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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 computationMon, 19 Oct 2009 11:51:02 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/19/t1255974690syutmqzyserieub.htm/, Retrieved Mon, 29 Apr 2024 20:25:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48001, Retrieved Mon, 29 Apr 2024 20:25:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws 3 vraag 3.1
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Variability] [workshop 3] [2009-10-19 08:30:47] [3e19a07d230ba260a720e0e03e0f40f2]
- RM D          [Central Tendency] [workshop 3] [2009-10-19 17:51:02] [100339cefec36dfa6f2b82a1c918e250] [Current]
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Dataseries X:
449
452
462
455
461
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48001&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48001&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean438.2295081967213.36710164175574130.150365157439
Geometric Mean437.441859921726
Harmonic Mean436.643707846105
Quadratic Mean439.004947879059
Winsorized Mean ( 1 / 20 )438.3114754098363.34643934282318130.978461136564
Winsorized Mean ( 2 / 20 )438.4098360655743.27103341311519134.027929616302
Winsorized Mean ( 3 / 20 )438.4098360655743.27103341311519134.027929616302
Winsorized Mean ( 4 / 20 )438.3442622950823.25994780590334134.463582975561
Winsorized Mean ( 5 / 20 )438.4262295081973.24276909061968135.201186780899
Winsorized Mean ( 6 / 20 )438.4262295081973.13480889129058139.857402703646
Winsorized Mean ( 7 / 20 )438.6557377049183.05002779221429143.820242826856
Winsorized Mean ( 8 / 20 )438.6557377049182.96130650219565148.129123878152
Winsorized Mean ( 9 / 20 )438.6557377049182.96130650219565148.129123878152
Winsorized Mean ( 10 / 20 )438.8196721311482.82509327634793155.329268525399
Winsorized Mean ( 11 / 20 )438.8196721311482.82509327634793155.329268525399
Winsorized Mean ( 12 / 20 )439.2131147540982.6955858223653162.937908008695
Winsorized Mean ( 13 / 20 )439.2131147540982.6955858223653162.937908008695
Winsorized Mean ( 14 / 20 )439.442622950822.6572433834703165.375375731265
Winsorized Mean ( 15 / 20 )439.1967213114752.62281078861182167.452689770248
Winsorized Mean ( 16 / 20 )439.9836065573772.49420002651821176.402695004207
Winsorized Mean ( 17 / 20 )440.5409836065572.40600044180208183.100957070729
Winsorized Mean ( 18 / 20 )440.5409836065572.31856062501144190.006238721657
Winsorized Mean ( 19 / 20 )441.7868852459022.04072133851600216.48564990611
Winsorized Mean ( 20 / 20 )441.7868852459022.04072133851600216.48564990611
Trimmed Mean ( 1 / 20 )438.4915254237293.29845729143527132.938366842678
Trimmed Mean ( 2 / 20 )438.6842105263163.23816119178315135.473246865993
Trimmed Mean ( 3 / 20 )438.8363636363643.21096224565251136.668179213420
Trimmed Mean ( 4 / 20 )4393.17430266161218138.298091517536
Trimmed Mean ( 5 / 20 )439.1960784313733.12987121301709140.324009692400
Trimmed Mean ( 6 / 20 )439.3877551020413.07707348466738142.794040276077
Trimmed Mean ( 7 / 20 )439.5957446808513.03961807670584144.622032632882
Trimmed Mean ( 8 / 20 )439.7777777777783.01140741767721146.037289805506
Trimmed Mean ( 9 / 20 )439.9767441860472.99288346985175147.007642836104
Trimmed Mean ( 10 / 20 )440.1951219512202.96261657426195148.583223956641
Trimmed Mean ( 11 / 20 )440.4102564102562.9502665651238149.278123413155
Trimmed Mean ( 12 / 20 )440.6486486486492.92555690553642150.620433263407
Trimmed Mean ( 13 / 20 )440.8571428571432.91652574975425151.158323527330
Trimmed Mean ( 14 / 20 )441.0909090909092.89342372051628152.446012646984
Trimmed Mean ( 15 / 20 )441.3225806451612.86107998887487154.250346848469
Trimmed Mean ( 16 / 20 )441.6206896551722.81201407103926157.047823552305
Trimmed Mean ( 17 / 20 )441.8518518518522.77026524474126159.498030988408
Trimmed Mean ( 18 / 20 )442.042.72364951244955162.296946791236
Trimmed Mean ( 19 / 20 )442.2608695652172.66600424263659165.889034417978
Trimmed Mean ( 20 / 20 )442.3333333333332.66488035408483165.986188706486
Median443
Midrange430.5
Midmean - Weighted Average at Xnp440.4375
Midmean - Weighted Average at X(n+1)p440.4375
Midmean - Empirical Distribution Function440.4375
Midmean - Empirical Distribution Function - Averaging440.4375
Midmean - Empirical Distribution Function - Interpolation440.4375
Midmean - Closest Observation440.4375
Midmean - True Basic - Statistics Graphics Toolkit440.4375
Midmean - MS Excel (old versions)440.4375
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 438.229508196721 & 3.36710164175574 & 130.150365157439 \tabularnewline
Geometric Mean & 437.441859921726 &  &  \tabularnewline
Harmonic Mean & 436.643707846105 &  &  \tabularnewline
