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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 computationThu, 18 Oct 2007 11:09:12 -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/18/7fpyx2oc51qwahv1192730776.htm/, Retrieved Mon, 29 Apr 2024 01:50:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=910, Retrieved Mon, 29 Apr 2024 01:50:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDuurzame consumptiegoederen, Workshop 2 Question 8, Central Tendency, kim, wim, hoyi
Estimated Impact236
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 2 Questi...] [2007-10-18 18:09:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
106,7
100,6
101,2
93,1
84,2
85,8
91,8
92,4
80,3
79,7
62,5
57,1
100,8
100,7
86,2
83,2
71,7
77,5
89,8
80,3
78,7
93,8
57,6
60,6
91
85,3
77,4
77,3
68,3
69,9
81,7
75,1
69,9
84
54,3
60
89,9
77
85,3
77,6
69,2
75,5
85,7
72,2
79,9
85,3
52,2
61,2
82,4
85,4
78,2
70,2
70,2
69,3
77,5
66,1
69
75,3
58,2
59,7




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=910&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]2 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=910&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=910&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean78.051.6436927902441447.4845424055228
Geometric Mean77.0042293573295
Harmonic Mean75.9335971363904
Quadratic Mean79.0645580101055
Winsorized Mean ( 1 / 20 )77.99333333333331.6098967694502248.446170470898
Winsorized Mean ( 2 / 20 )78.07333333333331.5845277088974049.272305492001
Winsorized Mean ( 3 / 20 )78.09333333333331.5777565182515149.4964415801479
Winsorized Mean ( 4 / 20 )78.12666666666671.5674241467273249.8439856434456
Winsorized Mean ( 5 / 20 )77.6851.4162890656621454.8510907013754
Winsorized Mean ( 6 / 20 )77.6451.3965320748762655.5984365821886
Winsorized Mean ( 7 / 20 )77.63333333333331.3665012990760956.8117523092164
Winsorized Mean ( 8 / 20 )77.63333333333331.3351837442408958.144306855287
Winsorized Mean ( 9 / 20 )77.70833333333331.2736914003900261.0103305318211
Winsorized Mean ( 10 / 20 )78.1251.1258107561917669.3944338072152
Winsorized Mean ( 11 / 20 )78.511.0527491586130374.5761697909449
Winsorized Mean ( 12 / 20 )77.930.90783563309839585.8415302933517
Winsorized Mean ( 13 / 20 )77.88666666666670.887386394946487.7708595829567
Winsorized Mean ( 14 / 20 )77.88666666666670.88000214004191188.507360519552
Winsorized Mean ( 15 / 20 )77.96166666666670.84420956132200792.3487132088163
Winsorized Mean ( 16 / 20 )77.9350.84023747315829492.7535399094462
Winsorized Mean ( 17 / 20 )78.020.82653315852837594.3942771018563
Winsorized Mean ( 18 / 20 )78.020.82653315852837594.3942771018563
Winsorized Mean ( 19 / 20 )78.14666666666670.699699155152613111.686095504320
Winsorized Mean ( 20 / 20 )78.24666666666670.664037754468598117.83466548417
Trimmed Mean ( 1 / 20 )78.0017241379311.5628523634229549.9098481491191
Trimmed Mean ( 2 / 20 )78.01071428571431.5048615558953851.8391303041152
Trimmed Mean ( 3 / 20 )77.97592592592591.4501161070292753.7721948938755
Trimmed Mean ( 4 / 20 )77.93076923076921.3849343942881256.2703688724744
Trimmed Mean ( 5 / 20 )77.8721.3066987223612159.5944563711559
Trimmed Mean ( 6 / 20 )77.918751.2630968368409461.6886589589427
Trimmed Mean ( 7 / 20 )77.97826086956521.2133592649063564.2664239066765
Trimmed Mean ( 8 / 20 )78.04545454545451.1580559571308567.3935089793215
Trimmed Mean ( 9 / 20 )78.11904761904761.0948524797093271.3512085571456
Trimmed Mean ( 10 / 20 )78.18751.0297198243535375.9308485190007
Trimmed Mean ( 11 / 20 )78.19736842105260.98740638205861879.1947164226557
Trimmed Mean ( 12 / 20 )78.150.95041761915152482.2270109741523
Trimmed Mean ( 13 / 20 )78.18235294117650.9391416283009583.2487354251566
Trimmed Mean ( 14 / 20 )78.2250.92611092835194684.4661234472254
Trimmed Mean ( 15 / 20 )78.27333333333330.90669202128172486.3284682076325
Trimmed Mean ( 16 / 20 )78.31785714285720.88660003287376588.3350487694017
Trimmed Mean ( 17 / 20 )78.3730769230770.85446443311329391.7218714856508
Trimmed Mean ( 18 / 20 )78.4250.80726434619502597.1490941841416
Trimmed Mean ( 19 / 20 )78.48636363636360.727811623936464107.838843259826
Trimmed Mean ( 20 / 20 )78.540.660876610825986118.842154062372
Median77.9
Midrange79.45
Midmean - Weighted Average at Xnp77.983870967742
Midmean - Weighted Average at X(n+1)p78.2733333333334
Midmean - Empirical Distribution Function77.983870967742
Midmean - Empirical Distribution Function - Averaging78.2733333333334
Midmean - Empirical Distribution Function - Interpolation78.2733333333334
Midmean - Closest Observation77.983870967742
Midmean - True Basic - Statistics Graphics Toolkit78.2733333333334
Midmean - MS Excel (old versions)78.225
