Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 08:04:42 -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/2008/Oct/20/t1224511701kzjearng5mdub79.htm/, Retrieved Sun, 19 May 2024 16:31:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17317, Retrieved Sun, 19 May 2024 16:31:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
F    D  [Central Tendency] [Central Tendency ...] [2008-10-19 17:30:48] [5305bc6b3d76cda90639c127230e61c1]
-    D      [Central Tendency] [Central Tendency ...] [2008-10-20 14:04:42] [0fc8b84b021dde8f76b6764c606a2f06] [Current]
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Dataseries X:
72.50
59.40
85.70
88.20
62.80
87.00
79.20
79.20
40.10
69.00
59.40
73.80
57.40
81.10
46.60
41.40
71.20
67.90
72.00
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
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
78.40
36.80
50.70
42.80




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17317&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17317&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17317&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean57.49272727272732.0442624884095028.1239457255112
Geometric Mean55.5779205739757
Harmonic Mean53.7561377820046
Quadratic Mean59.4228927419238
Winsorized Mean ( 1 / 18 )57.47272727272732.0379603828807928.2011013342104
Winsorized Mean ( 2 / 18 )57.442.0228020036889328.3962542528870
Winsorized Mean ( 3 / 18 )57.24363636363641.9519458712833129.3264466017193
Winsorized Mean ( 4 / 18 )57.28727272727271.9383756164915829.5542681407443
Winsorized Mean ( 5 / 18 )57.18727272727271.8949108781144130.1793996687478
Winsorized Mean ( 6 / 18 )57.23090909090911.8875150191875030.3207701709015
Winsorized Mean ( 7 / 18 )57.23090909090911.8488596407589830.9547073391764
Winsorized Mean ( 8 / 18 )56.56181818181821.7153407469583732.9741004999230
Winsorized Mean ( 9 / 18 )56.62727272727271.6985861709386633.3378863528482
Winsorized Mean ( 10 / 18 )56.42727272727271.6556330831527934.0819915363249
Winsorized Mean ( 11 / 18 )56.54727272727271.6358007636485734.5685574819925
Winsorized Mean ( 12 / 18 )56.59090909090911.5914211778051835.5599824107889
Winsorized Mean ( 13 / 18 )56.70909090909091.5092046932885737.5754800931086
Winsorized Mean ( 14 / 18 )56.761.4760868278093738.4530224988434
Winsorized Mean ( 15 / 18 )56.37818181818181.3648588459696141.3069688375946
Winsorized Mean ( 16 / 18 )56.40727272727271.2576522795265644.8512467599607
Winsorized Mean ( 17 / 18 )56.09818181818181.1765883766815147.6786809473702
Winsorized Mean ( 18 / 18 )55.05090909090910.94918314244095857.998195110522
Trimmed Mean ( 1 / 18 )57.30377358490572.0013275025839928.6328816802441
Trimmed Mean ( 2 / 18 )57.1215686274511.9542579229005429.2292884977385
Trimmed Mean ( 3 / 18 )56.94285714285711.9041196833989929.9050829836547
Trimmed Mean ( 4 / 18 )56.82553191489361.8743866541316730.3168675415151
Trimmed Mean ( 5 / 18 )56.68444444444441.8396776055821230.8121620181967
Trimmed Mean ( 6 / 18 )56.55581395348841.8082201325896031.2770624185526
Trimmed Mean ( 7 / 18 )56.55581395348841.7669939722022132.0067950673328
Trimmed Mean ( 8 / 18 )56.23846153846151.7221374197896932.6561985659249
Trimmed Mean ( 9 / 18 )56.17837837837841.7004333272808933.0376836757319
Trimmed Mean ( 10 / 18 )56.11.6717675444538033.5572969974896
Trimmed Mean ( 11 / 18 )56.04545454545451.6409767676801934.1537160362634
Trimmed Mean ( 12 / 18 )55.96451612903231.5991163446083234.9971509688621
Trimmed Mean ( 13 / 18 )55.86551724137931.5486548736839236.0735746812892
Trimmed Mean ( 14 / 18 )55.86551724137931.4971007118128537.3158043414002
Trimmed Mean ( 15 / 18 )55.73333333333331.4252312093130739.1047662787258
Trimmed Mean ( 16 / 18 )55.44347826086961.3545535280504840.9311829416336
Trimmed Mean ( 17 / 18 )55.28571428571431.2809275975651743.16068635792
Trimmed Mean ( 18 / 18 )55.14736842105261.1912293620642646.2945006035521
Median54.5
Midrange62.5
Midmean - Weighted Average at Xnp55.3178571428571
Midmean - Weighted Average at X(n+1)p55.8655172413793
Midmean - Empirical Distribution Function55.8655172413793
Midmean - Empirical Distribution Function - Averaging55.8655172413793
Midmean - Empirical Distribution Function - Interpolation55.7333333333333
Midmean - Closest Observation55.3178571428571
Midmean - True Basic - Statistics Graphics Toolkit55.8655172413793
Midmean - MS Excel (old versions)55.8655172413793
Number of observations55

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 57.4927272727273 & 2.04426248840950 & 28.1239457255112 \tabularnewline
