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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 19 Oct 2007 04:35:27 -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/2007/Oct/19/43pqf84ubmf2jal1192793806.htm/, Retrieved Thu, 31 Oct 2024 23:11:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1007, Retrieved Thu, 31 Oct 2024 23:11:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsaurelie
Estimated Impact255
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 2 ] [2007-10-19 11:35:27] [a2659e9a411aa0bcc5ca303430cc5df1] [Current]
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Dataseries X:
72,50
59,40
85,70
88,20
62,80
87,00
79,20
112,00
79,20
132,10
40,10
69,00
59,40
73,80
57,40
81,10
46,60
41,40
71,20
67,90
72,00
145,50
39,70
51,90
73,70
70,90
60,80
61,00
54,50
39,10
66,60
58,50
59,80
80,90
37,30
44,60
48,70
54,00
49,50
61,60
35,00
35,70
51,30
49,00
41,50
72,50
42,10
44,10
45,10
50,30
40,90
47,20
36,90
40,90
38,30
46,30
28,40
78,40
36,80
50,70
42,80




Summary of compuational 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 compuational 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=1007&T=0

[TABLE]
[ROW][C]Summary of compuational 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=1007&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1007&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 compuational 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 Mean59.84918032786892.8716977927431720.8410440956248
Geometric Mean56.4524800704516
Harmonic Mean53.5884811561598
Quadratic Mean63.8492230077119
Winsorized Mean ( 1 / 20 )59.73770491803282.7507834591232221.7166148501829
Winsorized Mean ( 2 / 20 )59.10163934426232.4844681367291323.7884473020738
Winsorized Mean ( 3 / 20 )57.98524590163932.1239099886065327.3011785869903
Winsorized Mean ( 4 / 20 )57.91311475409842.1044260869047027.5196715695918
Winsorized Mean ( 5 / 20 )57.83934426229512.0747931343173827.8771619712944
Winsorized Mean ( 6 / 20 )57.48524590163931.9625159998172429.2916062376015
Winsorized Mean ( 7 / 20 )57.55409836065571.9431715579597929.6186397566893
Winsorized Mean ( 8 / 20 )57.40983606557381.8869999680269030.4238670049386
Winsorized Mean ( 9 / 20 )57.46885245901641.8778352566922730.603777543428
Winsorized Mean ( 10 / 20 )57.46885245901641.8327120770288731.3572727431267
Winsorized Mean ( 11 / 20 )56.63934426229511.6829168646018533.655461807791
Winsorized Mean ( 12 / 20 )56.71803278688521.6643620813053334.0779409864964
Winsorized Mean ( 13 / 20 )56.4836065573771.618236543274334.9044191296592
Winsorized Mean ( 14 / 20 )56.62131147540981.5971766667051035.4508756956843
Winsorized Mean ( 15 / 20 )56.67049180327871.5509900667720836.5382686951834
Winsorized Mean ( 16 / 20 )56.80163934426231.4664899765712838.733056653457
Winsorized Mean ( 17 / 20 )56.85737704918031.4328283371728239.6819183248206
Winsorized Mean ( 18 / 20 )56.4442622950821.3215211565311342.7115843103436
Winsorized Mean ( 19 / 20 )56.47540983606561.2146704690135046.4944289638756
Winsorized Mean ( 20 / 20 )56.14754098360661.1347602875275549.4796492270122
Trimmed Mean ( 1 / 20 )58.93050847457632.5244465217177423.343932211516
Trimmed Mean ( 2 / 20 )58.06666666666672.2275647454273926.0673306066018
Trimmed Mean ( 3 / 20 )57.49272727272732.0442624884095028.1239457255112
Trimmed Mean ( 4 / 20 )57.30377358490572.0013275025839928.6328816802441
Trimmed Mean ( 5 / 20 )57.1215686274511.9542579229005429.2292884977385
Trimmed Mean ( 6 / 20 )56.94285714285711.9041196833989929.9050829836547
Trimmed Mean ( 7 / 20 )56.82553191489361.8743866541316730.3168675415151
Trimmed Mean ( 8 / 20 )56.68444444444441.8396776055821230.8121620181967
Trimmed Mean ( 9 / 20 )56.55581395348841.8082201325896031.2770624185526
Trimmed Mean ( 10 / 20 )56.40487804878051.7669939722022131.9213754750295
Trimmed Mean ( 11 / 20 )56.23846153846151.7221374197896932.6561985659249
Trimmed Mean ( 12 / 20 )56.17837837837841.7004333272808933.0376836757319
Trimmed Mean ( 13 / 20 )56.11.6717675444538033.5572969974896
Trimmed Mean ( 14 / 20 )56.04545454545451.6409767676801934.1537160362634
Trimmed Mean ( 15 / 20 )55.96451612903231.5991163446083234.9971509688621
Trimmed Mean ( 16 / 20 )55.86551724137931.5486548736839236.0735746812892
Trimmed Mean ( 17 / 20 )55.73333333333331.4971007118128537.2275110776251
Trimmed Mean ( 18 / 20 )55.5721.4252312093130738.9915682710768
Trimmed Mean ( 19 / 20 )55.44347826086961.3545535280504840.9311829416336
Trimmed Mean ( 20 / 20 )55.28571428571431.2809275975651743.16068635792
Median54.5
Midrange86.95
Midmean - Weighted Average at Xnp55.43
Midmean - Weighted Average at X(n+1)p55.9645161290323
Midmean - Empirical Distribution Function55.9645161290323
Midmean - Empirical Distribution Function - Averaging55.9645161290323
Midmean - Empirical Distribution Function - Interpolation55.9645161290323
Midmean - Closest Observation55.53125
