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rwasp_centraltendency.wasp

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Central Tendency

Date of computation

Sat, 11 Mar 2017 13:23:49 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/11/t1489238656folyozrea026crh.htm/, Retrieved Tue, 14 May 2024 02:46:00 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 02:46:00 +0200

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	99.0831944444444	0.337182344940812	293.856413098489
Geometric Mean	99.0423184122831
Harmonic Mean	99.0013123053754
Quadratic Mean	99.1239201636573
Winsorized Mean ( 1 / 24 )	99.0868055555556	0.335996568886	294.904218468893
Winsorized Mean ( 2 / 24 )	99.0823611111111	0.334625868036669	296.098928909625
Winsorized Mean ( 3 / 24 )	99.0744444444445	0.33226547784205	298.178568197632
Winsorized Mean ( 4 / 24 )	99.0827777777778	0.329036104862223	301.130411871568
Winsorized Mean ( 5 / 24 )	99.0834722222222	0.32716045843032	302.858947861896
Winsorized Mean ( 6 / 24 )	99.0901388888889	0.322412869491517	307.339279121102
Winsorized Mean ( 7 / 24 )	99.0697222222222	0.317396365365686	312.132503811377
Winsorized Mean ( 8 / 24 )	99.0730555555556	0.314545567262586	314.972029069634
Winsorized Mean ( 9 / 24 )	99.0868055555556	0.3112860035294	318.314361815491
Winsorized Mean ( 10 / 24 )	99.0576388888889	0.30538397115411	324.370786438232
Winsorized Mean ( 11 / 24 )	99.0454166666667	0.299585716654901	330.607940100025
Winsorized Mean ( 12 / 24 )	99.0720833333333	0.283953404445045	348.902607901316
Winsorized Mean ( 13 / 24 )	99.1226388888889	0.271293703564464	365.370215329512
Winsorized Mean ( 14 / 24 )	99.1226388888889	0.268945587420177	368.560197769776
Winsorized Mean ( 15 / 24 )	99.1330555555555	0.265434185224499	373.4750875126
Winsorized Mean ( 16 / 24 )	99.1486111111111	0.259711250636512	381.764790197241
Winsorized Mean ( 17 / 24 )	99.1745833333333	0.252959628112109	392.056962106934
Winsorized Mean ( 18 / 24 )	99.1920833333333	0.23941233946958	414.314832531583
Winsorized Mean ( 19 / 24 )	99.17625	0.236429362405916	419.475182738632
Winsorized Mean ( 20 / 24 )	99.1401388888889	0.22905513658692	432.822159616874
Winsorized Mean ( 21 / 24 )	99.1693055555556	0.216469603990571	458.121157554644
Winsorized Mean ( 22 / 24 )	99.16625	0.205745185312664	481.985762385158
Winsorized Mean ( 23 / 24 )	99.1438888888889	0.190318647587524	520.936283152676
Winsorized Mean ( 24 / 24 )	99.2938888888889	0.150844461182072	658.253462611658
Trimmed Mean ( 1 / 24 )	99.0892857142857	0.332400100743468	298.102453918203
Trimmed Mean ( 2 / 24 )	99.0919117647059	0.328021930769175	302.089288762939
Trimmed Mean ( 3 / 24 )	99.0971212121212	0.323556703068108	306.274357083128
Trimmed Mean ( 4 / 24 )	99.105625	0.319148162073916	310.531711528537
Trimmed Mean ( 5 / 24 )	99.1122580645161	0.31487764819763	314.764349365024
Trimmed Mean ( 6 / 24 )	99.1191666666667	0.310151529547418	319.583033529786
Trimmed Mean ( 7 / 24 )	99.1251724137931	0.305576052099004	324.387895363205
Trimmed Mean ( 8 / 24 )	99.1353571428571	0.301078792410445	329.267154119945
Trimmed Mean ( 9 / 24 )	99.1457407407407	0.296045518655716	334.900326108437
Trimmed Mean ( 10 / 24 )	99.1548076923077	0.290390267692435	341.453618539747
Trimmed Mean ( 11 / 24 )	99.1688	0.284458187451448	348.623468666819
Trimmed Mean ( 12 / 24 )	99.185625	0.278073078666204	356.68905985344
Trimmed Mean ( 13 / 24 )	99.2004347826087	0.273239460112347	363.05310639181
Trimmed Mean ( 14 / 24 )	99.2102272727273	0.26953712744144	368.076295145209
Trimmed Mean ( 15 / 24 )	99.2209523809524	0.264878691477908	374.590163622988
Trimmed Mean ( 16 / 24 )	99.2315	0.25921294829561	382.818453524301
Trimmed Mean ( 17 / 24 )	99.2413157894737	0.252702089051882	392.720599033507
Trimmed Mean ( 18 / 24 )	99.2491666666667	0.24527838896902	404.638855807236
Trimmed Mean ( 19 / 24 )	99.2558823529412	0.238312964605993	416.493842527798
Trimmed Mean ( 20 / 24 )	99.2653125	0.228972540426037	433.524964676124
Trimmed Mean ( 21 / 24 )	99.2803333333333	0.217445717011725	456.575253344631
Trimmed Mean ( 22 / 24 )	99.2939285714286	0.204578764075127	485.357945240911
Trimmed Mean ( 23 / 24 )	99.31	0.188852404721864	525.860394238881
Trimmed Mean ( 24 / 24 )	99.3316666666667	0.170475322990726	582.674752709344
Median	99.205
Midrange	98.87
Midmean - Weighted Average at Xnp	99.1737837837838