Geometric Mean & 55.5779205739757 &  &  \tabularnewline
Harmonic Mean & 53.7561377820046 &  &  \tabularnewline
Quadratic Mean & 59.4228927419238 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 57.4727272727273 & 2.03796038288079 & 28.2011013342104 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 57.44 & 2.02280200368893 & 28.3962542528870 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 57.2436363636364 & 1.95194587128331 & 29.3264466017193 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 57.2872727272727 & 1.93837561649158 & 29.5542681407443 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 57.1872727272727 & 1.89491087811441 & 30.1793996687478 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 57.2309090909091 & 1.88751501918750 & 30.3207701709015 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 57.2309090909091 & 1.84885964075898 & 30.9547073391764 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 56.5618181818182 & 1.71534074695837 & 32.9741004999230 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 56.6272727272727 & 1.69858617093866 & 33.3378863528482 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 56.4272727272727 & 1.65563308315279 & 34.0819915363249 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 56.5472727272727 & 1.63580076364857 & 34.5685574819925 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 56.5909090909091 & 1.59142117780518 & 35.5599824107889 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 56.7090909090909 & 1.50920469328857 & 37.5754800931086 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 56.76 & 1.47608682780937 & 38.4530224988434 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 56.3781818181818 & 1.36485884596961 & 41.3069688375946 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 56.4072727272727 & 1.25765227952656 & 44.8512467599607 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 56.0981818181818 & 1.17658837668151 & 47.6786809473702 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 55.0509090909091 & 0.949183142440958 & 57.998195110522 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 57.3037735849057 & 2.00132750258399 & 28.6328816802441 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 57.121568627451 & 1.95425792290054 & 29.2292884977385 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 56.9428571428571 & 1.90411968339899 & 29.9050829836547 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 56.8255319148936 & 1.87438665413167 & 30.3168675415151 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 56.6844444444444 & 1.83967760558212 & 30.8121620181967 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 56.5558139534884 & 1.80822013258960 & 31.2770624185526 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 56.5558139534884 & 1.76699397220221 & 32.0067950673328 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 56.2384615384615 & 1.72213741978969 & 32.6561985659249 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 56.1783783783784 & 1.70043332728089 & 33.0376836757319 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 56.1 & 1.67176754445380 & 33.5572969974896 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 56.0454545454545 & 1.64097676768019 & 34.1537160362634 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 55.9645161290323 & 1.59911634460832 & 34.9971509688621 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 55.8655172413793 & 1.54865487368392 & 36.0735746812892 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 55.8655172413793 & 1.49710071181285 & 37.3158043414002 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 55.7333333333333 & 1.42523120931307 & 39.1047662787258 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 55.4434782608696 & 1.35455352805048 & 40.9311829416336 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 55.2857142857143 & 1.28092759756517 & 43.16068635792 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 55.1473684210526 & 1.19122936206426 & 46.2945006035521 \tabularnewline
Median & 54.5 &  &  \tabularnewline
Midrange & 62.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 55.3178571428571 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 55.8655172413793 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 55.8655172413793 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 55.8655172413793 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 55.7333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 55.3178571428571 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 55.8655172413793 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 55.8655172413793 &  &  \tabularnewline
