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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, 26 Oct 2009 15:05:17 -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/26/t12565911785cb44ioaaprsn3m.htm/, Retrieved Thu, 02 May 2024 14:29:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50757, Retrieved Thu, 02 May 2024 14:29:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
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]
- RMPD      [Central Tendency] [] [2009-10-20 16:31:24] [ba905ddf7cdf9ecb063c35348c4dab2e]
- R PD          [Central Tendency] [Central Tendency] [2009-10-26 21:05:17] [f1100e00818182135823a11ccbd0f3b9] [Current]
Feedback Forum

Post a new message
Dataseries X:
345.0561798
413.1707317
348.9473684
414.2857143
356.1728395
396.9879518
460
408.3544304
506.7948718
476.25
338.4705882
408.7209302
436.2352941
431.25
430.7692308
513.75
534.7560976
449.2771084
525.4878049
432.8395062
461.25
501.4102564
378.4615385
431.6883117
449.6052632
460.2631579
364.4736842
372.6923077
397.375
376.75
440.8860759
391.6883117
353.6486486
512.173913
425.2238806
481.3846154
402.8125
541.1940299
413.6764706
375.5072464
418.8405797
502.8358209
457.1875
486.4516129
487.7966102
524.2622951
382.0895522
378.3823529
472.8787879
415.3125
448.28125
459.1044776
305.3521127
329.7183099
372.4637681
410.3125
415
459.3333333




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50757&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]2 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=50757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50757&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean429.0576762620697.407494832231557.9221026783783
Geometric Mean425.376500675384
Harmonic Mean421.661809294074
Quadratic Mean432.687110279137
Winsorized Mean ( 1 / 19 )429.3667842775867.2664431636086359.0889895661629
Winsorized Mean ( 2 / 19 )429.3489906775867.117755185845260.3208426627844
Winsorized Mean ( 3 / 19 )429.6262362879317.028641125987261.1250778901573
Winsorized Mean ( 4 / 19 )429.1696082534486.8078253200251463.0406316376907
Winsorized Mean ( 5 / 19 )429.4390214603456.6961463103434864.1322637764044
Winsorized Mean ( 6 / 19 )429.1436921189666.5261890161444965.7571656379166
Winsorized Mean ( 7 / 19 )429.6677017155176.2368655486315868.8916088322266
Winsorized Mean ( 8 / 19 )430.5731526672416.0014736050017871.7445715846173
Winsorized Mean ( 9 / 19 )428.4961533672415.5788725266429676.8069446507116
Winsorized Mean ( 10 / 19 )428.7495915396555.4515431505412378.6473810625692
Winsorized Mean ( 11 / 19 )428.0243039034485.2359058030711581.7478999817735
Winsorized Mean ( 12 / 19 )427.2996978689664.9914186643820285.606863819721
Winsorized Mean ( 13 / 19 )426.5618298603454.8601592002798187.7670488316076
Winsorized Mean ( 14 / 19 )424.6306085017244.2596231648787499.6873648361363
Winsorized Mean ( 15 / 19 )426.8578285189663.80084705115059112.305973582848
Winsorized Mean ( 16 / 19 )428.2472029189663.55803998392987120.360424518323
Winsorized Mean ( 17 / 19 )428.1652457724143.51005039377222121.982649175663
Winsorized Mean ( 18 / 19 )429.7817215896553.24578120461336132.41241306678
Winsorized Mean ( 19 / 19 )430.9692061275862.88858696386476149.197241252856
Trimmed Mean ( 1 / 19 )429.2642692964297.0601184749634860.8012841170699
Trimmed Mean ( 2 / 19 )429.1541606129636.8037494777807163.0761261881364
Trimmed Mean ( 3 / 19 )429.0455053846156.5845403366531365.1595226771282
Trimmed Mean ( 4 / 19 )428.8209561026.3521682525811267.5078082082845
Trimmed Mean ( 5 / 19 )428.7156340979176.147721163476469.7356992449358
Trimmed Mean ( 6 / 19 )428.5332146760875.9247482823378372.3293537977943
Trimmed Mean ( 7 / 19 )428.3990946318185.6920982571741875.2620694999203
Trimmed Mean ( 8 / 19 )428.1488252071435.4778008360912178.1607141293324
Trimmed Mean ( 9 / 19 )427.7094158555.2620475891284881.2819360924554
Trimmed Mean ( 10 / 19 )427.5759925342115.0990917910450783.853362531169
Trimmed Mean ( 11 / 19 )427.3869126944444.9101657031919587.0412402613243
Trimmed Mean ( 12 / 19 )427.2880659294124.7107109799990990.705642469599
Trimmed Mean ( 13 / 19 )427.2863090218754.5023555026634894.9028366971695
Trimmed Mean ( 14 / 19 )427.3940520766674.24076479060622100.782305357608
Trimmed Mean ( 15 / 19 )427.8029289321434.05692804476431105.449967120873
Trimmed Mean ( 16 / 19 )427.9434823269233.93882160865256108.647591804321
Trimmed Mean ( 17 / 19 )427.89760786253.83027354554164111.714634157282
Trimmed Mean ( 18 / 19 )427.8561025181823.65696783643954116.997502207935
Trimmed Mean ( 19 / 19 )427.545863893.46901670549794123.246989042283
Median427.9965557
Midrange423.2730713
Midmean - Weighted Average at Xnp426.226605596552
Midmean - Weighted Average at X(n+1)p427.394052076667
Midmean - Empirical Distribution Function427.394052076667
