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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 11:04:11 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444385082t5y429mjaotcf91.htm/, Retrieved Tue, 14 May 2024 10:20:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281793, Retrieved Tue, 14 May 2024 10:20:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 10:04:11] [9ae86903c100cf8412a224b1f49cfd85] [Current]
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Dataseries X:
91,04
91,37
91,36
91,4
91,54
91,57
91,57
91,47
91,55
91,71
91,71
92,12
93,28
94,02
94,26
94,19
94,34
94,62
94,9
96,08
96,85
96,61
96,47
96,68
96,43
96,35
96,14
95,39
95,08
94,86
94,8
95,62
96,35
96,77
96,97
96,78
97,71
98,04
98,41
100,05
100,9
100,61
100,71
100,06
100,57
101,03
100,93
100,98
100,46
101,52
101,29
101,84
102,03
101,72
102,23
102,38
102,5
101,5
101,96
101,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281793&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281793&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.88816666666670.485308247997484199.642530425671
Geometric Mean96.8163314772871
Harmonic Mean96.7444150449421
Quadratic Mean96.9598512873584
Winsorized Mean ( 1 / 20 )96.89150.483858597790064200.247552575348
Winsorized Mean ( 2 / 20 )96.88683333333330.4828444727238200.658470390641
Winsorized Mean ( 3 / 20 )96.87833333333330.480708291371802201.532478370345
Winsorized Mean ( 4 / 20 )96.87833333333330.478967590677094202.264903135473
Winsorized Mean ( 5 / 20 )96.87416666666670.476072342439051203.486231042857
Winsorized Mean ( 6 / 20 )96.86316666666670.473779042856577204.447976598216
Winsorized Mean ( 7 / 20 )96.85266666666670.471122404636692205.57856241491
Winsorized Mean ( 8 / 20 )96.84066666666670.469081014449275206.447636300869
Winsorized Mean ( 9 / 20 )96.85866666666670.464601430951504208.476901305061
Winsorized Mean ( 10 / 20 )96.82366666666670.458750080691917211.059726726654
Winsorized Mean ( 11 / 20 )96.85116666666670.436949304204097221.653097361217
Winsorized Mean ( 12 / 20 )97.07316666666670.39501244288967245.747111044246
Winsorized Mean ( 13 / 20 )97.22266666666670.368273638335725263.995726400696
Winsorized Mean ( 14 / 20 )97.25533333333330.361301982295346269.180181950488
Winsorized Mean ( 15 / 20 )97.22533333333330.350728738249768277.2094862215
Winsorized Mean ( 16 / 20 )97.220.343205313195541283.270672865746
Winsorized Mean ( 17 / 20 )97.2880.330224525570308294.611673169885
Winsorized Mean ( 18 / 20 )97.3090.317351299757267306.628648045333
Winsorized Mean ( 19 / 20 )97.20133333333330.293679700487355330.977364700487
Winsorized Mean ( 20 / 20 )97.21133333333330.291332169773627333.678678221047
Trimmed Mean ( 1 / 20 )96.89224137931030.481999204457442201.021579461684
Trimmed Mean ( 2 / 20 )96.89303571428570.479224002041481202.187359776481
Trimmed Mean ( 3 / 20 )96.89648148148150.475960036654845203.581128706712
Trimmed Mean ( 4 / 20 )96.90346153846150.472383951498287205.137073838151
Trimmed Mean ( 5 / 20 )96.9110.468035778328878207.058956787494
Trimmed Mean ( 6 / 20 )96.92020833333330.46296535813752209.346566929407
Trimmed Mean ( 7 / 20 )96.93260869565220.456652325468521212.267853002173
Trimmed Mean ( 8 / 20 )96.94818181818180.448755416879127216.037908784274
Trimmed Mean ( 9 / 20 )96.96738095238090.4385409050251221.113651751211
Trimmed Mean ( 10 / 20 )96.98550.425903255837911227.71720730144
Trimmed Mean ( 11 / 20 )97.01105263157890.41020894468979236.491802256874
Trimmed Mean ( 12 / 20 )97.03527777777780.394902134975379245.719810514135
Trimmed Mean ( 13 / 20 )97.02970588235290.385603327368142251.630883334461
Trimmed Mean ( 14 / 20 )97.0018750.379056936074635255.903179096294
Trimmed Mean ( 15 / 20 )96.96566666666670.370450698887872261.75052971358
Trimmed Mean ( 16 / 20 )96.92857142857140.36006712861996269.19583523237
Trimmed Mean ( 17 / 20 )96.88653846153850.345775802110911280.200458997016
Trimmed Mean ( 18 / 20 )96.82750.326725769202353296.357095543422
Trimmed Mean ( 19 / 20 )96.75454545454550.299721896546747322.814404183696
Trimmed Mean ( 20 / 20 )96.6840.266003957232139363.468276961101
Median96.54
Midrange96.77
Midmean - Weighted Average at Xnp96.8761290322581
Midmean - Weighted Average at X(n+1)p96.9656666666667
Midmean - Empirical Distribution Function96.8761290322581
Midmean - Empirical Distribution Function - Averaging96.9656666666667
Midmean - Empirical Distribution Function - Interpolation96.9656666666667
Midmean - Closest Observation96.8761290322581
Midmean - True Basic - Statistics Graphics Toolkit96.9656666666667
Midmean - MS Excel (old versions)97.001875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.8881666666667 & 0.485308247997484 & 199.642530425671 \tabularnewline
Geometric Mean & 96.8163314772871 &  &  \tabularnewline