Midmean - True Basic - Statistics Graphics Toolkit55.9645161290323
Midmean - MS Excel (old versions)55.9645161290323
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 59.8491803278689 & 2.87169779274317 & 20.8410440956248 \tabularnewline
Geometric Mean & 56.4524800704516 &  &  \tabularnewline
Harmonic Mean & 53.5884811561598 &  &  \tabularnewline
Quadratic Mean & 63.8492230077119 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 59.7377049180328 & 2.75078345912322 & 21.7166148501829 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 59.1016393442623 & 2.48446813672913 & 23.7884473020738 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 57.9852459016393 & 2.12390998860653 & 27.3011785869903 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 57.9131147540984 & 2.10442608690470 & 27.5196715695918 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 57.8393442622951 & 2.07479313431738 & 27.8771619712944 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 57.4852459016393 & 1.96251599981724 & 29.2916062376015 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 57.5540983606557 & 1.94317155795979 & 29.6186397566893 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 57.4098360655738 & 1.88699996802690 & 30.4238670049386 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 57.4688524590164 & 1.87783525669227 & 30.603777543428 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 57.4688524590164 & 1.83271207702887 & 31.3572727431267 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 56.6393442622951 & 1.68291686460185 & 33.655461807791 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 56.7180327868852 & 1.66436208130533 & 34.0779409864964 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 56.483606557377 & 1.6182365432743 & 34.9044191296592 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 56.6213114754098 & 1.59717666670510 & 35.4508756956843 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 56.6704918032787 & 1.55099006677208 & 36.5382686951834 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 56.8016393442623 & 1.46648997657128 & 38.733056653457 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 56.8573770491803 & 1.43282833717282 & 39.6819183248206 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 56.444262295082 & 1.32152115653113 & 42.7115843103436 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 56.4754098360656 & 1.21467046901350 & 46.4944289638756 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 56.1475409836066 & 1.13476028752755 & 49.4796492270122 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 58.9305084745763 & 2.52444652171774 & 23.343932211516 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 58.0666666666667 & 2.22756474542739 & 26.0673306066018 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 57.4927272727273 & 2.04426248840950 & 28.1239457255112 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 57.3037735849057 & 2.00132750258399 & 28.6328816802441 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 57.121568627451 & 1.95425792290054 & 29.2292884977385 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 56.9428571428571 & 1.90411968339899 & 29.9050829836547 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 56.8255319148936 & 1.87438665413167 & 30.3168675415151 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 56.6844444444444 & 1.83967760558212 & 30.8121620181967 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 56.5558139534884 & 1.80822013258960 & 31.2770624185526 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 56.4048780487805 & 1.76699397220221 & 31.9213754750295 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 56.2384615384615 & 1.72213741978969 & 32.6561985659249 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 56.1783783783784 & 1.70043332728089 & 33.0376836757319 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 56.1 & 1.67176754445380 & 33.5572969974896 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 56.0454545454545 & 1.64097676768019 & 34.1537160362634 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 55.9645161290323 & 1.59911634460832 & 34.9971509688621 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 55.8655172413793 & 1.54865487368392 & 36.0735746812892 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 55.7333333333333 & 1.49710071181285 & 37.2275110776251 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 55.572 & 1.42523120931307 & 38.9915682710768 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 55.4434782608696 & 1.35455352805048 & 40.9311829416336 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 55.2857142857143 & 1.28092759756517 & 43.16068635792 \tabularnewline
Median & 54.5 &  &  \tabularnewline
