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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 01 Dec 2007 09:43:38 -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/Dec/01/t1196526798jp2oe9zgb81qfzo.htm/, Retrieved Sun, 19 May 2024 17:00:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2264, Retrieved Sun, 19 May 2024 17:00:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 8, question 4, central tendency, investeringsgoederen
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 8, quest...] [2007-12-01 16:43:38] [181c187d2008ac66a37ecc12859b08c5] [Current]
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Dataseries X:
0.0693990238500725 
-0.202508879784000 
-18.0825451650144 
6.67897137919856 
14.9871944949232 
6.82249136991831 
1.20477877404993 
10.5148802743588 
5.85093737706826 
-3.73615461994183 
3.85281956420836 
-11.1862001862996 
15.0124192342109 
9.9585687417191 
0.786774498883611 
3.36539245418093 
4.4416035522114 
3.47164787845242 
2.04647126132675 
3.45954693245012 
-4.67092891436139 
-8.5989110651235 
1.58097313515991 
-2.66817956832325 
7.94842771374732 
4.84790403500832 
-8.81314695781482 
2.07410903714862 
-3.38628384324976 
4.06380361865556 
4.94898156698772 
4.04195625878557 
-11.9303577650716 
16.9273904984887 
3.70496180157471 
5.92387030376004 
-4.20185645636102 
-3.13453268699528 
5.59907399121433 
9.90827997409823 
2.64382654641493 
8.44006128237075 
-1.19528311634833 
0.314644349167505 
1.92084804404795 
3.51002113180532 
3.08440866080907 
8.05495940836078 
-1.55364521273671 




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=2264&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=2264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2264&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 Mean2.218405382269200.9751083491163682.27503475309127
Geometric MeanNaN
Harmonic Mean2.66058084324773
Quadratic Mean7.11065851246356
Winsorized Mean ( 1 / 16 )2.304879180956240.9155200012570412.51756289080692
Winsorized Mean ( 2 / 16 )2.334223378486210.9055768752286022.57760930334817
Winsorized Mean ( 3 / 16 )2.205697195297660.7913371378519372.78730403236851
Winsorized Mean ( 4 / 16 )2.177772653261060.7765632473072862.80437254893588
Winsorized Mean ( 5 / 16 )2.573455651540780.6715304569549333.8322247708766
Winsorized Mean ( 6 / 16 )2.451111214757860.6200159577290753.95330343389148
Winsorized Mean ( 7 / 16 )2.462625495102040.5944184633202944.14291555034536
Winsorized Mean ( 8 / 16 )2.502354324829160.5787478224491414.32373864361115
Winsorized Mean ( 9 / 16 )2.341789698539960.5303130965201484.4158624667324
Winsorized Mean ( 10 / 16 )2.407674010366950.5049442398049564.76819779407121
Winsorized Mean ( 11 / 16 )2.488363114073650.4245289974940785.86146795333661
Winsorized Mean ( 12 / 16 )2.558264135223840.404311817267176.32745328226044
Winsorized Mean ( 13 / 16 )2.754832320106190.343657328849168.01621874130134
Winsorized Mean ( 14 / 16 )2.646779599936900.2987101418786178.86069546648481
Winsorized Mean ( 15 / 16 )2.690912597897520.2803665551191349.5978373624275
Winsorized Mean ( 16 / 16 )2.712407999340520.23248110744016811.6672190235441
Trimmed Mean ( 1 / 16 )2.218405382269200.8622032538441042.57294944362424
Trimmed Mean ( 2 / 16 )2.337383370164180.792304355718372.95010793932201
Trimmed Mean ( 3 / 16 )2.39474331674310.7059105478170263.3924175295987
Trimmed Mean ( 4 / 16 )2.39474331674310.6571192444606173.64430556087088
Trimmed Mean ( 5 / 16 )2.561860810943940.5975844304695174.28702737273646
Trimmed Mean ( 6 / 16 )2.558789745056130.5634975824620994.54090634049568
Trimmed Mean ( 7 / 16 )2.583914735459060.5365870528186194.81546232225714
Trimmed Mean ( 8 / 16 )2.583914735459060.5082036205492835.08440835715867
Trimmed Mean ( 9 / 16 )2.630840873617760.473225492048065.55938113610875
Trimmed Mean ( 10 / 16 )2.685107186180260.4402355146074266.09925164391763
Trimmed Mean ( 11 / 16 )2.735456169938980.4006662161077046.8272693328445
Trimmed Mean ( 12 / 16 )2.779483659893160.3743519348778947.42478774899286
Trimmed Mean ( 13 / 16 )2.818758140722140.3409343899488948.26774365925558
Trimmed Mean ( 14 / 16 )2.830232005960890.3160566984828198.95482367419195
Trimmed Mean ( 15 / 16 )2.864025870228470.2952923739864549.6989496598373
Trimmed Mean ( 16 / 16 )2.864025870228470.26684185343771410.7330459346288