Harmonic Mean & 96.7444150449421 &  &  \tabularnewline
Quadratic Mean & 96.9598512873584 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 96.8915 & 0.483858597790064 & 200.247552575348 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 96.8868333333333 & 0.4828444727238 & 200.658470390641 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96.8783333333333 & 0.480708291371802 & 201.532478370345 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96.8783333333333 & 0.478967590677094 & 202.264903135473 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96.8741666666667 & 0.476072342439051 & 203.486231042857 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 96.8631666666667 & 0.473779042856577 & 204.447976598216 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 96.8526666666667 & 0.471122404636692 & 205.57856241491 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 96.8406666666667 & 0.469081014449275 & 206.447636300869 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 96.8586666666667 & 0.464601430951504 & 208.476901305061 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 96.8236666666667 & 0.458750080691917 & 211.059726726654 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 96.8511666666667 & 0.436949304204097 & 221.653097361217 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.0731666666667 & 0.39501244288967 & 245.747111044246 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.2226666666667 & 0.368273638335725 & 263.995726400696 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.2553333333333 & 0.361301982295346 & 269.180181950488 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.2253333333333 & 0.350728738249768 & 277.2094862215 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.22 & 0.343205313195541 & 283.270672865746 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.288 & 0.330224525570308 & 294.611673169885 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.309 & 0.317351299757267 & 306.628648045333 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.2013333333333 & 0.293679700487355 & 330.977364700487 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 97.2113333333333 & 0.291332169773627 & 333.678678221047 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96.8922413793103 & 0.481999204457442 & 201.021579461684 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96.8930357142857 & 0.479224002041481 & 202.187359776481 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 96.8964814814815 & 0.475960036654845 & 203.581128706712 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 96.9034615384615 & 0.472383951498287 & 205.137073838151 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 96.911 & 0.468035778328878 & 207.058956787494 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 96.9202083333333 & 0.46296535813752 & 209.346566929407 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 96.9326086956522 & 0.456652325468521 & 212.267853002173 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 96.9481818181818 & 0.448755416879127 & 216.037908784274 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 96.9673809523809 & 0.4385409050251 & 221.113651751211 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 96.9855 & 0.425903255837911 & 227.71720730144 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.0110526315789 & 0.41020894468979 & 236.491802256874 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.0352777777778 & 0.394902134975379 & 245.719810514135 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.0297058823529 & 0.385603327368142 & 251.630883334461 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.001875 & 0.379056936074635 & 255.903179096294 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 96.9656666666667 & 0.370450698887872 & 261.75052971358 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 96.9285714285714 & 0.36006712861996 & 269.19583523237 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 96.8865384615385 & 0.345775802110911 & 280.200458997016 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 96.8275 & 0.326725769202353 & 296.357095543422 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 96.7545454545455 & 0.299721896546747 & 322.814404183696 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 96.684 & 0.266003957232139 & 363.468276961101 \tabularnewline
Median & 96.54 &  &  \tabularnewline
Midrange & 96.77 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.8761290322581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.9656666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.8761290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.9656666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.9656666666667 &  &  \tabularnewline
