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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 computationFri, 05 Dec 2008 03:05:35 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t12284715684ch6yteealuo0pf.htm/, Retrieved Thu, 16 May 2024 23:52:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29115, Retrieved Thu, 16 May 2024 23:52:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact232
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 21:55:47] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMP     [Central Tendency] [central tendency ...] [2008-12-05 10:05:35] [a8228479d4547a92e2d3f176a5299609] [Current]
-   PD      [Central Tendency] [Central tendency ...] [2008-12-05 11:38:27] [4ad596f10399a71ad29b7d76e6ab90ac]
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Dataseries X:
44.9
48.1
52.3
48.9
52.6
60.3
50.5
41.6
56
51.4
52.9
54.9
43.9
51
51.9
54.3
50.3
57.2
48.8
41.1
58
63
53.8
54.7
55.5
56.1
69.6
69.4
57.2
68
53.3
47.9
60.8
61.7
57.8
51.4
50.5
48.1
58.7
54
56.1
60.4
51.2
50.7
56.4
53.3
52.6
47.7
49.5
48.5
55.3
49.8
57.4
64.6
53
41.5
55.9
58.4
53.5
50.6
58.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29115&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29115&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29115&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean53.89016393442620.78261054289293568.8594913828023
Geometric Mean53.5526068061033
Harmonic Mean53.2165991576140
Quadratic Mean54.2300518586343
Winsorized Mean ( 1 / 20 )53.89344262295080.77975710402039269.1156801843532
Winsorized Mean ( 2 / 20 )53.85081967213110.76419042827047870.4678018462057
Winsorized Mean ( 3 / 20 )53.79672131147540.68752731575387778.2466675560186
Winsorized Mean ( 4 / 20 )53.75737704918030.64586731206110483.2328499140617
Winsorized Mean ( 5 / 20 )53.88032786885250.57386533174029193.8901949442671
Winsorized Mean ( 6 / 20 )53.81147540983610.55091626787673897.6763231502103
Winsorized Mean ( 7 / 20 )53.78852459016390.537277585756738100.113099850247
Winsorized Mean ( 8 / 20 )53.77540983606560.534598852405168100.590208142291
Winsorized Mean ( 9 / 20 )53.59836065573770.479015907212045111.892652934407
Winsorized Mean ( 10 / 20 )53.61475409836070.4646218043994115.394399467900
Winsorized Mean ( 11 / 20 )53.61475409836070.458369860833013116.968323355564
Winsorized Mean ( 12 / 20 )53.65409836065570.425065560809499126.225465686931
Winsorized Mean ( 13 / 20 )53.67540983606560.407562766212468131.698511949160
Winsorized Mean ( 14 / 20 )53.69836065573770.374461301985376143.401628876019
Winsorized Mean ( 15 / 20 )53.69836065573770.359040097029213149.560901693296
Winsorized Mean ( 16 / 20 )53.69836065573770.359040097029213149.560901693296
Winsorized Mean ( 17 / 20 )53.50327868852460.319844285996764167.279144980773
Winsorized Mean ( 18 / 20 )53.4442622950820.302209754087085176.844928306587
Winsorized Mean ( 19 / 20 )53.53770491803280.288278894394211185.714965469591
Winsorized Mean ( 20 / 20 )53.57049180327870.273884665829388195.595075179015
Trimmed Mean ( 1 / 20 )53.84067796610170.73151132412533473.6019746932542
Trimmed Mean ( 2 / 20 )53.78421052631580.67086144015754280.1718615899064
Trimmed Mean ( 3 / 20 )53.74727272727270.60468348592566188.8849687121774
Trimmed Mean ( 4 / 20 )53.72830188679250.56223285776098695.5623655663916
Trimmed Mean ( 5 / 20 )53.71960784313730.526654402496892102.001630648961
Trimmed Mean ( 6 / 20 )53.67959183673470.508130992336387105.641247328599
Trimmed Mean ( 7 / 20 )53.65106382978720.491903666219514109.068233302911
Trimmed Mean ( 8 / 20 )53.62444444444440.475002983037476112.892858275405
Trimmed Mean ( 9 / 20 )53.59767441860460.453624365558901118.154311117235
Trimmed Mean ( 10 / 20 )53.59756097560980.441456676946293121.410692769135
Trimmed Mean ( 11 / 20 )53.59487179487180.428850717807433124.973258920689
Trimmed Mean ( 12 / 20 )53.59189189189190.413208684677329129.696915576064
Trimmed Mean ( 13 / 20 )53.58285714285710.400891563416153133.659228660880
Trimmed Mean ( 14 / 20 )53.5696969696970.388213781713392137.990198939527
Trimmed Mean ( 15 / 20 )53.55161290322580.379271258439552141.196074607802
Trimmed Mean ( 16 / 20 )53.53103448275860.369965497268808144.691964191094
Trimmed Mean ( 17 / 20 )53.50740740740740.355017993441748150.717452061164
Trimmed Mean ( 18 / 20 )53.5080.345587422610642154.83202367664
Trimmed Mean ( 19 / 20 )53.51739130434780.335787209929584159.378885561397
Trimmed Mean ( 20 / 20 )53.51428571428570.323837533802553165.250411482302
Median53.3
Midrange55.35
Midmean - Weighted Average at Xnp53.5516129032258
Midmean - Weighted Average at X(n+1)p53.5516129032258
Midmean - Empirical Distribution Function53.5516129032258
Midmean - Empirical Distribution Function - Averaging53.5516129032258
Midmean - Empirical Distribution Function - Interpolation53.5516129032258
Midmean - Closest Observation53.45
Midmean - True Basic - Statistics Graphics Toolkit53.5516129032258
Midmean - MS Excel (old versions)53.5516129032258