Median3.36539245418093
Midrange-0.57757733326285
Midmean - Weighted Average at Xnp2.65150642167753
Midmean - Weighted Average at X(n+1)p2.77948365989316
Midmean - Empirical Distribution Function2.77948365989316
Midmean - Empirical Distribution Function - Averaging2.77948365989316
Midmean - Empirical Distribution Function - Interpolation2.77948365989316
Midmean - Closest Observation2.61282485709970
Midmean - True Basic - Statistics Graphics Toolkit2.77948365989316
Midmean - MS Excel (old versions)2.77948365989316
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.21840538226920 & 0.975108349116368 & 2.27503475309127 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 2.66058084324773 &  &  \tabularnewline
Quadratic Mean & 7.11065851246356 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 2.30487918095624 & 0.915520001257041 & 2.51756289080692 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 2.33422337848621 & 0.905576875228602 & 2.57760930334817 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 2.20569719529766 & 0.791337137851937 & 2.78730403236851 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 2.17777265326106 & 0.776563247307286 & 2.80437254893588 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 2.57345565154078 & 0.671530456954933 & 3.8322247708766 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 2.45111121475786 & 0.620015957729075 & 3.95330343389148 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 2.46262549510204 & 0.594418463320294 & 4.14291555034536 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 2.50235432482916 & 0.578747822449141 & 4.32373864361115 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 2.34178969853996 & 0.530313096520148 & 4.4158624667324 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 2.40767401036695 & 0.504944239804956 & 4.76819779407121 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 2.48836311407365 & 0.424528997494078 & 5.86146795333661 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 2.55826413522384 & 0.40431181726717 & 6.32745328226044 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 2.75483232010619 & 0.34365732884916 & 8.01621874130134 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 2.64677959993690 & 0.298710141878617 & 8.86069546648481 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 2.69091259789752 & 0.280366555119134 & 9.5978373624275 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 2.71240799934052 & 0.232481107440168 & 11.6672190235441 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 2.21840538226920 & 0.862203253844104 & 2.57294944362424 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 2.33738337016418 & 0.79230435571837 & 2.95010793932201 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 2.3947433167431 & 0.705910547817026 & 3.3924175295987 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 2.3947433167431 & 0.657119244460617 & 3.64430556087088 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 2.56186081094394 & 0.597584430469517 & 4.28702737273646 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 2.55878974505613 & 0.563497582462099 & 4.54090634049568 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 2.58391473545906 & 0.536587052818619 & 4.81546232225714 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 2.58391473545906 & 0.508203620549283 & 5.08440835715867 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 2.63084087361776 & 0.47322549204806 & 5.55938113610875 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 2.68510718618026 & 0.440235514607426 & 6.09925164391763 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 2.73545616993898 & 0.400666216107704 & 6.8272693328445 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 2.77948365989316 & 0.374351934877894 & 7.42478774899286 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 2.81875814072214 & 0.340934389948894 & 8.26774365925558 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 2.83023200596089 & 0.316056698482819 & 8.95482367419195 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 2.86402587022847 & 0.295292373986454 & 9.6989496598373 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 2.86402587022847 & 0.266841853437714 & 10.7330459346288 \tabularnewline