Midrange & 86.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 55.43 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 55.9645161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 55.9645161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 55.9645161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 55.9645161290323 &  &  \tabularnewline
Midmean - Closest Observation & 55.53125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 55.9645161290323 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 55.9645161290323 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1007&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]59.8491803278689[/C][C]2.87169779274317[/C][C]20.8410440956248[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]56.4524800704516[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]53.5884811561598[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]63.8492230077119[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]59.7377049180328[/C][C]2.75078345912322[/C][C]21.7166148501829[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]59.1016393442623[/C][C]2.48446813672913[/C][C]23.7884473020738[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]57.9852459016393[/C][C]2.12390998860653[/C][C]27.3011785869903[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]57.9131147540984[/C][C]2.10442608690470[/C][C]27.5196715695918[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]57.8393442622951[/C][C]2.07479313431738[/C][C]27.8771619712944[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]57.4852459016393[/C][C]1.96251599981724[/C][C]29.2916062376015[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]57.5540983606557[/C][C]1.94317155795979[/C][C]29.6186397566893[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]57.4098360655738[/C][C]1.88699996802690[/C][C]30.4238670049386[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]57.4688524590164[/C][C]1.87783525669227[/C][C]30.603777543428[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]57.4688524590164[/C][C]1.83271207702887[/C][C]31.3572727431267[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]56.6393442622951[/C][C]1.68291686460185[/C][C]33.655461807791[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]56.7180327868852[/C][C]1.66436208130533[/C][C]34.0779409864964[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]56.483606557377[/C][C]1.6182365432743[/C][C]34.9044191296592[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]56.6213114754098[/C][C]1.59717666670510[/C][C]35.4508756956843[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]56.6704918032787[/C][C]1.55099006677208[/C][C]36.5382686951834[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]56.8016393442623[/C][C]1.46648997657128[/C][C]38.733056653457[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]56.8573770491803[/C][C]1.43282833717282[/C][C]39.6819183248206[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]56.444262295082[/C][C]1.32152115653113[/C][C]42.7115843103436[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]56.4754098360656[/C][C]1.21467046901350[/C][C]46.4944289638756[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]56.1475409836066[/C][C]1.13476028752755[/C][C]49.4796492270122[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]58.9305084745763[/C][C]2.52444652171774[/C][C]23.343932211516[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]58.0666666666667[/C][C]2.22756474542739[/C][C]26.0673306066018[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]57.4927272727273[/C][C]2.04426248840950[/C][C]28.1239457255112[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]57.3037735849057[/C][C]2.00132750258399[/C][C]28.6328816802441[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]57.121568627451[/C][C]1.95425792290054[/C][C]29.2292884977385[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]56.9428571428571[/C][C]1.90411968339899[/C][C]29.9050829836547[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]56.8255319148936[/C][C]1.87438665413167[/C][C]30.3168675415151[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]56.6844444444444[/C][C]1.83967760558212[/C][C]30.8121620181967[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]56.5558139534884[/C][C]1.80822013258960[/C][C]31.2770624185526[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]56.4048780487805[/C][C]1.76699397220221[/C][C]31.9213754750295[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]56.2384615384615[/C][C]1.72213741978969[/C][C]32.6561985659249[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]56.1783783783784[/C][C]1.70043332728089[/C][C]33.0376836757319[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]56.1[/C][C]1.67176754445380[/C][C]33.5572969974896[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]56.0454545454545[/C][C]1.64097676768019[/C][C]34.1537160362634[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]55.9645161290323[/C][C]1.59911634460832[/C][C]34.9971509688621[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]55.8655172413793[/C][C]1.54865487368392[/C][C]36.0735746812892[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]55.7333333333333[/C][C]1.49710071181285[/C][C]37.2275110776251[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]55.572[/C][C]1.42523120931307[/C][C]38.9915682710768[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]55.4434782608696[/C][C]1.35455352805048[/C][C]40.9311829416336[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]55.2857142857143[/C][C]1.28092759756517[/C][C]43.16068635792[/C][/ROW]
