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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 21 Dec 2010 10:51:48 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t12929285879frvzt4fzs80078.htm/, Retrieved Fri, 17 May 2024 22:29:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113253, Retrieved Fri, 17 May 2024 22:29:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [b-r0245787] [2010-12-19 16:05:46] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
- RMPD  [Central Tendency] [b-r0245787] [2010-12-19 16:33:24] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
-         [Central Tendency] [b-r0245095] [2010-12-19 16:39:33] [ec8d68d52c1e9c5e97bb689b42436a8c]
-    D        [Central Tendency] [b-r0245095] [2010-12-21 10:51:48] [4bfaadb29d89ff24ebcdd4f425066435] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.0
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3.0
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2.0
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5
4.8
3.2
2.7
2.1
1.9
0.6
0.7
-0.2
-1.0
-1.7
-0.7
-1.0
-0.9
0.0
0.3
0.8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113253&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113253&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ 72.249.76.132






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.216393442622950.20999844297977110.5543327425359
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.74924728893887
Winsorized Mean ( 1 / 20 )2.226229508196720.20624010675850910.7943578152016
Winsorized Mean ( 2 / 20 )2.216393442622950.20349649005268910.8915561248702
Winsorized Mean ( 3 / 20 )2.216393442622950.20090206852069811.0322081745744
Winsorized Mean ( 4 / 20 )2.209836065573770.19249164225746811.4801663057038
Winsorized Mean ( 5 / 20 )2.226229508196720.17654705156751212.6098368023179
Winsorized Mean ( 6 / 20 )2.206557377049180.16286151635885313.5486726783705
Winsorized Mean ( 7 / 20 )2.206557377049180.14771240800257114.9381992135066
Winsorized Mean ( 8 / 20 )2.180327868852460.12614112298461817.2848300162853
Winsorized Mean ( 9 / 20 )2.180327868852460.12035511372444418.1157891956663
Winsorized Mean ( 10 / 20 )2.147540983606560.10848198856764419.7962907203481
Winsorized Mean ( 11 / 20 )2.201639344262300.091421434611588324.082310167371
Winsorized Mean ( 12 / 20 )2.201639344262300.084720427510656925.9871132494622
Winsorized Mean ( 13 / 20 )2.180327868852460.08147612450346826.7603286501391
Winsorized Mean ( 14 / 20 )2.180327868852460.08147612450346826.7603286501391
Winsorized Mean ( 15 / 20 )2.180327868852460.073544888791698629.6462188559127
Winsorized Mean ( 16 / 20 )2.259016393442620.060434539810263237.3795581224727
Winsorized Mean ( 17 / 20 )2.259016393442620.060434539810263237.3795581224727
Winsorized Mean ( 18 / 20 )2.288524590163930.056010262557677740.8590227158332
Winsorized Mean ( 19 / 20 )2.288524590163930.056010262557677740.8590227158332
Winsorized Mean ( 20 / 20 )2.255737704918030.051135980198302444.1125347782601
Trimmed Mean ( 1 / 20 )2.220338983050850.19677082857300111.2838828760998
Trimmed Mean ( 2 / 20 )2.214035087719300.18505297278051911.9643313719972
Trimmed Mean ( 3 / 20 )2.212727272727270.17230961377617312.8415775779149
Trimmed Mean ( 4 / 20 )2.211320754716980.15746219343414514.0435028020984
Trimmed Mean ( 5 / 20 )2.211764705882350.14213076163356615.5614778986734
Trimmed Mean ( 6 / 20 )2.208163265306120.12876429762412817.1488782686635
Trimmed Mean ( 7 / 20 )2.208510638297870.11644716624978218.9657740022677
Trimmed Mean ( 8 / 20 )2.208888888888890.10564005124235420.9095779764568
Trimmed Mean ( 9 / 20 )2.213953488372090.098638651443946522.4450908032762
Trimmed Mean ( 10 / 20 )2.219512195121950.091145789956364924.3512311011240
Trimmed Mean ( 11 / 20 )2.230769230769230.084744105257506626.3235917588690
Trimmed Mean ( 12 / 20 )2.235135135135140.081393292790957927.4609253231175
Trimmed Mean ( 13 / 20 )2.240.078665337310137128.4750574597911
Trimmed Mean ( 14 / 20 )2.248484848484850.075643854038585529.7246204210841
Trimmed Mean ( 15 / 20 )2.258064516129030.071206830883570731.7113469046412
Trimmed Mean ( 16 / 20 )2.268965517241380.067339198773995633.6945725305776
Trimmed Mean ( 17 / 20 )2.270370370370370.066198100095565634.2966092243251
Trimmed Mean ( 18 / 20 )2.2720.064166450216085135.4079116477361
Trimmed Mean ( 19 / 20 )2.269565217391300.062375498955190136.3855240504246
Trimmed Mean ( 20 / 20 )2.266666666666670.059093684028527938.3571730876081
Median2.3
Midrange2.1
Midmean - Weighted Average at Xnp2.25806451612903
Midmean - Weighted Average at X(n+1)p2.25806451612903
Midmean - Empirical Distribution Function2.25806451612903
Midmean - Empirical Distribution Function - Averaging2.25806451612903