Quadratic Mean & 439.004947879059 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 438.311475409836 & 3.34643934282318 & 130.978461136564 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 438.409836065574 & 3.27103341311519 & 134.027929616302 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 438.409836065574 & 3.27103341311519 & 134.027929616302 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 438.344262295082 & 3.25994780590334 & 134.463582975561 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 438.426229508197 & 3.24276909061968 & 135.201186780899 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 438.426229508197 & 3.13480889129058 & 139.857402703646 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 438.655737704918 & 3.05002779221429 & 143.820242826856 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 438.655737704918 & 2.96130650219565 & 148.129123878152 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 438.655737704918 & 2.96130650219565 & 148.129123878152 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 438.819672131148 & 2.82509327634793 & 155.329268525399 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 438.819672131148 & 2.82509327634793 & 155.329268525399 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 439.213114754098 & 2.6955858223653 & 162.937908008695 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 439.213114754098 & 2.6955858223653 & 162.937908008695 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 439.44262295082 & 2.6572433834703 & 165.375375731265 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 439.196721311475 & 2.62281078861182 & 167.452689770248 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 439.983606557377 & 2.49420002651821 & 176.402695004207 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 440.540983606557 & 2.40600044180208 & 183.100957070729 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 440.540983606557 & 2.31856062501144 & 190.006238721657 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 441.786885245902 & 2.04072133851600 & 216.48564990611 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 441.786885245902 & 2.04072133851600 & 216.48564990611 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 438.491525423729 & 3.29845729143527 & 132.938366842678 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 438.684210526316 & 3.23816119178315 & 135.473246865993 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 438.836363636364 & 3.21096224565251 & 136.668179213420 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 439 & 3.17430266161218 & 138.298091517536 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 439.196078431373 & 3.12987121301709 & 140.324009692400 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 439.387755102041 & 3.07707348466738 & 142.794040276077 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 439.595744680851 & 3.03961807670584 & 144.622032632882 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 439.777777777778 & 3.01140741767721 & 146.037289805506 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 439.976744186047 & 2.99288346985175 & 147.007642836104 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 440.195121951220 & 2.96261657426195 & 148.583223956641 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 440.410256410256 & 2.9502665651238 & 149.278123413155 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 440.648648648649 & 2.92555690553642 & 150.620433263407 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 440.857142857143 & 2.91652574975425 & 151.158323527330 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 441.090909090909 & 2.89342372051628 & 152.446012646984 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 441.322580645161 & 2.86107998887487 & 154.250346848469 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 441.620689655172 & 2.81201407103926 & 157.047823552305 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 441.851851851852 & 2.77026524474126 & 159.498030988408 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 442.04 & 2.72364951244955 & 162.296946791236 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 442.260869565217 & 2.66600424263659 & 165.889034417978 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 442.333333333333 & 2.66488035408483 & 165.986188706486 \tabularnewline
Median & 443 &  &  \tabularnewline
Midrange & 430.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 440.4375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 440.4375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 440.4375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 440.4375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 440.4375 &  &  \tabularnewline
