 7 / 24 )7796358.8055555691402.846126154785.2966744032782
Winsorized Mean ( 8 / 24 )7794867.8055555690403.261287102686.2233031704533
Winsorized Mean ( 9 / 24 )7772793.4305555685953.356946376890.4303648710861
Winsorized Mean ( 10 / 24 )7775007.0416666784714.433047547891.7790128785112
Winsorized Mean ( 11 / 24 )7778813.584028.575159646392.5734309456157
Winsorized Mean ( 12 / 24 )7762587.8333333380019.011500537197.0092942635418
Winsorized Mean ( 13 / 24 )7755249.6944444474851.1484637908103.608960631994
Winsorized Mean ( 14 / 24 )7741466.572439.0317181808106.868718650432
Winsorized Mean ( 15 / 24 )7747686.569729.5377300198111.110538693052
Winsorized Mean ( 16 / 24 )7754073.8333333368581.1542441287113.064207197959
Winsorized Mean ( 17 / 24 )7766625.7361111166604.4412841623116.608225913576
Winsorized Mean ( 18 / 24 )7777251.9861111164254.6348088298121.037992189201
Winsorized Mean ( 19 / 24 )7790200.7561014.7252009105127.677388111612
Winsorized Mean ( 20 / 24 )7786125.1944444459557.8148468792130.732217333061
Winsorized Mean ( 21 / 24 )7779503.7777777856835.8309459671136.87674919671
Winsorized Mean ( 22 / 24 )7757817.8888888953358.7074274157145.389914091189
Winsorized Mean ( 23 / 24 )7769628.0694444448064.6410777449161.649559743451
Winsorized Mean ( 24 / 24 )7783195.7361111145422.6090727098171.350697262947
Trimmed Mean ( 1 / 24 )7746971.35714286109741.95154165970.592615206064
Trimmed Mean ( 2 / 24 )7748105.73529412105798.95495178873.2342369433126
Trimmed Mean ( 3 / 24 )7749484.83333333101319.54005372976.4855903335514
Trimmed Mean ( 4 / 24 )7755405.562597540.909678532479.5092601459188
Trimmed Mean ( 5 / 24 )7763110.8225806493677.88062732582.8702653240451
Trimmed Mean ( 6 / 24 )7771226.2666666789582.191106126186.7496783759203
Trimmed Mean ( 7 / 24 )7777626.2758620785544.990029405990.9185479265183
Trimmed Mean ( 8 / 24 )7774185.6071428683634.677110124292.9540936339883
Trimmed Mean ( 9 / 24 )7770738.5740740781499.662905844795.3468799380371
Trimmed Mean ( 10 / 24 )7770422.4423076979889.084353895297.2651333426984
Trimmed Mean ( 11 / 24 )7769762.2678114.327217591799.4665452133628
Trimmed Mean ( 12 / 24 )776852875988.2279000042102.233309220251
Trimmed Mean ( 13 / 24 )7769302.8043478374159.4959525928104.764773607879
Trimmed Mean ( 14 / 24 )7771071.7272727372902.5348464758106.59535698776
Trimmed Mean ( 15 / 24 )7774696.8571428671700.3640754114108.433157312364
Trimmed Mean ( 16 / 24 )7777938.170628.6782737248110.12436152148
Trimmed Mean ( 17 / 24 )7780764.1315789569353.3196651593112.190219143724
Trimmed Mean ( 18 / 24 )7782427.4722222267996.1363637377114.453965892871
Trimmed Mean ( 19 / 24 )7783036.3529411866599.0913235785116.864002169737
Trimmed Mean ( 20 / 24 )7782187.937565351.4156954158119.082163021082
Trimmed Mean ( 21 / 24 )7781715.4666666763804.3286544163121.962187061239
Trimmed Mean ( 22 / 24 )7781986.2857142962191.5644894264125.129289632798
Trimmed Mean ( 23 / 24 )7785028.4615384660678.6534725917128.299294991029
Trimmed Mean ( 24 / 24 )7787037.2083333359936.2507625472129.921993939589
Median7750132.5
Midrange7879834
Midmean - Weighted Average at Xnp7763091.64864865
Midmean - Weighted Average at X(n+1)p7782427.47222222
Midmean - Empirical Distribution Function7763091.64864865
Midmean - Empirical Distribution Function - Averaging7782427.47222222
Midmean - Empirical Distribution Function - Interpolation7782427.47222222
Midmean - Closest Observation7763091.64864865
Midmean - True Basic - Statistics Graphics Toolkit7782427.47222222
Midmean - MS Excel (old versions)7780764.13157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7750661.98611111 & 115513.482911217 & 67.0974659474882 \tabularnewline
Geometric Mean & 7687854.36750296 &  &  \tabularnewline
Harmonic Mean & 7623221.67017239 &  &  \tabularnewline
Quadratic Mean & 7811538.90850463 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7745900 & 113056.874349399 & 68.5133039859349 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7745577.38888889 & 112684.961564896 & 68.7365668082353 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7733696.22222222 & 109281.465595711 & 70.7685990489292 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7728865.22222222 & 107417.552374369 & 71.9516042898259 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7729296.47222222 & 105586.001752686 & 73.2037992150377 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7740292.88888889 & 102413.002244809 & 75.5792010704504 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7796358.80555556 & 91402.8461261547 & 85.2966744032782 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7794867.80555556 & 90403.2612871026 & 86.2233031704533 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7772793.43055556 & 85953.3569463768 & 90.4303648710861 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7775007.04166667 & 84714.4330475478 & 91.7790128785112 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7778813.5 & 84028.5751596463 & 92.5734309456157 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7762587.83333333 & 80019.0115005371 & 97.0092942635418 