Midmean - Weighted Average at X(n+1)p	99.2491666666667
Midmean - Empirical Distribution Function	99.1737837837838
Midmean - Empirical Distribution Function - Averaging	99.2491666666667
Midmean - Empirical Distribution Function - Interpolation	99.2491666666667
Midmean - Closest Observation	99.1737837837838
Midmean - True Basic - Statistics Graphics Toolkit	99.2491666666667
Midmean - MS Excel (old versions)	99.2413157894737
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.0831944444444 & 0.337182344940812 & 293.856413098489 \tabularnewline
Geometric Mean & 99.0423184122831 &  &  \tabularnewline
Harmonic Mean & 99.0013123053754 &  &  \tabularnewline
Quadratic Mean & 99.1239201636573 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.0868055555556 & 0.335996568886 & 294.904218468893 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.0823611111111 & 0.334625868036669 & 296.098928909625 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.0744444444445 & 0.33226547784205 & 298.178568197632 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.0827777777778 & 0.329036104862223 & 301.130411871568 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.0834722222222 & 0.32716045843032 & 302.858947861896 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.0901388888889 & 0.322412869491517 & 307.339279121102 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.0697222222222 & 0.317396365365686 & 312.132503811377 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.0730555555556 & 0.314545567262586 & 314.972029069634 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.0868055555556 & 0.3112860035294 & 318.314361815491 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.0576388888889 & 0.30538397115411 & 324.370786438232 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.0454166666667 & 0.299585716654901 & 330.607940100025 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.0720833333333 & 0.283953404445045 & 348.902607901316 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.1226388888889 & 0.271293703564464 & 365.370215329512 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.1226388888889 & 0.268945587420177 & 368.560197769776 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.1330555555555 & 0.265434185224499 & 373.4750875126 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.1486111111111 & 0.259711250636512 & 381.764790197241 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.1745833333333 & 0.252959628112109 & 392.056962106934 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.1920833333333 & 0.23941233946958 & 414.314832531583 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.17625 & 0.236429362405916 & 419.475182738632 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.1401388888889 & 0.22905513658692 & 432.822159616874 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.1693055555556 & 0.216469603990571 & 458.121157554644 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 99.16625 & 0.205745185312664 & 481.985762385158 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 99.1438888888889 & 0.190318647587524 & 520.936283152676 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 99.2938888888889 & 0.150844461182072 & 658.253462611658 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.0892857142857 & 0.332400100743468 & 298.102453918203 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.0919117647059 & 0.328021930769175 & 302.089288762939 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.0971212121212 & 0.323556703068108 & 306.274357083128 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.105625 & 0.319148162073916 & 310.531711528537 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.1122580645161 & 0.31487764819763 & 314.764349365024 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.1191666666667 & 0.310151529547418 & 319.583033529786 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.1251724137931 & 0.305576052099004 & 324.387895363205 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.1353571428571 & 0.301078792410445 & 329.267154119945 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 99.1457407407407 & 0.296045518655716 & 334.900326108437 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.1548076923077 & 0.290390267692435 & 341.453618539747 