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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 15 Dec 2010 20:17:31 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/15/t12924441113es6fdi9g3wfz1f.htm/, Retrieved Fri, 03 May 2024 06:44:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110711, Retrieved Fri, 03 May 2024 06:44:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2010-12-13 22:17:35] [2db311435ed525bc1ed0ddec922afb8f]
-    D  [Central Tendency] [] [2010-12-15 15:45:08] [2db311435ed525bc1ed0ddec922afb8f]
-    D      [Central Tendency] [] [2010-12-15 20:17:31] [6fde1c772c7be11768d9b6a0344566b2] [Current]
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Dataseries X:
461
463
462
456
455
456
472
472
471
465
459
465
468
467
463
460
462
461
476
476
471
453
443
442
444
438
427
424
416
406
431
434
418
412
404
409
412
406
398
397
385
390
413
413
401
397
397
409
419
424
428
430
424
433
456
459
446
441
439
454
460




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110711&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110711&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean437.5901639344263.33022070923681131.399748587447
Geometric Mean436.819998336909
Harmonic Mean436.040924788303
Quadratic Mean438.349830352986
Winsorized Mean ( 1 / 20 )437.6721311475413.30959206304298132.243528148036
Winsorized Mean ( 2 / 20 )437.7704918032793.23365105553680135.379632583951
Winsorized Mean ( 3 / 20 )437.7704918032793.23365105553680135.379632583951
Winsorized Mean ( 4 / 20 )437.7049180327873.22222000842197135.839550647923
Winsorized Mean ( 5 / 20 )437.7868852459023.20511158975565136.590216279889
Winsorized Mean ( 6 / 20 )437.7868852459023.095838450666141.411411552086
Winsorized Mean ( 7 / 20 )438.0163934426233.01077226293819145.483070517982
Winsorized Mean ( 8 / 20 )438.0163934426232.92085882677418149.961507700244
Winsorized Mean ( 9 / 20 )438.0163934426232.92085882677418149.961507700244
Winsorized Mean ( 10 / 20 )438.1803278688522.78329405391491157.432279658888
Winsorized Mean ( 11 / 20 )438.1803278688522.78329405391491157.432279658888
Winsorized Mean ( 12 / 20 )438.5737704918032.65332650441155165.292047459146
Winsorized Mean ( 13 / 20 )438.5737704918032.65332650441155165.292047459146
Winsorized Mean ( 14 / 20 )438.5737704918032.58171999857356169.876582562835
Winsorized Mean ( 15 / 20 )438.5737704918032.58171999857356169.876582562835
Winsorized Mean ( 16 / 20 )439.0983606557382.41610092319343181.738418474410
Winsorized Mean ( 17 / 20 )439.6557377049182.32847486916645188.817042230869
Winsorized Mean ( 18 / 20 )439.6557377049182.24020457276006196.256959320120
Winsorized Mean ( 19 / 20 )441.2131147540982.00887576341610219.631857175584
Winsorized Mean ( 20 / 20 )440.2295081967211.86693891105418235.802845818957
Trimmed Mean ( 1 / 20 )437.8305084745763.25904330481164134.343261971440
Trimmed Mean ( 2 / 20 )4383.19578356298633137.055589456348
Trimmed Mean ( 3 / 20 )438.1272727272733.16558243484848138.403368651571
Trimmed Mean ( 4 / 20 )438.2641509433963.12547830225219140.223066219205
Trimmed Mean ( 5 / 20 )438.431372549023.07720969889113142.476924048110
Trimmed Mean ( 6 / 20 )438.5918367346943.0199053865415145.233635030197
Trimmed Mean ( 7 / 20 )438.7659574468082.97774861808768147.348219652130
Trimmed Mean ( 8 / 20 )438.9111111111112.94423288738747149.074861907603
Trimmed Mean ( 9 / 20 )439.0697674418602.92001064729722150.365810428899
Trimmed Mean ( 10 / 20 )439.2439024390242.88304134971254152.354354016747
Trimmed Mean ( 11 / 20 )439.4102564102562.86345062092203153.454804912531
Trimmed Mean ( 12 / 20 )439.5945945945952.83014114278374155.326032313076
Trimmed Mean ( 13 / 20 )439.7428571428572.81124478459197156.422827194923
Trimmed Mean ( 14 / 20 )439.9090909090912.77617148230680158.458904182517
Trimmed Mean ( 15 / 20 )440.0967741935482.73737761594539160.773132515572
Trimmed Mean ( 16 / 20 )440.3103448275862.67173835417913164.802943424027
Trimmed Mean ( 17 / 20 )440.4814814814812.61943773482769168.15879057742
Trimmed Mean ( 18 / 20 )440.62.55929677841395172.156665735753
Trimmed Mean ( 19 / 20 )440.7391304347832.48490891133773177.366312472804
Trimmed Mean ( 20 / 20 )440.6666666666672.44494944278563180.235492380815
Median441
Midrange430.5
Midmean - Weighted Average at Xnp438.548387096774
Midmean - Weighted Average at X(n+1)p439.909090909091
Midmean - Empirical Distribution Function439.909090909091
Midmean - Empirical Distribution Function - Averaging439.909090909091
Midmean - Empirical Distribution Function - Interpolation439.909090909091
Midmean - Closest Observation439.909090909091
Midmean - True Basic - Statistics Graphics Toolkit439.909090909091
Midmean - MS Excel (old versions)439.909090909091
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 437.590163934426 & 3.33022070923681 & 131.399748587447 \tabularnewline