Midmean - Closest Observation & 96.8761290322581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.9656666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.001875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281793&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]96.8881666666667[/C][C]0.485308247997484[/C][C]199.642530425671[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.8163314772871[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.7444150449421[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.9598512873584[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]96.8915[/C][C]0.483858597790064[/C][C]200.247552575348[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]96.8868333333333[/C][C]0.4828444727238[/C][C]200.658470390641[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96.8783333333333[/C][C]0.480708291371802[/C][C]201.532478370345[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96.8783333333333[/C][C]0.478967590677094[/C][C]202.264903135473[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96.8741666666667[/C][C]0.476072342439051[/C][C]203.486231042857[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]96.8631666666667[/C][C]0.473779042856577[/C][C]204.447976598216[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]96.8526666666667[/C][C]0.471122404636692[/C][C]205.57856241491[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]96.8406666666667[/C][C]0.469081014449275[/C][C]206.447636300869[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]96.8586666666667[/C][C]0.464601430951504[/C][C]208.476901305061[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]96.8236666666667[/C][C]0.458750080691917[/C][C]211.059726726654[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]96.8511666666667[/C][C]0.436949304204097[/C][C]221.653097361217[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.0731666666667[/C][C]0.39501244288967[/C][C]245.747111044246[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.2226666666667[/C][C]0.368273638335725[/C][C]263.995726400696[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.2553333333333[/C][C]0.361301982295346[/C][C]269.180181950488[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.2253333333333[/C][C]0.350728738249768[/C][C]277.2094862215[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.22[/C][C]0.343205313195541[/C][C]283.270672865746[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.288[/C][C]0.330224525570308[/C][C]294.611673169885[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.309[/C][C]0.317351299757267[/C][C]306.628648045333[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.2013333333333[/C][C]0.293679700487355[/C][C]330.977364700487[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]97.2113333333333[/C][C]0.291332169773627[/C][C]333.678678221047[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96.8922413793103[/C][C]0.481999204457442[/C][C]201.021579461684[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96.8930357142857[/C][C]0.479224002041481[/C][C]202.187359776481[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]96.8964814814815[/C][C]0.475960036654845[/C][C]203.581128706712[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]96.9034615384615[/C][C]0.472383951498287[/C][C]205.137073838151[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]96.911[/C][C]0.468035778328878[/C][C]207.058956787494[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]96.9202083333333[/C][C]0.46296535813752[/C][C]209.346566929407[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]96.9326086956522[/C][C]0.456652325468521[/C][C]212.267853002173[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]96.9481818181818[/C][C]0.448755416879127[/C][C]216.037908784274[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]96.9673809523809[/C][C]0.4385409050251[/C][C]221.113651751211[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]96.9855[/C][C]0.425903255837911[/C][C]227.71720730144[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.0110526315789[/C][C]0.41020894468979[/C][C]236.491802256874[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.0352777777778[/C][C]0.394902134975379[/C][C]245.719810514135[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.0297058823529[/C][C]0.385603327368142[/C][C]251.630883334461[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.001875[/C][C]0.379056936074635[/C][C]255.903179096294[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]96.9656666666667[/C][C]0.370450698887872[/C][C]261.75052971358[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]96.9285714285714[/C][C]0.36006712861996[/C][C]269.19583523237[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]96.8865384615385[/C][C]0.345775802110911[/C][C]280.200458997016[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]96.8275[/C][C]0.326725769202353[/C][C]296.357095543422[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]96.7545454545455[/C][C]0.299721896546747[/C][C]322.814404183696[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]96.684[/C][C]0.266003957232139[/C][C]363.468276961101[/C][/ROW]