Midmean - Closest Observation & 440.4375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 440.4375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 440.4375 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48001&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]438.229508196721[/C][C]3.36710164175574[/C][C]130.150365157439[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]437.441859921726[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]436.643707846105[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]439.004947879059[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]438.311475409836[/C][C]3.34643934282318[/C][C]130.978461136564[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]438.409836065574[/C][C]3.27103341311519[/C][C]134.027929616302[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]438.409836065574[/C][C]3.27103341311519[/C][C]134.027929616302[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]438.344262295082[/C][C]3.25994780590334[/C][C]134.463582975561[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]438.426229508197[/C][C]3.24276909061968[/C][C]135.201186780899[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]438.426229508197[/C][C]3.13480889129058[/C][C]139.857402703646[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]438.655737704918[/C][C]3.05002779221429[/C][C]143.820242826856[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]438.655737704918[/C][C]2.96130650219565[/C][C]148.129123878152[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]438.655737704918[/C][C]2.96130650219565[/C][C]148.129123878152[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]438.819672131148[/C][C]2.82509327634793[/C][C]155.329268525399[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]438.819672131148[/C][C]2.82509327634793[/C][C]155.329268525399[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]439.213114754098[/C][C]2.6955858223653[/C][C]162.937908008695[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]439.213114754098[/C][C]2.6955858223653[/C][C]162.937908008695[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]439.44262295082[/C][C]2.6572433834703[/C][C]165.375375731265[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]439.196721311475[/C][C]2.62281078861182[/C][C]167.452689770248[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]439.983606557377[/C][C]2.49420002651821[/C][C]176.402695004207[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]440.540983606557[/C][C]2.40600044180208[/C][C]183.100957070729[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]440.540983606557[/C][C]2.31856062501144[/C][C]190.006238721657[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]441.786885245902[/C][C]2.04072133851600[/C][C]216.48564990611[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]441.786885245902[/C][C]2.04072133851600[/C][C]216.48564990611[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]438.491525423729[/C][C]3.29845729143527[/C][C]132.938366842678[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]438.684210526316[/C][C]3.23816119178315[/C][C]135.473246865993[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]438.836363636364[/C][C]3.21096224565251[/C][C]136.668179213420[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]439[/C][C]3.17430266161218[/C][C]138.298091517536[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]439.196078431373[/C][C]3.12987121301709[/C][C]140.324009692400[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]439.387755102041[/C][C]3.07707348466738[/C][C]142.794040276077[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]439.595744680851[/C][C]3.03961807670584[/C][C]144.622032632882[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]439.777777777778[/C][C]3.01140741767721[/C][C]146.037289805506[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]439.976744186047[/C][C]2.99288346985175[/C][C]147.007642836104[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]440.195121951220[/C][C]2.96261657426195[/C][C]148.583223956641[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]440.410256410256[/C][C]2.9502665651238[/C][C]149.278123413155[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]440.648648648649[/C][C]2.92555690553642[/C][C]150.620433263407[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]440.857142857143[/C][C]2.91652574975425[/C][C]151.158323527330[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]441.090909090909[/C][C]2.89342372051628[/C][C]152.446012646984[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]441.322580645161[/C][C]2.86107998887487[/C][C]154.250346848469[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]441.620689655172[/C][C]2.81201407103926[/C][C]157.047823552305[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]441.851851851852[/C][C]2.77026524474126[/C][C]159.498030988408[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]442.04[/C][C]2.72364951244955[/C][C]162.296946791236[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]442.260869565217[/C][C]2.66600424263659[/C][C]165.889034417978[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]442.333333333333[/C][C]2.66488035408483[/C][C]165.986188706486[/C][/ROW]