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 78.05 & 1.64369279024414 & 47.4845424055228 \tabularnewline
Geometric Mean & 77.0042293573295 &  &  \tabularnewline
Harmonic Mean & 75.9335971363904 &  &  \tabularnewline
Quadratic Mean & 79.0645580101055 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 77.9933333333333 & 1.60989676945022 & 48.446170470898 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 78.0733333333333 & 1.58452770889740 & 49.272305492001 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 78.0933333333333 & 1.57775651825151 & 49.4964415801479 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 78.1266666666667 & 1.56742414672732 & 49.8439856434456 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 77.685 & 1.41628906566214 & 54.8510907013754 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 77.645 & 1.39653207487626 & 55.5984365821886 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 77.6333333333333 & 1.36650129907609 & 56.8117523092164 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 77.6333333333333 & 1.33518374424089 & 58.144306855287 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 77.7083333333333 & 1.27369140039002 & 61.0103305318211 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 78.125 & 1.12581075619176 & 69.3944338072152 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 78.51 & 1.05274915861303 & 74.5761697909449 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 77.93 & 0.907835633098395 & 85.8415302933517 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 77.8866666666667 & 0.8873863949464 & 87.7708595829567 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 77.8866666666667 & 0.880002140041911 & 88.507360519552 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 77.9616666666667 & 0.844209561322007 & 92.3487132088163 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 77.935 & 0.840237473158294 & 92.7535399094462 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 78.02 & 0.826533158528375 & 94.3942771018563 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 78.02 & 0.826533158528375 & 94.3942771018563 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 78.1466666666667 & 0.699699155152613 & 111.686095504320 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 78.2466666666667 & 0.664037754468598 & 117.83466548417 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 78.001724137931 & 1.56285236342295 & 49.9098481491191 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 78.0107142857143 & 1.50486155589538 & 51.8391303041152 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 77.9759259259259 & 1.45011610702927 & 53.7721948938755 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 77.9307692307692 & 1.38493439428812 & 56.2703688724744 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 77.872 & 1.30669872236121 & 59.5944563711559 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 77.91875 & 1.26309683684094 & 61.6886589589427 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 77.9782608695652 & 1.21335926490635 & 64.2664239066765 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 78.0454545454545 & 1.15805595713085 & 67.3935089793215 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 78.1190476190476 & 1.09485247970932 & 71.3512085571456 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 78.1875 & 1.02971982435353 & 75.9308485190007 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 78.1973684210526 & 0.987406382058618 & 79.1947164226557 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 78.15 & 0.950417619151524 & 82.2270109741523 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 78.1823529411765 & 0.93914162830095 & 83.2487354251566 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 78.225 & 0.926110928351946 & 84.4661234472254 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 78.2733333333333 & 0.906692021281724 & 86.3284682076325 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 78.3178571428572 & 0.886600032873765 & 88.3350487694017 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 78.373076923077 & 0.854464433113293 & 91.7218714856508 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 78.425 & 0.807264346195025 & 97.1490941841416 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 78.4863636363636 & 0.727811623936464 & 107.838843259826 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 78.54 & 0.660876610825986 & 118.842154062372 \tabularnewline
Median & 77.9 &  &  \tabularnewline
Midrange & 79.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 77.983870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 78.2733333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 77.983870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 78.2733333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 78.2733333333334 &  &  \tabularnewline