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 53.8901639344262 & 0.782610542892935 & 68.8594913828023 \tabularnewline
Geometric Mean & 53.5526068061033 &  &  \tabularnewline
Harmonic Mean & 53.2165991576140 &  &  \tabularnewline
Quadratic Mean & 54.2300518586343 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 53.8934426229508 & 0.779757104020392 & 69.1156801843532 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 53.8508196721311 & 0.764190428270478 & 70.4678018462057 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 53.7967213114754 & 0.687527315753877 & 78.2466675560186 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 53.7573770491803 & 0.645867312061104 & 83.2328499140617 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 53.8803278688525 & 0.573865331740291 & 93.8901949442671 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 53.8114754098361 & 0.550916267876738 & 97.6763231502103 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 53.7885245901639 & 0.537277585756738 & 100.113099850247 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 53.7754098360656 & 0.534598852405168 & 100.590208142291 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 53.5983606557377 & 0.479015907212045 & 111.892652934407 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 53.6147540983607 & 0.4646218043994 & 115.394399467900 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 53.6147540983607 & 0.458369860833013 & 116.968323355564 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 53.6540983606557 & 0.425065560809499 & 126.225465686931 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 53.6754098360656 & 0.407562766212468 & 131.698511949160 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 53.6983606557377 & 0.374461301985376 & 143.401628876019 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 53.6983606557377 & 0.359040097029213 & 149.560901693296 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 53.6983606557377 & 0.359040097029213 & 149.560901693296 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 53.5032786885246 & 0.319844285996764 & 167.279144980773 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 53.444262295082 & 0.302209754087085 & 176.844928306587 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 53.5377049180328 & 0.288278894394211 & 185.714965469591 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 53.5704918032787 & 0.273884665829388 & 195.595075179015 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 53.8406779661017 & 0.731511324125334 & 73.6019746932542 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 53.7842105263158 & 0.670861440157542 & 80.1718615899064 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 53.7472727272727 & 0.604683485925661 & 88.8849687121774 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 53.7283018867925 & 0.562232857760986 & 95.5623655663916 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 53.7196078431373 & 0.526654402496892 & 102.001630648961 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 53.6795918367347 & 0.508130992336387 & 105.641247328599 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 53.6510638297872 & 0.491903666219514 & 109.068233302911 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 53.6244444444444 & 0.475002983037476 & 112.892858275405 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 53.5976744186046 & 0.453624365558901 & 118.154311117235 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 53.5975609756098 & 0.441456676946293 & 121.410692769135 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 53.5948717948718 & 0.428850717807433 & 124.973258920689 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 53.5918918918919 & 0.413208684677329 & 129.696915576064 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 53.5828571428571 & 0.400891563416153 & 133.659228660880 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 53.569696969697 & 0.388213781713392 & 137.990198939527 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 53.5516129032258 & 0.379271258439552 & 141.196074607802 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 53.5310344827586 & 0.369965497268808 & 144.691964191094 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 53.5074074074074 & 0.355017993441748 & 150.717452061164 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 53.508 & 0.345587422610642 & 154.83202367664 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 53.5173913043478 & 0.335787209929584 & 159.378885561397 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 53.5142857142857 & 0.323837533802553 & 165.250411482302 \tabularnewline
Median & 53.3 &  &  \tabularnewline
Midrange & 55.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 53.5516129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 53.5516129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 53.5516129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 53.5516129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 53.5516129032258 &  &  \tabularnewline