[ROW][C]Median[/C][C]443[/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]440.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]440.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]440.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]440.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]440.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]440.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]440.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]440.4375[/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=48001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48001&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 Mean438.2295081967213.36710164175574130.150365157439
Geometric Mean437.441859921726
Harmonic Mean436.643707846105
Quadratic Mean439.004947879059
Winsorized Mean ( 1 / 20 )438.3114754098363.34643934282318130.978461136564
Winsorized Mean ( 2 / 20 )438.4098360655743.27103341311519134.027929616302
Winsorized Mean ( 3 / 20 )438.4098360655743.27103341311519134.027929616302
Winsorized Mean ( 4 / 20 )438.3442622950823.25994780590334134.463582975561
Winsorized Mean ( 5 / 20 )438.4262295081973.24276909061968135.201186780899
Winsorized Mean ( 6 / 20 )438.4262295081973.13480889129058139.857402703646
Winsorized Mean ( 7 / 20 )438.6557377049183.05002779221429143.820242826856
Winsorized Mean ( 8 / 20 )438.6557377049182.96130650219565148.129123878152
Winsorized Mean ( 9 / 20 )438.6557377049182.96130650219565148.129123878152
Winsorized Mean ( 10 / 20 )438.8196721311482.82509327634793155.329268525399
Winsorized Mean ( 11 / 20 )438.8196721311482.82509327634793155.329268525399
Winsorized Mean ( 12 / 20 )439.2131147540982.6955858223653162.937908008695
Winsorized Mean ( 13 / 20 )439.2131147540982.6955858223653162.937908008695
Winsorized Mean ( 14 / 20 )439.442622950822.6572433834703165.375375731265
Winsorized Mean ( 15 / 20 )439.1967213114752.62281078861182167.452689770248
Winsorized Mean ( 16 / 20 )439.9836065573772.49420002651821176.402695004207
Winsorized Mean ( 17 / 20 )440.5409836065572.40600044180208183.100957070729
Winsorized Mean ( 18 / 20 )440.5409836065572.31856062501144190.006238721657
Winsorized Mean ( 19 / 20 )441.7868852459022.04072133851600216.48564990611
Winsorized Mean ( 20 / 20 )441.7868852459022.04072133851600216.48564990611
Trimmed Mean ( 1 / 20 )438.4915254237293.29845729143527132.938366842678
Trimmed Mean ( 2 / 20 )438.6842105263163.23816119178315135.473246865993
Trimmed Mean ( 3 / 20 )438.8363636363643.21096224565251136.668179213420
Trimmed Mean ( 4 / 20 )4393.17430266161218138.298091517536
Trimmed Mean ( 5 / 20 )439.1960784313733.12987121301709140.324009692400
Trimmed Mean ( 6 / 20 )439.3877551020413.07707348466738142.794040276077
Trimmed Mean ( 7 / 20 )439.5957446808513.03961807670584144.622032632882
Trimmed Mean ( 8 / 20 )439.7777777777783.01140741767721146.037289805506
Trimmed Mean ( 9 / 20 )439.9767441860472.99288346985175147.007642836104
Trimmed Mean ( 10 / 20 )440.1951219512202.96261657426195148.583223956641
Trimmed Mean ( 11 / 20 )440.4102564102562.9502665651238149.278123413155
Trimmed Mean ( 12 / 20 )440.6486486486492.92555690553642150.620433263407
Trimmed Mean ( 13 / 20 )440.8571428571432.91652574975425151.158323527330
Trimmed Mean ( 14 / 20 )441.0909090909092.89342372051628152.446012646984
Trimmed Mean ( 15 / 20 )441.3225806451612.86107998887487154.250346848469
Trimmed Mean ( 16 / 20 )441.6206896551722.81201407103926157.047823552305
Trimmed Mean ( 17 / 20 )441.8518518518522.77026524474126159.498030988408
Trimmed Mean ( 18 / 20 )442.042.72364951244955162.296946791236
Trimmed Mean ( 19 / 20 )442.2608695652172.66600424263659165.889034417978
Trimmed Mean ( 20 / 20 )442.3333333333332.66488035408483165.986188706486
Median443
Midrange430.5
Midmean - Weighted Average at Xnp440.4375
Midmean - Weighted Average at X(n+1)p440.4375
Midmean - Empirical Distribution Function440.4375
Midmean - Empirical Distribution Function - Averaging440.4375
Midmean - Empirical Distribution Function - Interpolation440.4375
Midmean - Closest Observation440.4375
Midmean - True Basic - Statistics Graphics Toolkit440.4375
Midmean - MS Excel (old versions)440.4375
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')