Midmean - Closest Observation & 77.983870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 78.2733333333334 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 78.225 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=910&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]78.05[/C][C]1.64369279024414[/C][C]47.4845424055228[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]77.0042293573295[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]75.9335971363904[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]79.0645580101055[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]77.9933333333333[/C][C]1.60989676945022[/C][C]48.446170470898[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]78.0733333333333[/C][C]1.58452770889740[/C][C]49.272305492001[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]78.0933333333333[/C][C]1.57775651825151[/C][C]49.4964415801479[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]78.1266666666667[/C][C]1.56742414672732[/C][C]49.8439856434456[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]77.685[/C][C]1.41628906566214[/C][C]54.8510907013754[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]77.645[/C][C]1.39653207487626[/C][C]55.5984365821886[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]77.6333333333333[/C][C]1.36650129907609[/C][C]56.8117523092164[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]77.6333333333333[/C][C]1.33518374424089[/C][C]58.144306855287[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]77.7083333333333[/C][C]1.27369140039002[/C][C]61.0103305318211[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]78.125[/C][C]1.12581075619176[/C][C]69.3944338072152[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]78.51[/C][C]1.05274915861303[/C][C]74.5761697909449[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]77.93[/C][C]0.907835633098395[/C][C]85.8415302933517[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]77.8866666666667[/C][C]0.8873863949464[/C][C]87.7708595829567[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]77.8866666666667[/C][C]0.880002140041911[/C][C]88.507360519552[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]77.9616666666667[/C][C]0.844209561322007[/C][C]92.3487132088163[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]77.935[/C][C]0.840237473158294[/C][C]92.7535399094462[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]78.02[/C][C]0.826533158528375[/C][C]94.3942771018563[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]78.02[/C][C]0.826533158528375[/C][C]94.3942771018563[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]78.1466666666667[/C][C]0.699699155152613[/C][C]111.686095504320[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]78.2466666666667[/C][C]0.664037754468598[/C][C]117.83466548417[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]78.001724137931[/C][C]1.56285236342295[/C][C]49.9098481491191[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]78.0107142857143[/C][C]1.50486155589538[/C][C]51.8391303041152[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]77.9759259259259[/C][C]1.45011610702927[/C][C]53.7721948938755[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]77.9307692307692[/C][C]1.38493439428812[/C][C]56.2703688724744[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]77.872[/C][C]1.30669872236121[/C][C]59.5944563711559[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]77.91875[/C][C]1.26309683684094[/C][C]61.6886589589427[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]77.9782608695652[/C][C]1.21335926490635[/C][C]64.2664239066765[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]78.0454545454545[/C][C]1.15805595713085[/C][C]67.3935089793215[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]78.1190476190476[/C][C]1.09485247970932[/C][C]71.3512085571456[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]78.1875[/C][C]1.02971982435353[/C][C]75.9308485190007[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]78.1973684210526[/C][C]0.987406382058618[/C][C]79.1947164226557[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]78.15[/C][C]0.950417619151524[/C][C]82.2270109741523[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]78.1823529411765[/C][C]0.93914162830095[/C][C]83.2487354251566[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]78.225[/C][C]0.926110928351946[/C][C]84.4661234472254[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]78.2733333333333[/C][C]0.906692021281724[/C][C]86.3284682076325[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]78.3178571428572[/C][C]0.886600032873765[/C][C]88.3350487694017[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]78.373076923077[/C][C]0.854464433113293[/C][C]91.7218714856508[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]78.425[/C][C]0.807264346195025[/C][C]97.1490941841416[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]78.4863636363636[/C][C]0.727811623936464[/C][C]107.838843259826[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]78.54[/C][C]0.660876610825986[/C][C]118.842154062372[/C][/ROW]