Midmean - Empirical Distribution Function - Interpolation2.25806451612903
Midmean - Closest Observation2.17352941176471
Midmean - True Basic - Statistics Graphics Toolkit2.25806451612903
Midmean - MS Excel (old versions)2.25806451612903
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.21639344262295 & 0.209998442979771 & 10.5543327425359 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.74924728893887 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.22622950819672 & 0.206240106758509 & 10.7943578152016 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.21639344262295 & 0.203496490052689 & 10.8915561248702 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.21639344262295 & 0.200902068520698 & 11.0322081745744 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.20983606557377 & 0.192491642257468 & 11.4801663057038 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.22622950819672 & 0.176547051567512 & 12.6098368023179 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.20655737704918 & 0.162861516358853 & 13.5486726783705 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.20655737704918 & 0.147712408002571 & 14.9381992135066 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.18032786885246 & 0.126141122984618 & 17.2848300162853 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.18032786885246 & 0.120355113724444 & 18.1157891956663 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.14754098360656 & 0.108481988567644 & 19.7962907203481 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.20163934426230 & 0.0914214346115883 & 24.082310167371 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.20163934426230 & 0.0847204275106569 & 25.9871132494622 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.18032786885246 & 0.081476124503468 & 26.7603286501391 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.18032786885246 & 0.081476124503468 & 26.7603286501391 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.18032786885246 & 0.0735448887916986 & 29.6462188559127 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.25901639344262 & 0.0604345398102632 & 37.3795581224727 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.25901639344262 & 0.0604345398102632 & 37.3795581224727 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.28852459016393 & 0.0560102625576777 & 40.8590227158332 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.28852459016393 & 0.0560102625576777 & 40.8590227158332 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.25573770491803 & 0.0511359801983024 & 44.1125347782601 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.22033898305085 & 0.196770828573001 & 11.2838828760998 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.21403508771930 & 0.185052972780519 & 11.9643313719972 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.21272727272727 & 0.172309613776173 & 12.8415775779149 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.21132075471698 & 0.157462193434145 & 14.0435028020984 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.21176470588235 & 0.142130761633566 & 15.5614778986734 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.20816326530612 & 0.128764297624128 & 17.1488782686635 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.20851063829787 & 0.116447166249782 & 18.9657740022677 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.20888888888889 & 0.105640051242354 & 20.9095779764568 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.21395348837209 & 0.0986386514439465 & 22.4450908032762 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.21951219512195 & 0.0911457899563649 & 24.3512311011240 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.23076923076923 & 0.0847441052575066 & 26.3235917588690 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.23513513513514 & 0.0813932927909579 & 27.4609253231175 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.24 & 0.0786653373101371 & 28.4750574597911 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.24848484848485 & 0.0756438540385855 & 29.7246204210841 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.25806451612903 & 0.0712068308835707 & 31.7113469046412 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.26896551724138 & 0.0673391987739956 & 33.6945725305776 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.27037037037037 & 0.0661981000955656 & 34.2966092243251 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.272 & 0.0641664502160851 & 35.4079116477361 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.26956521739130 & 0.0623754989551901 & 36.3855240504246 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.26666666666667 & 0.0590936840285279 & 38.3571730876081 \tabularnewline