Midmean - Empirical Distribution Function - Averaging427.394052076667
Midmean - Empirical Distribution Function - Interpolation427.802928932143
Midmean - Closest Observation427.394052076667
Midmean - True Basic - Statistics Graphics Toolkit427.394052076667
Midmean - MS Excel (old versions)427.394052076667
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 429.057676262069 & 7.4074948322315 & 57.9221026783783 \tabularnewline
Geometric Mean & 425.376500675384 &  &  \tabularnewline
Harmonic Mean & 421.661809294074 &  &  \tabularnewline
Quadratic Mean & 432.687110279137 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 429.366784277586 & 7.26644316360863 & 59.0889895661629 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 429.348990677586 & 7.1177551858452 & 60.3208426627844 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 429.626236287931 & 7.0286411259872 & 61.1250778901573 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 429.169608253448 & 6.80782532002514 & 63.0406316376907 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 429.439021460345 & 6.69614631034348 & 64.1322637764044 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 429.143692118966 & 6.52618901614449 & 65.7571656379166 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 429.667701715517 & 6.23686554863158 & 68.8916088322266 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 430.573152667241 & 6.00147360500178 & 71.7445715846173 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 428.496153367241 & 5.57887252664296 & 76.8069446507116 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 428.749591539655 & 5.45154315054123 & 78.6473810625692 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 428.024303903448 & 5.23590580307115 & 81.7478999817735 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 427.299697868966 & 4.99141866438202 & 85.606863819721 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 426.561829860345 & 4.86015920027981 & 87.7670488316076 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 424.630608501724 & 4.25962316487874 & 99.6873648361363 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 426.857828518966 & 3.80084705115059 & 112.305973582848 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 428.247202918966 & 3.55803998392987 & 120.360424518323 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 428.165245772414 & 3.51005039377222 & 121.982649175663 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 429.781721589655 & 3.24578120461336 & 132.41241306678 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 430.969206127586 & 2.88858696386476 & 149.197241252856 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 429.264269296429 & 7.06011847496348 & 60.8012841170699 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 429.154160612963 & 6.80374947778071 & 63.0761261881364 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 429.045505384615 & 6.58454033665313 & 65.1595226771282 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 428.820956102 & 6.35216825258112 & 67.5078082082845 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 428.715634097917 & 6.1477211634764 & 69.7356992449358 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 428.533214676087 & 5.92474828233783 & 72.3293537977943 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 428.399094631818 & 5.69209825717418 & 75.2620694999203 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 428.148825207143 & 5.47780083609121 & 78.1607141293324 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 427.709415855 & 5.26204758912848 & 81.2819360924554 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 427.575992534211 & 5.09909179104507 & 83.853362531169 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 427.386912694444 & 4.91016570319195 & 87.0412402613243 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 427.288065929412 & 4.71071097999909 & 90.705642469599 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 427.286309021875 & 4.50235550266348 & 94.9028366971695 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 427.394052076667 & 4.24076479060622 & 100.782305357608 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 427.802928932143 & 4.05692804476431 & 105.449967120873 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 427.943482326923 & 3.93882160865256 & 108.647591804321 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 427.8976078625 & 3.83027354554164 & 111.714634157282 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 427.856102518182 & 3.65696783643954 & 116.997502207935 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 427.54586389 & 3.46901670549794 & 123.246989042283 \tabularnewline
Median & 427.9965557 &  &  \tabularnewline