Median & 3.36539245418093 &  &  \tabularnewline
Midrange & -0.57757733326285 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.65150642167753 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.77948365989316 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.77948365989316 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.77948365989316 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.77948365989316 &  &  \tabularnewline
Midmean - Closest Observation & 2.61282485709970 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.77948365989316 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.77948365989316 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2264&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]2.21840538226920[/C][C]0.975108349116368[/C][C]2.27503475309127[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.66058084324773[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.11065851246356[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]2.30487918095624[/C][C]0.915520001257041[/C][C]2.51756289080692[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]2.33422337848621[/C][C]0.905576875228602[/C][C]2.57760930334817[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]2.20569719529766[/C][C]0.791337137851937[/C][C]2.78730403236851[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]2.17777265326106[/C][C]0.776563247307286[/C][C]2.80437254893588[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]2.57345565154078[/C][C]0.671530456954933[/C][C]3.8322247708766[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]2.45111121475786[/C][C]0.620015957729075[/C][C]3.95330343389148[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]2.46262549510204[/C][C]0.594418463320294[/C][C]4.14291555034536[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]2.50235432482916[/C][C]0.578747822449141[/C][C]4.32373864361115[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]2.34178969853996[/C][C]0.530313096520148[/C][C]4.4158624667324[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]2.40767401036695[/C][C]0.504944239804956[/C][C]4.76819779407121[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]2.48836311407365[/C][C]0.424528997494078[/C][C]5.86146795333661[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]2.55826413522384[/C][C]0.40431181726717[/C][C]6.32745328226044[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]2.75483232010619[/C][C]0.34365732884916[/C][C]8.01621874130134[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]2.64677959993690[/C][C]0.298710141878617[/C][C]8.86069546648481[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]2.69091259789752[/C][C]0.280366555119134[/C][C]9.5978373624275[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]2.71240799934052[/C][C]0.232481107440168[/C][C]11.6672190235441[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]2.21840538226920[/C][C]0.862203253844104[/C][C]2.57294944362424[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]2.33738337016418[/C][C]0.79230435571837[/C][C]2.95010793932201[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]2.3947433167431[/C][C]0.705910547817026[/C][C]3.3924175295987[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]2.3947433167431[/C][C]0.657119244460617[/C][C]3.64430556087088[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]2.56186081094394[/C][C]0.597584430469517[/C][C]4.28702737273646[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]2.55878974505613[/C][C]0.563497582462099[/C][C]4.54090634049568[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]2.58391473545906[/C][C]0.536587052818619[/C][C]4.81546232225714[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]2.58391473545906[/C][C]0.508203620549283[/C][C]5.08440835715867[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]2.63084087361776[/C][C]0.47322549204806[/C][C]5.55938113610875[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]2.68510718618026[/C][C]0.440235514607426[/C][C]6.09925164391763[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]2.73545616993898[/C][C]0.400666216107704[/C][C]6.8272693328445[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]2.77948365989316[/C][C]0.374351934877894[/C][C]7.42478774899286[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]2.81875814072214[/C][C]0.340934389948894[/C][C]8.26774365925558[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]2.83023200596089[/C][C]0.316056698482819[/C][C]8.95482367419195[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]2.86402587022847[/C][C]0.295292373986454[/C][C]9.6989496598373[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]2.86402587022847[/C][C]0.266841853437714[/C][C]10.7330459346288[/C][/ROW]