Midmean - Closest Observation & 53.45 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 53.5516129032258 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 53.5516129032258 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29115&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]53.8901639344262[/C][C]0.782610542892935[/C][C]68.8594913828023[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]53.5526068061033[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]53.2165991576140[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]54.2300518586343[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]53.8934426229508[/C][C]0.779757104020392[/C][C]69.1156801843532[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]53.8508196721311[/C][C]0.764190428270478[/C][C]70.4678018462057[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]53.7967213114754[/C][C]0.687527315753877[/C][C]78.2466675560186[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]53.7573770491803[/C][C]0.645867312061104[/C][C]83.2328499140617[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]53.8803278688525[/C][C]0.573865331740291[/C][C]93.8901949442671[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]53.8114754098361[/C][C]0.550916267876738[/C][C]97.6763231502103[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]53.7885245901639[/C][C]0.537277585756738[/C][C]100.113099850247[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]53.7754098360656[/C][C]0.534598852405168[/C][C]100.590208142291[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]53.5983606557377[/C][C]0.479015907212045[/C][C]111.892652934407[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]53.6147540983607[/C][C]0.4646218043994[/C][C]115.394399467900[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]53.6147540983607[/C][C]0.458369860833013[/C][C]116.968323355564[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]53.6540983606557[/C][C]0.425065560809499[/C][C]126.225465686931[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]53.6754098360656[/C][C]0.407562766212468[/C][C]131.698511949160[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]53.6983606557377[/C][C]0.374461301985376[/C][C]143.401628876019[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]53.6983606557377[/C][C]0.359040097029213[/C][C]149.560901693296[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]53.6983606557377[/C][C]0.359040097029213[/C][C]149.560901693296[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]53.5032786885246[/C][C]0.319844285996764[/C][C]167.279144980773[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]53.444262295082[/C][C]0.302209754087085[/C][C]176.844928306587[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]53.5377049180328[/C][C]0.288278894394211[/C][C]185.714965469591[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]53.5704918032787[/C][C]0.273884665829388[/C][C]195.595075179015[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]53.8406779661017[/C][C]0.731511324125334[/C][C]73.6019746932542[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]53.7842105263158[/C][C]0.670861440157542[/C][C]80.1718615899064[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]53.7472727272727[/C][C]0.604683485925661[/C][C]88.8849687121774[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]53.7283018867925[/C][C]0.562232857760986[/C][C]95.5623655663916[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]53.7196078431373[/C][C]0.526654402496892[/C][C]102.001630648961[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]53.6795918367347[/C][C]0.508130992336387[/C][C]105.641247328599[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]53.6510638297872[/C][C]0.491903666219514[/C][C]109.068233302911[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]53.6244444444444[/C][C]0.475002983037476[/C][C]112.892858275405[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]53.5976744186046[/C][C]0.453624365558901[/C][C]118.154311117235[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]53.5975609756098[/C][C]0.441456676946293[/C][C]121.410692769135[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]53.5948717948718[/C][C]0.428850717807433[/C][C]124.973258920689[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]53.5918918918919[/C][C]0.413208684677329[/C][C]129.696915576064[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]53.5828571428571[/C][C]0.400891563416153[/C][C]133.659228660880[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]53.569696969697[/C][C]0.388213781713392[/C][C]137.990198939527[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]53.5516129032258[/C][C]0.379271258439552[/C][C]141.196074607802[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]53.5310344827586[/C][C]0.369965497268808[/C][C]144.691964191094[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]53.5074074074074[/C][C]0.355017993441748[/C][C]150.717452061164[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]53.508[/C][C]0.345587422610642[/C][C]154.83202367664[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]53.5173913043478[/C][C]0.335787209929584[/C][C]159.378885561397[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]53.5142857142857[/C][C]0.323837533802553[/C][C]165.250411482302[/C][/ROW]