[ROW][C]Median[/C][C]77.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]79.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]77.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]78.2733333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]77.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]78.2733333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]78.2733333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]77.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]78.2733333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]78.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=910&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=910&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 Mean78.051.6436927902441447.4845424055228
Geometric Mean77.0042293573295
Harmonic Mean75.9335971363904
Quadratic Mean79.0645580101055
Winsorized Mean ( 1 / 20 )77.99333333333331.6098967694502248.446170470898
Winsorized Mean ( 2 / 20 )78.07333333333331.5845277088974049.272305492001
Winsorized Mean ( 3 / 20 )78.09333333333331.5777565182515149.4964415801479
Winsorized Mean ( 4 / 20 )78.12666666666671.5674241467273249.8439856434456
Winsorized Mean ( 5 / 20 )77.6851.4162890656621454.8510907013754
Winsorized Mean ( 6 / 20 )77.6451.3965320748762655.5984365821886
Winsorized Mean ( 7 / 20 )77.63333333333331.3665012990760956.8117523092164
Winsorized Mean ( 8 / 20 )77.63333333333331.3351837442408958.144306855287
Winsorized Mean ( 9 / 20 )77.70833333333331.2736914003900261.0103305318211
Winsorized Mean ( 10 / 20 )78.1251.1258107561917669.3944338072152
Winsorized Mean ( 11 / 20 )78.511.0527491586130374.5761697909449
Winsorized Mean ( 12 / 20 )77.930.90783563309839585.8415302933517
Winsorized Mean ( 13 / 20 )77.88666666666670.887386394946487.7708595829567
Winsorized Mean ( 14 / 20 )77.88666666666670.88000214004191188.507360519552
Winsorized Mean ( 15 / 20 )77.96166666666670.84420956132200792.3487132088163
Winsorized Mean ( 16 / 20 )77.9350.84023747315829492.7535399094462
Winsorized Mean ( 17 / 20 )78.020.82653315852837594.3942771018563
Winsorized Mean ( 18 / 20 )78.020.82653315852837594.3942771018563
Winsorized Mean ( 19 / 20 )78.14666666666670.699699155152613111.686095504320
Winsorized Mean ( 20 / 20 )78.24666666666670.664037754468598117.83466548417
Trimmed Mean ( 1 / 20 )78.0017241379311.5628523634229549.9098481491191
Trimmed Mean ( 2 / 20 )78.01071428571431.5048615558953851.8391303041152
Trimmed Mean ( 3 / 20 )77.97592592592591.4501161070292753.7721948938755
Trimmed Mean ( 4 / 20 )77.93076923076921.3849343942881256.2703688724744
Trimmed Mean ( 5 / 20 )77.8721.3066987223612159.5944563711559
Trimmed Mean ( 6 / 20 )77.918751.2630968368409461.6886589589427
Trimmed Mean ( 7 / 20 )77.97826086956521.2133592649063564.2664239066765
Trimmed Mean ( 8 / 20 )78.04545454545451.1580559571308567.3935089793215
Trimmed Mean ( 9 / 20 )78.11904761904761.0948524797093271.3512085571456
Trimmed Mean ( 10 / 20 )78.18751.0297198243535375.9308485190007
Trimmed Mean ( 11 / 20 )78.19736842105260.98740638205861879.1947164226557
Trimmed Mean ( 12 / 20 )78.150.95041761915152482.2270109741523
Trimmed Mean ( 13 / 20 )78.18235294117650.9391416283009583.2487354251566
Trimmed Mean ( 14 / 20 )78.2250.92611092835194684.4661234472254
Trimmed Mean ( 15 / 20 )78.27333333333330.90669202128172486.3284682076325
Trimmed Mean ( 16 / 20 )78.31785714285720.88660003287376588.3350487694017
Trimmed Mean ( 17 / 20 )78.3730769230770.85446443311329391.7218714856508
Trimmed Mean ( 18 / 20 )78.4250.80726434619502597.1490941841416
Trimmed Mean ( 19 / 20 )78.48636363636360.727811623936464107.838843259826
Trimmed Mean ( 20 / 20 )78.540.660876610825986118.842154062372
Median77.9
Midrange79.45
Midmean - Weighted Average at Xnp77.983870967742
Midmean - Weighted Average at X(n+1)p78.2733333333334
Midmean - Empirical Distribution Function77.983870967742
Midmean - Empirical Distribution Function - Averaging78.2733333333334
Midmean - Empirical Distribution Function - Interpolation78.2733333333334
Midmean - Closest Observation77.983870967742
Midmean - True Basic - Statistics Graphics Toolkit78.2733333333334
Midmean - MS Excel (old versions)78.225
Number of observations60



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')