Geometric Mean & 436.819998336909 &  &  \tabularnewline
Harmonic Mean & 436.040924788303 &  &  \tabularnewline
Quadratic Mean & 438.349830352986 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 437.672131147541 & 3.30959206304298 & 132.243528148036 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 437.770491803279 & 3.23365105553680 & 135.379632583951 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 437.770491803279 & 3.23365105553680 & 135.379632583951 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 437.704918032787 & 3.22222000842197 & 135.839550647923 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 437.786885245902 & 3.20511158975565 & 136.590216279889 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 437.786885245902 & 3.095838450666 & 141.411411552086 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 438.016393442623 & 3.01077226293819 & 145.483070517982 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 438.016393442623 & 2.92085882677418 & 149.961507700244 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 438.016393442623 & 2.92085882677418 & 149.961507700244 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 438.180327868852 & 2.78329405391491 & 157.432279658888 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 438.180327868852 & 2.78329405391491 & 157.432279658888 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 438.573770491803 & 2.65332650441155 & 165.292047459146 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 438.573770491803 & 2.65332650441155 & 165.292047459146 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 438.573770491803 & 2.58171999857356 & 169.876582562835 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 438.573770491803 & 2.58171999857356 & 169.876582562835 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 439.098360655738 & 2.41610092319343 & 181.738418474410 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 439.655737704918 & 2.32847486916645 & 188.817042230869 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 439.655737704918 & 2.24020457276006 & 196.256959320120 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 441.213114754098 & 2.00887576341610 & 219.631857175584 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 440.229508196721 & 1.86693891105418 & 235.802845818957 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 437.830508474576 & 3.25904330481164 & 134.343261971440 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 438 & 3.19578356298633 & 137.055589456348 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 438.127272727273 & 3.16558243484848 & 138.403368651571 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 438.264150943396 & 3.12547830225219 & 140.223066219205 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 438.43137254902 & 3.07720969889113 & 142.476924048110 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 438.591836734694 & 3.0199053865415 & 145.233635030197 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 438.765957446808 & 2.97774861808768 & 147.348219652130 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 438.911111111111 & 2.94423288738747 & 149.074861907603 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 439.069767441860 & 2.92001064729722 & 150.365810428899 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 439.243902439024 & 2.88304134971254 & 152.354354016747 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 439.410256410256 & 2.86345062092203 & 153.454804912531 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 439.594594594595 & 2.83014114278374 & 155.326032313076 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 439.742857142857 & 2.81124478459197 & 156.422827194923 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 439.909090909091 & 2.77617148230680 & 158.458904182517 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 440.096774193548 & 2.73737761594539 & 160.773132515572 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 440.310344827586 & 2.67173835417913 & 164.802943424027 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 440.481481481481 & 2.61943773482769 & 168.15879057742 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 440.6 & 2.55929677841395 & 172.156665735753 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 440.739130434783 & 2.48490891133773 & 177.366312472804 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 440.666666666667 & 2.44494944278563 & 180.235492380815 \tabularnewline
Median & 441 &  &  \tabularnewline
Midrange & 430.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 438.548387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 439.909090909091 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 439.909090909091 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 439.909090909091 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 439.909090909091 &  &  \tabularnewline