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7755249.69444444 & 74851.1484637908 & 103.608960631994 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7741466.5 & 72439.0317181808 & 106.868718650432 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7747686.5 & 69729.5377300198 & 111.110538693052 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7754073.83333333 & 68581.1542441287 & 113.064207197959 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7766625.73611111 & 66604.4412841623 & 116.608225913576 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7777251.98611111 & 64254.6348088298 & 121.037992189201 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7790200.75 & 61014.7252009105 & 127.677388111612 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7786125.19444444 & 59557.8148468792 & 130.732217333061 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7779503.77777778 & 56835.8309459671 & 136.87674919671 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7757817.88888889 & 53358.7074274157 & 145.389914091189 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7769628.06944444 & 48064.6410777449 & 161.649559743451 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7783195.73611111 & 45422.6090727098 & 171.350697262947 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7746971.35714286 & 109741.951541659 & 70.592615206064 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7748105.73529412 & 105798.954951788 & 73.2342369433126 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7749484.83333333 & 101319.540053729 & 76.4855903335514 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7755405.5625 & 97540.9096785324 & 79.5092601459188 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7763110.82258064 & 93677.880627325 & 82.8702653240451 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7771226.26666667 & 89582.1911061261 & 86.7496783759203 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7777626.27586207 & 85544.9900294059 & 90.9185479265183 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7774185.60714286 & 83634.6771101242 & 92.9540936339883 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7770738.57407407 & 81499.6629058447 & 95.3468799380371 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7770422.44230769 & 79889.0843538952 & 97.2651333426984 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7769762.26 & 78114.3272175917 & 99.4665452133628 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7768528 & 75988.2279000042 & 102.233309220251 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7769302.80434783 & 74159.4959525928 & 104.764773607879 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7771071.72727273 & 72902.5348464758 & 106.59535698776 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7774696.85714286 & 71700.3640754114 & 108.433157312364 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7777938.1 & 70628.6782737248 & 110.12436152148 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7780764.13157895 & 69353.3196651593 & 112.190219143724 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7782427.47222222 & 67996.1363637377 & 114.453965892871 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7783036.35294118 & 66599.0913235785 & 116.864002169737 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7782187.9375 & 65351.4156954158 & 119.082163021082 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7781715.46666667 & 63804.3286544163 & 121.962187061239 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7781986.28571429 & 62191.5644894264 & 125.129289632798 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7785028.46153846 & 60678.6534725917 & 128.299294991029 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7787037.20833333 & 59936.2507625472 & 129.921993939589 \tabularnewline
Median & 7750132.5 &  &  \tabularnewline
Midrange & 7879834 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7763091.64864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7782427.47222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7763091.64864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7782427.47222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7782427.47222222 &  &  \tabularnewline
Midmean - Closest Observation & 7763091.64864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7782427.47222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7780764.13157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240415&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]7750661.98611111[/C][C]115513.482911217[/C][C]67.0974659474882[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7687854.36750296[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7623221.67017239[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7811538.90850463[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7745900[/C][C]113056.874349399[/C][C]68.5133039859349[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7745577.38888889[/C][C]112684.961564896[/C][C]68.7365668082353[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7733696.22222222[/