[ROW][C]Median[/C][C]96.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.8761290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.9656666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.8761290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.9656666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.9656666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.8761290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.9656666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.001875[/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=281793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281793&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 Mean96.88816666666670.485308247997484199.642530425671
Geometric Mean96.8163314772871
Harmonic Mean96.7444150449421
Quadratic Mean96.9598512873584
Winsorized Mean ( 1 / 20 )96.89150.483858597790064200.247552575348
Winsorized Mean ( 2 / 20 )96.88683333333330.4828444727238200.658470390641
Winsorized Mean ( 3 / 20 )96.87833333333330.480708291371802201.532478370345
Winsorized Mean ( 4 / 20 )96.87833333333330.478967590677094202.264903135473
Winsorized Mean ( 5 / 20 )96.87416666666670.476072342439051203.486231042857
Winsorized Mean ( 6 / 20 )96.86316666666670.473779042856577204.447976598216
Winsorized Mean ( 7 / 20 )96.85266666666670.471122404636692205.57856241491
Winsorized Mean ( 8 / 20 )96.84066666666670.469081014449275206.447636300869
Winsorized Mean ( 9 / 20 )96.85866666666670.464601430951504208.476901305061
Winsorized Mean ( 10 / 20 )96.82366666666670.458750080691917211.059726726654
Winsorized Mean ( 11 / 20 )96.85116666666670.436949304204097221.653097361217
Winsorized Mean ( 12 / 20 )97.07316666666670.39501244288967245.747111044246
Winsorized Mean ( 13 / 20 )97.22266666666670.368273638335725263.995726400696
Winsorized Mean ( 14 / 20 )97.25533333333330.361301982295346269.180181950488
Winsorized Mean ( 15 / 20 )97.22533333333330.350728738249768277.2094862215
Winsorized Mean ( 16 / 20 )97.220.343205313195541283.270672865746
Winsorized Mean ( 17 / 20 )97.2880.330224525570308294.611673169885
Winsorized Mean ( 18 / 20 )97.3090.317351299757267306.628648045333
Winsorized Mean ( 19 / 20 )97.20133333333330.293679700487355330.977364700487
Winsorized Mean ( 20 / 20 )97.21133333333330.291332169773627333.678678221047
Trimmed Mean ( 1 / 20 )96.89224137931030.481999204457442201.021579461684
Trimmed Mean ( 2 / 20 )96.89303571428570.479224002041481202.187359776481
Trimmed Mean ( 3 / 20 )96.89648148148150.475960036654845203.581128706712
Trimmed Mean ( 4 / 20 )96.90346153846150.472383951498287205.137073838151
Trimmed Mean ( 5 / 20 )96.9110.468035778328878207.058956787494
Trimmed Mean ( 6 / 20 )96.92020833333330.46296535813752209.346566929407
Trimmed Mean ( 7 / 20 )96.93260869565220.456652325468521212.267853002173
Trimmed Mean ( 8 / 20 )96.94818181818180.448755416879127216.037908784274
Trimmed Mean ( 9 / 20 )96.96738095238090.4385409050251221.113651751211
Trimmed Mean ( 10 / 20 )96.98550.425903255837911227.71720730144
Trimmed Mean ( 11 / 20 )97.01105263157890.41020894468979236.491802256874
Trimmed Mean ( 12 / 20 )97.03527777777780.394902134975379245.719810514135
Trimmed Mean ( 13 / 20 )97.02970588235290.385603327368142251.630883334461
Trimmed Mean ( 14 / 20 )97.0018750.379056936074635255.903179096294
Trimmed Mean ( 15 / 20 )96.96566666666670.370450698887872261.75052971358
Trimmed Mean ( 16 / 20 )96.92857142857140.36006712861996269.19583523237
Trimmed Mean ( 17 / 20 )96.88653846153850.345775802110911280.200458997016
Trimmed Mean ( 18 / 20 )96.82750.326725769202353296.357095543422
Trimmed Mean ( 19 / 20 )96.75454545454550.299721896546747322.814404183696
Trimmed Mean ( 20 / 20 )96.6840.266003957232139363.468276961101
Median96.54
Midrange96.77
Midmean - Weighted Average at Xnp96.8761290322581
Midmean - Weighted Average at X(n+1)p96.9656666666667
Midmean - Empirical Distribution Function96.8761290322581
Midmean - Empirical Distribution Function - Averaging96.9656666666667
Midmean - Empirical Distribution Function - Interpolation96.9656666666667
Midmean - Closest Observation96.8761290322581
Midmean - True Basic - Statistics Graphics Toolkit96.9656666666667
Midmean - MS Excel (old versions)97.001875
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')