[ROW][C]Median[/C][C]3.36539245418093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.57757733326285[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.65150642167753[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.77948365989316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.77948365989316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.77948365989316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.77948365989316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.61282485709970[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.77948365989316[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.77948365989316[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2264&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 Mean2.218405382269200.9751083491163682.27503475309127
Geometric MeanNaN
Harmonic Mean2.66058084324773
Quadratic Mean7.11065851246356
Winsorized Mean ( 1 / 16 )2.304879180956240.9155200012570412.51756289080692
Winsorized Mean ( 2 / 16 )2.334223378486210.9055768752286022.57760930334817
Winsorized Mean ( 3 / 16 )2.205697195297660.7913371378519372.78730403236851
Winsorized Mean ( 4 / 16 )2.177772653261060.7765632473072862.80437254893588
Winsorized Mean ( 5 / 16 )2.573455651540780.6715304569549333.8322247708766
Winsorized Mean ( 6 / 16 )2.451111214757860.6200159577290753.95330343389148
Winsorized Mean ( 7 / 16 )2.462625495102040.5944184633202944.14291555034536
Winsorized Mean ( 8 / 16 )2.502354324829160.5787478224491414.32373864361115
Winsorized Mean ( 9 / 16 )2.341789698539960.5303130965201484.4158624667324
Winsorized Mean ( 10 / 16 )2.407674010366950.5049442398049564.76819779407121
Winsorized Mean ( 11 / 16 )2.488363114073650.4245289974940785.86146795333661
Winsorized Mean ( 12 / 16 )2.558264135223840.404311817267176.32745328226044
Winsorized Mean ( 13 / 16 )2.754832320106190.343657328849168.01621874130134
Winsorized Mean ( 14 / 16 )2.646779599936900.2987101418786178.86069546648481
Winsorized Mean ( 15 / 16 )2.690912597897520.2803665551191349.5978373624275
Winsorized Mean ( 16 / 16 )2.712407999340520.23248110744016811.6672190235441
Trimmed Mean ( 1 / 16 )2.218405382269200.8622032538441042.57294944362424
Trimmed Mean ( 2 / 16 )2.337383370164180.792304355718372.95010793932201
Trimmed Mean ( 3 / 16 )2.39474331674310.7059105478170263.3924175295987
Trimmed Mean ( 4 / 16 )2.39474331674310.6571192444606173.64430556087088
Trimmed Mean ( 5 / 16 )2.561860810943940.5975844304695174.28702737273646
Trimmed Mean ( 6 / 16 )2.558789745056130.5634975824620994.54090634049568
Trimmed Mean ( 7 / 16 )2.583914735459060.5365870528186194.81546232225714
Trimmed Mean ( 8 / 16 )2.583914735459060.5082036205492835.08440835715867
Trimmed Mean ( 9 / 16 )2.630840873617760.473225492048065.55938113610875
Trimmed Mean ( 10 / 16 )2.685107186180260.4402355146074266.09925164391763
Trimmed Mean ( 11 / 16 )2.735456169938980.4006662161077046.8272693328445
Trimmed Mean ( 12 / 16 )2.779483659893160.3743519348778947.42478774899286
Trimmed Mean ( 13 / 16 )2.818758140722140.3409343899488948.26774365925558
Trimmed Mean ( 14 / 16 )2.830232005960890.3160566984828198.95482367419195
Trimmed Mean ( 15 / 16 )2.864025870228470.2952923739864549.6989496598373
Trimmed Mean ( 16 / 16 )2.864025870228470.26684185343771410.7330459346288
Median3.36539245418093
Midrange-0.57757733326285
Midmean - Weighted Average at Xnp2.65150642167753
Midmean - Weighted Average at X(n+1)p2.77948365989316
Midmean - Empirical Distribution Function2.77948365989316
Midmean - Empirical Distribution Function - Averaging2.77948365989316
Midmean - Empirical Distribution Function - Interpolation2.77948365989316
Midmean - Closest Observation2.61282485709970
Midmean - True Basic - Statistics Graphics Toolkit2.77948365989316
Midmean - MS Excel (old versions)2.77948365989316
Number of observations49



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')