C][C]109281.465595711[/C][C]70.7685990489292[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7728865.22222222[/C][C]107417.552374369[/C][C]71.9516042898259[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7729296.47222222[/C][C]105586.001752686[/C][C]73.2037992150377[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7740292.88888889[/C][C]102413.002244809[/C][C]75.5792010704504[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7796358.80555556[/C][C]91402.8461261547[/C][C]85.2966744032782[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7794867.80555556[/C][C]90403.2612871026[/C][C]86.2233031704533[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7772793.43055556[/C][C]85953.3569463768[/C][C]90.4303648710861[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7775007.04166667[/C][C]84714.4330475478[/C][C]91.7790128785112[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7778813.5[/C][C]84028.5751596463[/C][C]92.5734309456157[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7762587.83333333[/C][C]80019.0115005371[/C][C]97.0092942635418[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7755249.69444444[/C][C]74851.1484637908[/C][C]103.608960631994[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7741466.5[/C][C]72439.0317181808[/C][C]106.868718650432[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7747686.5[/C][C]69729.5377300198[/C][C]111.110538693052[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7754073.83333333[/C][C]68581.1542441287[/C][C]113.064207197959[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7766625.73611111[/C][C]66604.4412841623[/C][C]116.608225913576[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7777251.98611111[/C][C]64254.6348088298[/C][C]121.037992189201[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7790200.75[/C][C]61014.7252009105[/C][C]127.677388111612[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7786125.19444444[/C][C]59557.8148468792[/C][C]130.732217333061[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7779503.77777778[/C][C]56835.8309459671[/C][C]136.87674919671[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7757817.88888889[/C][C]53358.7074274157[/C][C]145.389914091189[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7769628.06944444[/C][C]48064.6410777449[/C][C]161.649559743451[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7783195.73611111[/C][C]45422.6090727098[/C][C]171.350697262947[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7746971.35714286[/C][C]109741.951541659[/C][C]70.592615206064[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7748105.73529412[/C][C]105798.954951788[/C][C]73.2342369433126[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7749484.83333333[/C][C]101319.540053729[/C][C]76.4855903335514[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7755405.5625[/C][C]97540.9096785324[/C][C]79.5092601459188[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7763110.82258064[/C][C]93677.880627325[/C][C]82.8702653240451[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7771226.26666667[/C][C]89582.1911061261[/C][C]86.7496783759203[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7777626.27586207[/C][C]85544.9900294059[/C][C]90.9185479265183[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7774185.60714286[/C][C]83634.6771101242[/C][C]92.9540936339883[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7770738.57407407[/C][C]81499.6629058447[/C][C]95.3468799380371[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7770422.44230769[/C][C]79889.0843538952[/C][C]97.2651333426984[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7769762.26[/C][C]78114.3272175917[/C][C]99.4665452133628[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7768528[/C][C]75988.2279000042[/C][C]102.233309220251[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7769302.80434783[/C][C]74159.4959525928[/C][C]104.764773607879[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7771071.72727273[/C][C]72902.5348464758[/C][C]106.59535698776[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7774696.85714286[/C][C]71700.3640754114[/C][C]108.433157312364[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7777938.1[/C][C]70628.6782737248[/C][C]110.12436152148[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7780764.13157895[/C][C]69353.3196651593[/C][C]112.190219143724[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7782427.47222222[/C][C]67996.1363637377[/C][C]114.453965892871[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7783036.35294118[/C][C]66599.0913235785[/C][C]116.864002169737[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7782187.9375[/C][C]65351.4156954158[/C][C]119.082163021082[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7781715.46666667[/C][C]63804.3286544163[/C][C]121.962187061239[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7781986.28571429[/C][C]62191.5644894264[/C][C]125.129289632798[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7785028.46153846[/C][C]60678.6534725917[/C][C]128.299294991029[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7787037.20833333[/C][C]59936.2507625472[/C][C]129.921993939589[/C][/ROW]