Midrange & 423.2730713 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 426.226605596552 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 427.394052076667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 427.394052076667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 427.394052076667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 427.802928932143 &  &  \tabularnewline
Midmean - Closest Observation & 427.394052076667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 427.394052076667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 427.394052076667 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50757&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]429.057676262069[/C][C]7.4074948322315[/C][C]57.9221026783783[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]425.376500675384[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]421.661809294074[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]432.687110279137[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]429.366784277586[/C][C]7.26644316360863[/C][C]59.0889895661629[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]429.348990677586[/C][C]7.1177551858452[/C][C]60.3208426627844[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]429.626236287931[/C][C]7.0286411259872[/C][C]61.1250778901573[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]429.169608253448[/C][C]6.80782532002514[/C][C]63.0406316376907[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]429.439021460345[/C][C]6.69614631034348[/C][C]64.1322637764044[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]429.143692118966[/C][C]6.52618901614449[/C][C]65.7571656379166[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]429.667701715517[/C][C]6.23686554863158[/C][C]68.8916088322266[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]430.573152667241[/C][C]6.00147360500178[/C][C]71.7445715846173[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]428.496153367241[/C][C]5.57887252664296[/C][C]76.8069446507116[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]428.749591539655[/C][C]5.45154315054123[/C][C]78.6473810625692[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]428.024303903448[/C][C]5.23590580307115[/C][C]81.7478999817735[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]427.299697868966[/C][C]4.99141866438202[/C][C]85.606863819721[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]426.561829860345[/C][C]4.86015920027981[/C][C]87.7670488316076[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]424.630608501724[/C][C]4.25962316487874[/C][C]99.6873648361363[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]426.857828518966[/C][C]3.80084705115059[/C][C]112.305973582848[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]428.247202918966[/C][C]3.55803998392987[/C][C]120.360424518323[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]428.165245772414[/C][C]3.51005039377222[/C][C]121.982649175663[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]429.781721589655[/C][C]3.24578120461336[/C][C]132.41241306678[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]430.969206127586[/C][C]2.88858696386476[/C][C]149.197241252856[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]429.264269296429[/C][C]7.06011847496348[/C][C]60.8012841170699[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]429.154160612963[/C][C]6.80374947778071[/C][C]63.0761261881364[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]429.045505384615[/C][C]6.58454033665313[/C][C]65.1595226771282[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]428.820956102[/C][C]6.35216825258112[/C][C]67.5078082082845[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]428.715634097917[/C][C]6.1477211634764[/C][C]69.7356992449358[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]428.533214676087[/C][C]5.92474828233783[/C][C]72.3293537977943[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]428.399094631818[/C][C]5.69209825717418[/C][C]75.2620694999203[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]428.148825207143[/C][C]5.47780083609121[/C][C]78.1607141293324[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]427.709415855[/C][C]5.26204758912848[/C][C]81.2819360924554[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]427.575992534211[/C][C]5.09909179104507[/C][C]83.853362531169[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]427.386912694444[/C][C]4.91016570319195[/C][C]87.0412402613243[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]427.288065929412[/C][C]4.71071097999909[/C][C]90.705642469599[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]427.286309021875[/C][C]4.50235550266348[/C][C]94.9028366971695[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]427.394052076667[/C][C]4.24076479060622[/C][C]100.782305357608[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]427.802928932143[/C][C]4.05692804476431[/C][C]105.449967120873[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]427.943482326923[/C][C]3.93882160865256[/C][C]108.647591804321[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]427.8976078625[/C][C]3.83027354554164[/C][C]111.714634157282[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]427.856102518182[/C][C]3.65696783643954[/C][C]116.997502207935[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]427.54586389[/C][C]3.46901670549794[/C][C]123.246989042283[/C][/ROW]