Number of observations & 55 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17317&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]57.4927272727273[/C][C]2.04426248840950[/C][C]28.1239457255112[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]55.5779205739757[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]53.7561377820046[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]59.4228927419238[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]57.4727272727273[/C][C]2.03796038288079[/C][C]28.2011013342104[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]57.44[/C][C]2.02280200368893[/C][C]28.3962542528870[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]57.2436363636364[/C][C]1.95194587128331[/C][C]29.3264466017193[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]57.2872727272727[/C][C]1.93837561649158[/C][C]29.5542681407443[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]57.1872727272727[/C][C]1.89491087811441[/C][C]30.1793996687478[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]57.2309090909091[/C][C]1.88751501918750[/C][C]30.3207701709015[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]57.2309090909091[/C][C]1.84885964075898[/C][C]30.9547073391764[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]56.5618181818182[/C][C]1.71534074695837[/C][C]32.9741004999230[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]56.6272727272727[/C][C]1.69858617093866[/C][C]33.3378863528482[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]56.4272727272727[/C][C]1.65563308315279[/C][C]34.0819915363249[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]56.5472727272727[/C][C]1.63580076364857[/C][C]34.5685574819925[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]56.5909090909091[/C][C]1.59142117780518[/C][C]35.5599824107889[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]56.7090909090909[/C][C]1.50920469328857[/C][C]37.5754800931086[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]56.76[/C][C]1.47608682780937[/C][C]38.4530224988434[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]56.3781818181818[/C][C]1.36485884596961[/C][C]41.3069688375946[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]56.4072727272727[/C][C]1.25765227952656[/C][C]44.8512467599607[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]56.0981818181818[/C][C]1.17658837668151[/C][C]47.6786809473702[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]55.0509090909091[/C][C]0.949183142440958[/C][C]57.998195110522[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]57.3037735849057[/C][C]2.00132750258399[/C][C]28.6328816802441[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]57.121568627451[/C][C]1.95425792290054[/C][C]29.2292884977385[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]56.9428571428571[/C][C]1.90411968339899[/C][C]29.9050829836547[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]56.8255319148936[/C][C]1.87438665413167[/C][C]30.3168675415151[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]56.6844444444444[/C][C]1.83967760558212[/C][C]30.8121620181967[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]56.5558139534884[/C][C]1.80822013258960[/C][C]31.2770624185526[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]56.5558139534884[/C][C]1.76699397220221[/C][C]32.0067950673328[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]56.2384615384615[/C][C]1.72213741978969[/C][C]32.6561985659249[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]56.1783783783784[/C][C]1.70043332728089[/C][C]33.0376836757319[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]56.1[/C][C]1.67176754445380[/C][C]33.5572969974896[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]56.0454545454545[/C][C]1.64097676768019[/C][C]34.1537160362634[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]55.9645161290323[/C][C]1.59911634460832[/C][C]34.9971509688621[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]55.8655172413793[/C][C]1.54865487368392[/C][C]36.0735746812892[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]55.8655172413793[/C][C]1.49710071181285[/C][C]37.3158043414002[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]55.7333333333333[/C][C]1.42523120931307[/C][C]39.1047662787258[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]55.4434782608696[/C][C]1.35455352805048[/C][C]40.9311829416336[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]55.2857142857143[/C][C]1.28092759756517[/C][C]43.16068635792[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]55.1473684210526[/C][C]1.19122936206426[/C][C]46.2945006035521[/C][/ROW]