[ROW][C]Median[/C][C]53.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]55.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]53.5516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]53.5516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]53.5516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]53.5516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]53.5516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]53.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]53.5516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]53.5516129032258[/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=29115&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29115&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 Mean53.89016393442620.78261054289293568.8594913828023
Geometric Mean53.5526068061033
Harmonic Mean53.2165991576140
Quadratic Mean54.2300518586343
Winsorized Mean ( 1 / 20 )53.89344262295080.77975710402039269.1156801843532
Winsorized Mean ( 2 / 20 )53.85081967213110.76419042827047870.4678018462057
Winsorized Mean ( 3 / 20 )53.79672131147540.68752731575387778.2466675560186
Winsorized Mean ( 4 / 20 )53.75737704918030.64586731206110483.2328499140617
Winsorized Mean ( 5 / 20 )53.88032786885250.57386533174029193.8901949442671
Winsorized Mean ( 6 / 20 )53.81147540983610.55091626787673897.6763231502103
Winsorized Mean ( 7 / 20 )53.78852459016390.537277585756738100.113099850247
Winsorized Mean ( 8 / 20 )53.77540983606560.534598852405168100.590208142291
Winsorized Mean ( 9 / 20 )53.59836065573770.479015907212045111.892652934407
Winsorized Mean ( 10 / 20 )53.61475409836070.4646218043994115.394399467900
Winsorized Mean ( 11 / 20 )53.61475409836070.458369860833013116.968323355564
Winsorized Mean ( 12 / 20 )53.65409836065570.425065560809499126.225465686931
Winsorized Mean ( 13 / 20 )53.67540983606560.407562766212468131.698511949160
Winsorized Mean ( 14 / 20 )53.69836065573770.374461301985376143.401628876019
Winsorized Mean ( 15 / 20 )53.69836065573770.359040097029213149.560901693296
Winsorized Mean ( 16 / 20 )53.69836065573770.359040097029213149.560901693296
Winsorized Mean ( 17 / 20 )53.50327868852460.319844285996764167.279144980773
Winsorized Mean ( 18 / 20 )53.4442622950820.302209754087085176.844928306587
Winsorized Mean ( 19 / 20 )53.53770491803280.288278894394211185.714965469591
Winsorized Mean ( 20 / 20 )53.57049180327870.273884665829388195.595075179015
Trimmed Mean ( 1 / 20 )53.84067796610170.73151132412533473.6019746932542
Trimmed Mean ( 2 / 20 )53.78421052631580.67086144015754280.1718615899064
Trimmed Mean ( 3 / 20 )53.74727272727270.60468348592566188.8849687121774
Trimmed Mean ( 4 / 20 )53.72830188679250.56223285776098695.5623655663916
Trimmed Mean ( 5 / 20 )53.71960784313730.526654402496892102.001630648961
Trimmed Mean ( 6 / 20 )53.67959183673470.508130992336387105.641247328599
Trimmed Mean ( 7 / 20 )53.65106382978720.491903666219514109.068233302911
Trimmed Mean ( 8 / 20 )53.62444444444440.475002983037476112.892858275405
Trimmed Mean ( 9 / 20 )53.59767441860460.453624365558901118.154311117235
Trimmed Mean ( 10 / 20 )53.59756097560980.441456676946293121.410692769135
Trimmed Mean ( 11 / 20 )53.59487179487180.428850717807433124.973258920689
Trimmed Mean ( 12 / 20 )53.59189189189190.413208684677329129.696915576064
Trimmed Mean ( 13 / 20 )53.58285714285710.400891563416153133.659228660880
Trimmed Mean ( 14 / 20 )53.5696969696970.388213781713392137.990198939527
Trimmed Mean ( 15 / 20 )53.55161290322580.379271258439552141.196074607802
Trimmed Mean ( 16 / 20 )53.53103448275860.369965497268808144.691964191094
Trimmed Mean ( 17 / 20 )53.50740740740740.355017993441748150.717452061164
Trimmed Mean ( 18 / 20 )53.5080.345587422610642154.83202367664
Trimmed Mean ( 19 / 20 )53.51739130434780.335787209929584159.378885561397
Trimmed Mean ( 20 / 20 )53.51428571428570.323837533802553165.250411482302
Median53.3
Midrange55.35
Midmean - Weighted Average at Xnp53.5516129032258
Midmean - Weighted Average at X(n+1)p53.5516129032258
Midmean - Empirical Distribution Function53.5516129032258
Midmean - Empirical Distribution Function - Averaging53.5516129032258
Midmean - Empirical Distribution Function - Interpolation53.5516129032258
Midmean - Closest Observation53.45
Midmean - True Basic - Statistics Graphics Toolkit53.5516129032258
Midmean - MS Excel (old versions)53.5516129032258
Number of observations61



Parameters (Session):
par1 = grey ;
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')