Midmean - Closest Observation & 439.909090909091 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 439.909090909091 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 439.909090909091 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110711&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]437.590163934426[/C][C]3.33022070923681[/C][C]131.399748587447[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]436.819998336909[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]436.040924788303[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]438.349830352986[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]437.672131147541[/C][C]3.30959206304298[/C][C]132.243528148036[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]437.770491803279[/C][C]3.23365105553680[/C][C]135.379632583951[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]437.770491803279[/C][C]3.23365105553680[/C][C]135.379632583951[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]437.704918032787[/C][C]3.22222000842197[/C][C]135.839550647923[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]437.786885245902[/C][C]3.20511158975565[/C][C]136.590216279889[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]437.786885245902[/C][C]3.095838450666[/C][C]141.411411552086[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]438.016393442623[/C][C]3.01077226293819[/C][C]145.483070517982[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]438.016393442623[/C][C]2.92085882677418[/C][C]149.961507700244[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]438.016393442623[/C][C]2.92085882677418[/C][C]149.961507700244[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]438.180327868852[/C][C]2.78329405391491[/C][C]157.432279658888[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]438.180327868852[/C][C]2.78329405391491[/C][C]157.432279658888[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]438.573770491803[/C][C]2.65332650441155[/C][C]165.292047459146[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]438.573770491803[/C][C]2.65332650441155[/C][C]165.292047459146[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]438.573770491803[/C][C]2.58171999857356[/C][C]169.876582562835[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]438.573770491803[/C][C]2.58171999857356[/C][C]169.876582562835[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]439.098360655738[/C][C]2.41610092319343[/C][C]181.738418474410[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]439.655737704918[/C][C]2.32847486916645[/C][C]188.817042230869[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]439.655737704918[/C][C]2.24020457276006[/C][C]196.256959320120[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]441.213114754098[/C][C]2.00887576341610[/C][C]219.631857175584[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]440.229508196721[/C][C]1.86693891105418[/C][C]235.802845818957[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]437.830508474576[/C][C]3.25904330481164[/C][C]134.343261971440[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]438[/C][C]3.19578356298633[/C][C]137.055589456348[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]438.127272727273[/C][C]3.16558243484848[/C][C]138.403368651571[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]438.264150943396[/C][C]3.12547830225219[/C][C]140.223066219205[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]438.43137254902[/C][C]3.07720969889113[/C][C]142.476924048110[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]438.591836734694[/C][C]3.0199053865415[/C][C]145.233635030197[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]438.765957446808[/C][C]2.97774861808768[/C][C]147.348219652130[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]438.911111111111[/C][C]2.94423288738747[/C][C]149.074861907603[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]439.069767441860[/C][C]2.92001064729722[/C][C]150.365810428899[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]439.243902439024[/C][C]2.88304134971254[/C][C]152.354354016747[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]439.410256410256[/C][C]2.86345062092203[/C][C]153.454804912531[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]439.594594594595[/C][C]2.83014114278374[/C][C]155.326032313076[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]439.742857142857[/C][C]2.81124478459197[/C][C]156.422827194923[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]439.909090909091[/C][C]2.77617148230680[/C][C]158.458904182517[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]440.096774193548[/C][C]2.73737761594539[/C][C]160.773132515572[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]440.310344827586[/C][C]2.67173835417913[/C][C]164.802943424027[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]440.481481481481[/C][C]2.61943773482769[/C][C]168.15879057742[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]440.6[/C][C]2.55929677841395[/C][C]172.156665735753[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]440.739130434783[/C][C]2.48490891133773[/C][C]177.366312472804[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]440.666666666667[/C][C]2.44494944278563[/C][C]180.235492380815[/C][/ROW]