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.1688 & 0.284458187451448 & 348.623468666819 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.185625 & 0.278073078666204 & 356.68905985344 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.2004347826087 & 0.273239460112347 & 363.05310639181 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.2102272727273 & 0.26953712744144 & 368.076295145209 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.2209523809524 & 0.264878691477908 & 374.590163622988 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.2315 & 0.25921294829561 & 382.818453524301 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.2413157894737 & 0.252702089051882 & 392.720599033507 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.2491666666667 & 0.24527838896902 & 404.638855807236 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.2558823529412 & 0.238312964605993 & 416.493842527798 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.2653125 & 0.228972540426037 & 433.524964676124 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.2803333333333 & 0.217445717011725 & 456.575253344631 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.2939285714286 & 0.204578764075127 & 485.357945240911 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.31 & 0.188852404721864 & 525.860394238881 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.3316666666667 & 0.170475322990726 & 582.674752709344 \tabularnewline
Median & 99.205 &  &  \tabularnewline
Midrange & 98.87 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.1737837837838 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.2491666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.1737837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.2491666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.2491666666667 &  &  \tabularnewline
Midmean - Closest Observation & 99.1737837837838 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.2491666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.2413157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]99.0831944444444[/C][C]0.337182344940812[/C][C]293.856413098489[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.0423184122831[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.0013123053754[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.1239201636573[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.0868055555556[/C][C]0.335996568886[/C][C]294.904218468893[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.0823611111111[/C][C]0.334625868036669[/C][C]296.098928909625[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.0744444444445[/C][C]0.33226547784205[/C][C]298.178568197632[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.0827777777778[/C][C]0.329036104862223[/C][C]301.130411871568[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.0834722222222[/C][C]0.32716045843032[/C][C]302.858947861896[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.0901388888889[/C][C]0.322412869491517[/C][C]307.339279121102[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.0697222222222[/C][C]0.317396365365686[/C][C]312.132503811377[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.0730555555556[/C][C]0.314545567262586[/C][C]314.972029069634[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.0868055555556[/C][C]0.3112860035294[/C][C]318.314361815491[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.0576388888889[/C][C]0.30538397115411[/C][C]324.370786438232[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.0454166666667[/C][C]0.299585716654901[/C][C]330.607940100025[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.0720833333333[/C][C]0.283953404445045[/C][C]348.902607901316[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.1226388888889[/C][C]0.271293703564464[/C][C]365.370215329512[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.1226388888889[/C][C]0.268945587420177[/C][C]368.560197769776[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.1330555555555[/C][C]0.265434185224499[/C][C]373.4750875126[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.1486111111111[/C][C]0.259711250636512[/C][C]381.764790197241[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.1745833333333[/C][C]0.252959628112109[/C][C]392.056962106934[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