[ROW][C]Median[/C][C]54.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]86.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]55.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]55.9645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]55.9645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]55.9645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]55.9645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]55.53125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]55.9645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]55.9645161290323[/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=1007&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1007&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 Mean59.84918032786892.8716977927431720.8410440956248
Geometric Mean56.4524800704516
Harmonic Mean53.5884811561598
Quadratic Mean63.8492230077119
Winsorized Mean ( 1 / 20 )59.73770491803282.7507834591232221.7166148501829
Winsorized Mean ( 2 / 20 )59.10163934426232.4844681367291323.7884473020738
Winsorized Mean ( 3 / 20 )57.98524590163932.1239099886065327.3011785869903
Winsorized Mean ( 4 / 20 )57.91311475409842.1044260869047027.5196715695918
Winsorized Mean ( 5 / 20 )57.83934426229512.0747931343173827.8771619712944
Winsorized Mean ( 6 / 20 )57.48524590163931.9625159998172429.2916062376015
Winsorized Mean ( 7 / 20 )57.55409836065571.9431715579597929.6186397566893
Winsorized Mean ( 8 / 20 )57.40983606557381.8869999680269030.4238670049386
Winsorized Mean ( 9 / 20 )57.46885245901641.8778352566922730.603777543428
Winsorized Mean ( 10 / 20 )57.46885245901641.8327120770288731.3572727431267
Winsorized Mean ( 11 / 20 )56.63934426229511.6829168646018533.655461807791
Winsorized Mean ( 12 / 20 )56.71803278688521.6643620813053334.0779409864964
Winsorized Mean ( 13 / 20 )56.4836065573771.618236543274334.9044191296592
Winsorized Mean ( 14 / 20 )56.62131147540981.5971766667051035.4508756956843
Winsorized Mean ( 15 / 20 )56.67049180327871.5509900667720836.5382686951834
Winsorized Mean ( 16 / 20 )56.80163934426231.4664899765712838.733056653457
Winsorized Mean ( 17 / 20 )56.85737704918031.4328283371728239.6819183248206
Winsorized Mean ( 18 / 20 )56.4442622950821.3215211565311342.7115843103436
Winsorized Mean ( 19 / 20 )56.47540983606561.2146704690135046.4944289638756
Winsorized Mean ( 20 / 20 )56.14754098360661.1347602875275549.4796492270122
Trimmed Mean ( 1 / 20 )58.93050847457632.5244465217177423.343932211516
Trimmed Mean ( 2 / 20 )58.06666666666672.2275647454273926.0673306066018
Trimmed Mean ( 3 / 20 )57.49272727272732.0442624884095028.1239457255112
Trimmed Mean ( 4 / 20 )57.30377358490572.0013275025839928.6328816802441
Trimmed Mean ( 5 / 20 )57.1215686274511.9542579229005429.2292884977385
Trimmed Mean ( 6 / 20 )56.94285714285711.9041196833989929.9050829836547
Trimmed Mean ( 7 / 20 )56.82553191489361.8743866541316730.3168675415151
Trimmed Mean ( 8 / 20 )56.68444444444441.8396776055821230.8121620181967
Trimmed Mean ( 9 / 20 )56.55581395348841.8082201325896031.2770624185526
Trimmed Mean ( 10 / 20 )56.40487804878051.7669939722022131.9213754750295
Trimmed Mean ( 11 / 20 )56.23846153846151.7221374197896932.6561985659249
Trimmed Mean ( 12 / 20 )56.17837837837841.7004333272808933.0376836757319
Trimmed Mean ( 13 / 20 )56.11.6717675444538033.5572969974896
Trimmed Mean ( 14 / 20 )56.04545454545451.6409767676801934.1537160362634
Trimmed Mean ( 15 / 20 )55.96451612903231.5991163446083234.9971509688621
Trimmed Mean ( 16 / 20 )55.86551724137931.5486548736839236.0735746812892
Trimmed Mean ( 17 / 20 )55.73333333333331.4971007118128537.2275110776251
Trimmed Mean ( 18 / 20 )55.5721.4252312093130738.9915682710768
Trimmed Mean ( 19 / 20 )55.44347826086961.3545535280504840.9311829416336
Trimmed Mean ( 20 / 20 )55.28571428571431.2809275975651743.16068635792
Median54.5
Midrange86.95
Midmean - Weighted Average at Xnp55.43
Midmean - Weighted Average at X(n+1)p55.9645161290323
Midmean - Empirical Distribution Function55.9645161290323
Midmean - Empirical Distribution Function - Averaging55.9645161290323
Midmean - Empirical Distribution Function - Interpolation55.9645161290323
Midmean - Closest Observation55.53125
Midmean - True Basic - Statistics Graphics Toolkit55.9645161290323
Midmean - MS Excel (old versions)55.9645161290323
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')