[ROW][C]Median[/C][C]427.9965557[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]423.2730713[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]426.226605596552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]427.394052076667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]427.394052076667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]427.394052076667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]427.802928932143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]427.394052076667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]427.394052076667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]427.394052076667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50757&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 Mean429.0576762620697.407494832231557.9221026783783
Geometric Mean425.376500675384
Harmonic Mean421.661809294074
Quadratic Mean432.687110279137
Winsorized Mean ( 1 / 19 )429.3667842775867.2664431636086359.0889895661629
Winsorized Mean ( 2 / 19 )429.3489906775867.117755185845260.3208426627844
Winsorized Mean ( 3 / 19 )429.6262362879317.028641125987261.1250778901573
Winsorized Mean ( 4 / 19 )429.1696082534486.8078253200251463.0406316376907
Winsorized Mean ( 5 / 19 )429.4390214603456.6961463103434864.1322637764044
Winsorized Mean ( 6 / 19 )429.1436921189666.5261890161444965.7571656379166
Winsorized Mean ( 7 / 19 )429.6677017155176.2368655486315868.8916088322266
Winsorized Mean ( 8 / 19 )430.5731526672416.0014736050017871.7445715846173
Winsorized Mean ( 9 / 19 )428.4961533672415.5788725266429676.8069446507116
Winsorized Mean ( 10 / 19 )428.7495915396555.4515431505412378.6473810625692
Winsorized Mean ( 11 / 19 )428.0243039034485.2359058030711581.7478999817735
Winsorized Mean ( 12 / 19 )427.2996978689664.9914186643820285.606863819721
Winsorized Mean ( 13 / 19 )426.5618298603454.8601592002798187.7670488316076
Winsorized Mean ( 14 / 19 )424.6306085017244.2596231648787499.6873648361363
Winsorized Mean ( 15 / 19 )426.8578285189663.80084705115059112.305973582848
Winsorized Mean ( 16 / 19 )428.2472029189663.55803998392987120.360424518323
Winsorized Mean ( 17 / 19 )428.1652457724143.51005039377222121.982649175663
Winsorized Mean ( 18 / 19 )429.7817215896553.24578120461336132.41241306678
Winsorized Mean ( 19 / 19 )430.9692061275862.88858696386476149.197241252856
Trimmed Mean ( 1 / 19 )429.2642692964297.0601184749634860.8012841170699
Trimmed Mean ( 2 / 19 )429.1541606129636.8037494777807163.0761261881364
Trimmed Mean ( 3 / 19 )429.0455053846156.5845403366531365.1595226771282
Trimmed Mean ( 4 / 19 )428.8209561026.3521682525811267.5078082082845
Trimmed Mean ( 5 / 19 )428.7156340979176.147721163476469.7356992449358
Trimmed Mean ( 6 / 19 )428.5332146760875.9247482823378372.3293537977943
Trimmed Mean ( 7 / 19 )428.3990946318185.6920982571741875.2620694999203
Trimmed Mean ( 8 / 19 )428.1488252071435.4778008360912178.1607141293324
Trimmed Mean ( 9 / 19 )427.7094158555.2620475891284881.2819360924554
Trimmed Mean ( 10 / 19 )427.5759925342115.0990917910450783.853362531169
Trimmed Mean ( 11 / 19 )427.3869126944444.9101657031919587.0412402613243
Trimmed Mean ( 12 / 19 )427.2880659294124.7107109799990990.705642469599
Trimmed Mean ( 13 / 19 )427.2863090218754.5023555026634894.9028366971695
Trimmed Mean ( 14 / 19 )427.3940520766674.24076479060622100.782305357608
Trimmed Mean ( 15 / 19 )427.8029289321434.05692804476431105.449967120873
Trimmed Mean ( 16 / 19 )427.9434823269233.93882160865256108.647591804321
Trimmed Mean ( 17 / 19 )427.89760786253.83027354554164111.714634157282
Trimmed Mean ( 18 / 19 )427.8561025181823.65696783643954116.997502207935
Trimmed Mean ( 19 / 19 )427.545863893.46901670549794123.246989042283
Median427.9965557
Midrange423.2730713
Midmean - Weighted Average at Xnp426.226605596552
Midmean - Weighted Average at X(n+1)p427.394052076667
Midmean - Empirical Distribution Function427.394052076667
Midmean - Empirical Distribution Function - Averaging427.394052076667
Midmean - Empirical Distribution Function - Interpolation427.802928932143
Midmean - Closest Observation427.394052076667
Midmean - True Basic - Statistics Graphics Toolkit427.394052076667
Midmean - MS Excel (old versions)427.394052076667
Number of observations58



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')