[ROW][C]Median[/C][C]441[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]430.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]438.548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]439.909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]439.909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]439.909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]439.909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]439.909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]439.909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]439.909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110711&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 Mean437.5901639344263.33022070923681131.399748587447
Geometric Mean436.819998336909
Harmonic Mean436.040924788303
Quadratic Mean438.349830352986
Winsorized Mean ( 1 / 20 )437.6721311475413.30959206304298132.243528148036
Winsorized Mean ( 2 / 20 )437.7704918032793.23365105553680135.379632583951
Winsorized Mean ( 3 / 20 )437.7704918032793.23365105553680135.379632583951
Winsorized Mean ( 4 / 20 )437.7049180327873.22222000842197135.839550647923
Winsorized Mean ( 5 / 20 )437.7868852459023.20511158975565136.590216279889
Winsorized Mean ( 6 / 20 )437.7868852459023.095838450666141.411411552086
Winsorized Mean ( 7 / 20 )438.0163934426233.01077226293819145.483070517982
Winsorized Mean ( 8 / 20 )438.0163934426232.92085882677418149.961507700244
Winsorized Mean ( 9 / 20 )438.0163934426232.92085882677418149.961507700244
Winsorized Mean ( 10 / 20 )438.1803278688522.78329405391491157.432279658888
Winsorized Mean ( 11 / 20 )438.1803278688522.78329405391491157.432279658888
Winsorized Mean ( 12 / 20 )438.5737704918032.65332650441155165.292047459146
Winsorized Mean ( 13 / 20 )438.5737704918032.65332650441155165.292047459146
Winsorized Mean ( 14 / 20 )438.5737704918032.58171999857356169.876582562835
Winsorized Mean ( 15 / 20 )438.5737704918032.58171999857356169.876582562835
Winsorized Mean ( 16 / 20 )439.0983606557382.41610092319343181.738418474410
Winsorized Mean ( 17 / 20 )439.6557377049182.32847486916645188.817042230869
Winsorized Mean ( 18 / 20 )439.6557377049182.24020457276006196.256959320120
Winsorized Mean ( 19 / 20 )441.2131147540982.00887576341610219.631857175584
Winsorized Mean ( 20 / 20 )440.2295081967211.86693891105418235.802845818957
Trimmed Mean ( 1 / 20 )437.8305084745763.25904330481164134.343261971440
Trimmed Mean ( 2 / 20 )4383.19578356298633137.055589456348
Trimmed Mean ( 3 / 20 )438.1272727272733.16558243484848138.403368651571
Trimmed Mean ( 4 / 20 )438.2641509433963.12547830225219140.223066219205
Trimmed Mean ( 5 / 20 )438.431372549023.07720969889113142.476924048110
Trimmed Mean ( 6 / 20 )438.5918367346943.0199053865415145.233635030197
Trimmed Mean ( 7 / 20 )438.7659574468082.97774861808768147.348219652130
Trimmed Mean ( 8 / 20 )438.9111111111112.94423288738747149.074861907603
Trimmed Mean ( 9 / 20 )439.0697674418602.92001064729722150.365810428899
Trimmed Mean ( 10 / 20 )439.2439024390242.88304134971254152.354354016747
Trimmed Mean ( 11 / 20 )439.4102564102562.86345062092203153.454804912531
Trimmed Mean ( 12 / 20 )439.5945945945952.83014114278374155.326032313076
Trimmed Mean ( 13 / 20 )439.7428571428572.81124478459197156.422827194923
Trimmed Mean ( 14 / 20 )439.9090909090912.77617148230680158.458904182517
Trimmed Mean ( 15 / 20 )440.0967741935482.73737761594539160.773132515572
Trimmed Mean ( 16 / 20 )440.3103448275862.67173835417913164.802943424027
Trimmed Mean ( 17 / 20 )440.4814814814812.61943773482769168.15879057742
Trimmed Mean ( 18 / 20 )440.62.55929677841395172.156665735753
Trimmed Mean ( 19 / 20 )440.7391304347832.48490891133773177.366312472804
Trimmed Mean ( 20 / 20 )440.6666666666672.44494944278563180.235492380815
Median441
Midrange430.5
Midmean - Weighted Average at Xnp438.548387096774
Midmean - Weighted Average at X(n+1)p439.909090909091
Midmean - Empirical Distribution Function439.909090909091
Midmean - Empirical Distribution Function - Averaging439.909090909091
Midmean - Empirical Distribution Function - Interpolation439.909090909091
Midmean - Closest Observation439.909090909091
Midmean - True Basic - Statistics Graphics Toolkit439.909090909091
Midmean - MS Excel (old versions)439.909090909091
Number of observations61



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')