.1920833333333[/C][C]0.23941233946958[/C][C]414.314832531583[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.17625[/C][C]0.236429362405916[/C][C]419.475182738632[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.1401388888889[/C][C]0.22905513658692[/C][C]432.822159616874[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.1693055555556[/C][C]0.216469603990571[/C][C]458.121157554644[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]99.16625[/C][C]0.205745185312664[/C][C]481.985762385158[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]99.1438888888889[/C][C]0.190318647587524[/C][C]520.936283152676[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]99.2938888888889[/C][C]0.150844461182072[/C][C]658.253462611658[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.0892857142857[/C][C]0.332400100743468[/C][C]298.102453918203[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.0919117647059[/C][C]0.328021930769175[/C][C]302.089288762939[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.0971212121212[/C][C]0.323556703068108[/C][C]306.274357083128[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.105625[/C][C]0.319148162073916[/C][C]310.531711528537[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.1122580645161[/C][C]0.31487764819763[/C][C]314.764349365024[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.1191666666667[/C][C]0.310151529547418[/C][C]319.583033529786[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.1251724137931[/C][C]0.305576052099004[/C][C]324.387895363205[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.1353571428571[/C][C]0.301078792410445[/C][C]329.267154119945[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]99.1457407407407[/C][C]0.296045518655716[/C][C]334.900326108437[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.1548076923077[/C][C]0.290390267692435[/C][C]341.453618539747[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.1688[/C][C]0.284458187451448[/C][C]348.623468666819[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.185625[/C][C]0.278073078666204[/C][C]356.68905985344[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.2004347826087[/C][C]0.273239460112347[/C][C]363.05310639181[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.2102272727273[/C][C]0.26953712744144[/C][C]368.076295145209[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.2209523809524[/C][C]0.264878691477908[/C][C]374.590163622988[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.2315[/C][C]0.25921294829561[/C][C]382.818453524301[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.2413157894737[/C][C]0.252702089051882[/C][C]392.720599033507[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.2491666666667[/C][C]0.24527838896902[/C][C]404.638855807236[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.2558823529412[/C][C]0.238312964605993[/C][C]416.493842527798[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.2653125[/C][C]0.228972540426037[/C][C]433.524964676124[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.2803333333333[/C][C]0.217445717011725[/C][C]456.575253344631[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.2939285714286[/C][C]0.204578764075127[/C][C]485.357945240911[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.31[/C][C]0.188852404721864[/C][C]525.860394238881[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.3316666666667[/C][C]0.170475322990726[/C][C]582.674752709344[/C][/ROW]
[ROW][C]Median[/C][C]99.205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.87[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.1737837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.2491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.1737837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.2491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.2491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.1737837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.2491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.2413157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

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

As an alternative you can also use a QR Code:

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

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	99.0831944444444	0.337182344940812	293.856413098489