[ROW][C]Median[/C][C]7750132.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7879834[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7763091.64864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7782427.47222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7763091.64864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7782427.47222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7782427.47222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7763091.64864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7782427.47222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7780764.13157895[/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=240415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240415&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 Mean7750661.98611111115513.48291121767.0974659474882
Geometric Mean7687854.36750296
Harmonic Mean7623221.67017239
Quadratic Mean7811538.90850463
Winsorized Mean ( 1 / 24 )7745900113056.87434939968.5133039859349
Winsorized Mean ( 2 / 24 )7745577.38888889112684.96156489668.7365668082353
Winsorized Mean ( 3 / 24 )7733696.22222222109281.46559571170.7685990489292
Winsorized Mean ( 4 / 24 )7728865.22222222107417.55237436971.9516042898259
Winsorized Mean ( 5 / 24 )7729296.47222222105586.00175268673.2037992150377
Winsorized Mean ( 6 / 24 )7740292.88888889102413.00224480975.5792010704504
Winsorized Mean ( 7 / 24 )7796358.8055555691402.846126154785.2966744032782
Winsorized Mean ( 8 / 24 )7794867.8055555690403.261287102686.2233031704533
Winsorized Mean ( 9 / 24 )7772793.4305555685953.356946376890.4303648710861
Winsorized Mean ( 10 / 24 )7775007.0416666784714.433047547891.7790128785112
Winsorized Mean ( 11 / 24 )7778813.584028.575159646392.5734309456157
Winsorized Mean ( 12 / 24 )7762587.8333333380019.011500537197.0092942635418
Winsorized Mean ( 13 / 24 )7755249.6944444474851.1484637908103.608960631994
Winsorized Mean ( 14 / 24 )7741466.572439.0317181808106.868718650432
Winsorized Mean ( 15 / 24 )7747686.569729.5377300198111.110538693052
Winsorized Mean ( 16 / 24 )7754073.8333333368581.1542441287113.064207197959
Winsorized Mean ( 17 / 24 )7766625.7361111166604.4412841623116.608225913576
Winsorized Mean ( 18 / 24 )7777251.9861111164254.6348088298121.037992189201
Winsorized Mean ( 19 / 24 )7790200.7561014.7252009105127.677388111612
Winsorized Mean ( 20 / 24 )7786125.1944444459557.8148468792130.732217333061
Winsorized Mean ( 21 / 24 )7779503.7777777856835.8309459671136.87674919671
Winsorized Mean ( 22 / 24 )7757817.8888888953358.7074274157145.389914091189
Winsorized Mean ( 23 / 24 )7769628.0694444448064.6410777449161.649559743451
Winsorized Mean ( 24 / 24 )7783195.7361111145422.6090727098171.350697262947
Trimmed Mean ( 1 / 24 )7746971.35714286109741.95154165970.592615206064
Trimmed Mean ( 2 / 24 )7748105.73529412105798.95495178873.2342369433126
Trimmed Mean ( 3 / 24 )7749484.83333333101319.54005372976.4855903335514
Trimmed Mean ( 4 / 24 )7755405.562597540.909678532479.5092601459188
Trimmed Mean ( 5 / 24 )7763110.8225806493677.88062732582.8702653240451
Trimmed Mean ( 6 / 24 )7771226.2666666789582.191106126186.7496783759203
Trimmed Mean ( 7 / 24 )7777626.2758620785544.990029405990.9185479265183
Trimmed Mean ( 8 / 24 )7774185.6071428683634.677110124292.9540936339883
Trimmed Mean ( 9 / 24 )7770738.5740740781499.662905844795.3468799380371
Trimmed Mean ( 10 / 24 )7770422.4423076979889.084353895297.2651333426984
Trimmed Mean ( 11 / 24 )7769762.2678114.327217591799.4665452133628
Trimmed Mean ( 12 / 24 )776852875988.2279000042102.233309220251
Trimmed Mean ( 13 / 24 )7769302.8043478374159.4959525928104.764773607879
Trimmed Mean ( 14 / 24 )7771071.7272727372902.5348464758106.59535698776
Trimmed Mean ( 15 / 24 )7774696.8571428671700.3640754114108.433157312364
Trimmed Mean ( 16 / 24 )7777938.170628.6782737248110.12436152148
Trimmed Mean ( 17 / 24 )7780764.1315789569353.3196651593112.190219143724
Trimmed Mean ( 18 / 24 )7782427.4722222267996.1363637377114.453965892871
Trimmed Mean ( 19 / 24 )7783036.3529411866599.0913235785116.864002169737
Trimmed Mean ( 20 / 24 )7782187.937565351.4156954158119.082163021082
Trimmed Mean ( 21 / 24 )7781715.4666666763804.3286544163121.962187061239
Trimmed Mean ( 22 / 24 )7781986.2857142962191.5644894264125.129289632798
Trimmed Mean ( 23 / 24 )7785028.4615384660678.6534725917128.299294991029
Trimmed Mean ( 24 / 24 )7787037.2083333359936.2507625472129.921993939589
Median7750132.5
Midrange7879834
Midmean - Weighted Average at Xnp7763091.64864865
Midmean - Weighted Average at X(n+1)p7782427.47222222
Midmean - Empirical Distribution Function7763091.64864865
Midmean - Empirical Distribution Function - Averaging7782427.47222222
Midmean - Empirical Distribution Function - Interpolation7782427.47222222
Midmean - Closest Observation7763091.64864865
Midmean - True Basic - Statistics Graphics Toolkit7782427.47222222
Midmean - MS Excel (old versions)7780764.13157895
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')