[ROW][C]Median[/C][C]54.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]62.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]55.3178571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]55.8655172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]55.8655172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]55.8655172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]55.7333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]55.3178571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]55.8655172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]55.8655172413793[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]55[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17317&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17317&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 Mean57.49272727272732.0442624884095028.1239457255112
Geometric Mean55.5779205739757
Harmonic Mean53.7561377820046
Quadratic Mean59.4228927419238
Winsorized Mean ( 1 / 18 )57.47272727272732.0379603828807928.2011013342104
Winsorized Mean ( 2 / 18 )57.442.0228020036889328.3962542528870
Winsorized Mean ( 3 / 18 )57.24363636363641.9519458712833129.3264466017193
Winsorized Mean ( 4 / 18 )57.28727272727271.9383756164915829.5542681407443
Winsorized Mean ( 5 / 18 )57.18727272727271.8949108781144130.1793996687478
Winsorized Mean ( 6 / 18 )57.23090909090911.8875150191875030.3207701709015
Winsorized Mean ( 7 / 18 )57.23090909090911.8488596407589830.9547073391764
Winsorized Mean ( 8 / 18 )56.56181818181821.7153407469583732.9741004999230
Winsorized Mean ( 9 / 18 )56.62727272727271.6985861709386633.3378863528482
Winsorized Mean ( 10 / 18 )56.42727272727271.6556330831527934.0819915363249
Winsorized Mean ( 11 / 18 )56.54727272727271.6358007636485734.5685574819925
Winsorized Mean ( 12 / 18 )56.59090909090911.5914211778051835.5599824107889
Winsorized Mean ( 13 / 18 )56.70909090909091.5092046932885737.5754800931086
Winsorized Mean ( 14 / 18 )56.761.4760868278093738.4530224988434
Winsorized Mean ( 15 / 18 )56.37818181818181.3648588459696141.3069688375946
Winsorized Mean ( 16 / 18 )56.40727272727271.2576522795265644.8512467599607
Winsorized Mean ( 17 / 18 )56.09818181818181.1765883766815147.6786809473702
Winsorized Mean ( 18 / 18 )55.05090909090910.94918314244095857.998195110522
Trimmed Mean ( 1 / 18 )57.30377358490572.0013275025839928.6328816802441
Trimmed Mean ( 2 / 18 )57.1215686274511.9542579229005429.2292884977385
Trimmed Mean ( 3 / 18 )56.94285714285711.9041196833989929.9050829836547
Trimmed Mean ( 4 / 18 )56.82553191489361.8743866541316730.3168675415151
Trimmed Mean ( 5 / 18 )56.68444444444441.8396776055821230.8121620181967
Trimmed Mean ( 6 / 18 )56.55581395348841.8082201325896031.2770624185526
Trimmed Mean ( 7 / 18 )56.55581395348841.7669939722022132.0067950673328
Trimmed Mean ( 8 / 18 )56.23846153846151.7221374197896932.6561985659249
Trimmed Mean ( 9 / 18 )56.17837837837841.7004333272808933.0376836757319
Trimmed Mean ( 10 / 18 )56.11.6717675444538033.5572969974896
Trimmed Mean ( 11 / 18 )56.04545454545451.6409767676801934.1537160362634
Trimmed Mean ( 12 / 18 )55.96451612903231.5991163446083234.9971509688621
Trimmed Mean ( 13 / 18 )55.86551724137931.5486548736839236.0735746812892
Trimmed Mean ( 14 / 18 )55.86551724137931.4971007118128537.3158043414002
Trimmed Mean ( 15 / 18 )55.73333333333331.4252312093130739.1047662787258
Trimmed Mean ( 16 / 18 )55.44347826086961.3545535280504840.9311829416336
Trimmed Mean ( 17 / 18 )55.28571428571431.2809275975651743.16068635792
Trimmed Mean ( 18 / 18 )55.14736842105261.1912293620642646.2945006035521
Median54.5
Midrange62.5
Midmean - Weighted Average at Xnp55.3178571428571
Midmean - Weighted Average at X(n+1)p55.8655172413793
Midmean - Empirical Distribution Function55.8655172413793
Midmean - Empirical Distribution Function - Averaging55.8655172413793
Midmean - Empirical Distribution Function - Interpolation55.7333333333333
Midmean - Closest Observation55.3178571428571
Midmean - True Basic - Statistics Graphics Toolkit55.8655172413793
Midmean - MS Excel (old versions)55.8655172413793
Number of observations55



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')