Geometric Mean	99.0423184122831
Harmonic Mean	99.0013123053754
Quadratic Mean	99.1239201636573
Winsorized Mean ( 1 / 24 )	99.0868055555556	0.335996568886	294.904218468893
Winsorized Mean ( 2 / 24 )	99.0823611111111	0.334625868036669	296.098928909625
Winsorized Mean ( 3 / 24 )	99.0744444444445	0.33226547784205	298.178568197632
Winsorized Mean ( 4 / 24 )	99.0827777777778	0.329036104862223	301.130411871568
Winsorized Mean ( 5 / 24 )	99.0834722222222	0.32716045843032	302.858947861896
Winsorized Mean ( 6 / 24 )	99.0901388888889	0.322412869491517	307.339279121102
Winsorized Mean ( 7 / 24 )	99.0697222222222	0.317396365365686	312.132503811377
Winsorized Mean ( 8 / 24 )	99.0730555555556	0.314545567262586	314.972029069634
Winsorized Mean ( 9 / 24 )	99.0868055555556	0.3112860035294	318.314361815491
Winsorized Mean ( 10 / 24 )	99.0576388888889	0.30538397115411	324.370786438232
Winsorized Mean ( 11 / 24 )	99.0454166666667	0.299585716654901	330.607940100025
Winsorized Mean ( 12 / 24 )	99.0720833333333	0.283953404445045	348.902607901316
Winsorized Mean ( 13 / 24 )	99.1226388888889	0.271293703564464	365.370215329512
Winsorized Mean ( 14 / 24 )	99.1226388888889	0.268945587420177	368.560197769776
Winsorized Mean ( 15 / 24 )	99.1330555555555	0.265434185224499	373.4750875126
Winsorized Mean ( 16 / 24 )	99.1486111111111	0.259711250636512	381.764790197241
Winsorized Mean ( 17 / 24 )	99.1745833333333	0.252959628112109	392.056962106934
Winsorized Mean ( 18 / 24 )	99.1920833333333	0.23941233946958	414.314832531583
Winsorized Mean ( 19 / 24 )	99.17625	0.236429362405916	419.475182738632
Winsorized Mean ( 20 / 24 )	99.1401388888889	0.22905513658692	432.822159616874
Winsorized Mean ( 21 / 24 )	99.1693055555556	0.216469603990571	458.121157554644
Winsorized Mean ( 22 / 24 )	99.16625	0.205745185312664	481.985762385158
Winsorized Mean ( 23 / 24 )	99.1438888888889	0.190318647587524	520.936283152676
Winsorized Mean ( 24 / 24 )	99.2938888888889	0.150844461182072	658.253462611658
Trimmed Mean ( 1 / 24 )	99.0892857142857	0.332400100743468	298.102453918203
Trimmed Mean ( 2 / 24 )	99.0919117647059	0.328021930769175	302.089288762939
Trimmed Mean ( 3 / 24 )	99.0971212121212	0.323556703068108	306.274357083128
Trimmed Mean ( 4 / 24 )	99.105625	0.319148162073916	310.531711528537
Trimmed Mean ( 5 / 24 )	99.1122580645161	0.31487764819763	314.764349365024
Trimmed Mean ( 6 / 24 )	99.1191666666667	0.310151529547418	319.583033529786
Trimmed Mean ( 7 / 24 )	99.1251724137931	0.305576052099004	324.387895363205
Trimmed Mean ( 8 / 24 )	99.1353571428571	0.301078792410445	329.267154119945
Trimmed Mean ( 9 / 24 )	99.1457407407407	0.296045518655716	334.900326108437
Trimmed Mean ( 10 / 24 )	99.1548076923077	0.290390267692435	341.453618539747
Trimmed Mean ( 11 / 24 )	99.1688	0.284458187451448	348.623468666819
Trimmed Mean ( 12 / 24 )	99.185625	0.278073078666204	356.68905985344
Trimmed Mean ( 13 / 24 )	99.2004347826087	0.273239460112347	363.05310639181
Trimmed Mean ( 14 / 24 )	99.2102272727273	0.26953712744144	368.076295145209
Trimmed Mean ( 15 / 24 )	99.2209523809524	0.264878691477908	374.590163622988
Trimmed Mean ( 16 / 24 )	99.2315	0.25921294829561	382.818453524301
Trimmed Mean ( 17 / 24 )	99.2413157894737	0.252702089051882	392.720599033507
Trimmed Mean ( 18 / 24 )	99.2491666666667	0.24527838896902	404.638855807236
Trimmed Mean ( 19 / 24 )	99.2558823529412	0.238312964605993	416.493842527798
Trimmed Mean ( 20 / 24 )	99.2653125	0.228972540426037	433.524964676124
Trimmed Mean ( 21 / 24 )	99.2803333333333	0.217445717011725	456.575253344631
Trimmed Mean ( 22 / 24 )	99.2939285714286	0.204578764075127	485.357945240911
Trimmed Mean ( 23 / 24 )	99.31	0.188852404721864	525.860394238881
Trimmed Mean ( 24 / 24 )	99.3316666666667	0.170475322990726	582.674752709344
Median	99.205
Midrange	98.87
Midmean - Weighted Average at Xnp	99.1737837837838
Midmean - Weighted Average at X(n+1)p	99.2491666666667
Midmean - Empirical Distribution Function	99.1737837837838
Midmean - Empirical Distribution Function - Averaging	99.2491666666667
Midmean - Empirical Distribution Function - Interpolation	99.2491666666667
Midmean - Closest Observation	99.1737837837838
Midmean - True Basic - Statistics Graphics Toolkit	99.2491666666667
Midmean - MS Excel (old versions)	99.2413157894737
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code