Median & 2.3 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.25806451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.25806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.25806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.25806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.25806451612903 &  &  \tabularnewline
Midmean - Closest Observation & 2.17352941176471 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.25806451612903 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.25806451612903 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113253&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]2.21639344262295[/C][C]0.209998442979771[/C][C]10.5543327425359[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.74924728893887[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.22622950819672[/C][C]0.206240106758509[/C][C]10.7943578152016[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.21639344262295[/C][C]0.203496490052689[/C][C]10.8915561248702[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.21639344262295[/C][C]0.200902068520698[/C][C]11.0322081745744[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.20983606557377[/C][C]0.192491642257468[/C][C]11.4801663057038[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.22622950819672[/C][C]0.176547051567512[/C][C]12.6098368023179[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.20655737704918[/C][C]0.162861516358853[/C][C]13.5486726783705[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.20655737704918[/C][C]0.147712408002571[/C][C]14.9381992135066[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.18032786885246[/C][C]0.126141122984618[/C][C]17.2848300162853[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.18032786885246[/C][C]0.120355113724444[/C][C]18.1157891956663[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.14754098360656[/C][C]0.108481988567644[/C][C]19.7962907203481[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.20163934426230[/C][C]0.0914214346115883[/C][C]24.082310167371[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.20163934426230[/C][C]0.0847204275106569[/C][C]25.9871132494622[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.18032786885246[/C][C]0.081476124503468[/C][C]26.7603286501391[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.18032786885246[/C][C]0.081476124503468[/C][C]26.7603286501391[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.18032786885246[/C][C]0.0735448887916986[/C][C]29.6462188559127[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.25901639344262[/C][C]0.0604345398102632[/C][C]37.3795581224727[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.25901639344262[/C][C]0.0604345398102632[/C][C]37.3795581224727[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.28852459016393[/C][C]0.0560102625576777[/C][C]40.8590227158332[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.28852459016393[/C][C]0.0560102625576777[/C][C]40.8590227158332[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.25573770491803[/C][C]0.0511359801983024[/C][C]44.1125347782601[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.22033898305085[/C][C]0.196770828573001[/C][C]11.2838828760998[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.21403508771930[/C][C]0.185052972780519[/C][C]11.9643313719972[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.21272727272727[/C][C]0.172309613776173[/C][C]12.8415775779149[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.21132075471698[/C][C]0.157462193434145[/C][C]14.0435028020984[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.21176470588235[/C][C]0.142130761633566[/C][C]15.5614778986734[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.20816326530612[/C][C]0.128764297624128[/C][C]17.1488782686635[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.20851063829787[/C][C]0.116447166249782[/C][C]18.9657740022677[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.20888888888889[/C][C]0.105640051242354[/C][C]20.9095779764568[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.21395348837209[/C][C]0.0986386514439465[/C][C]22.4450908032762[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.21951219512195[/C][C]0.0911457899563649[/C][C]24.3512311011240[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.23076923076923[/C][C]0.0847441052575066[/C][C]26.3235917588690[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.23513513513514[/C][C]0.0813932927909579[/C][C]27.4609253231175[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.24[/C][C]0.0786653373101371[/C][C]28.4750574597911[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.24848484848485[/C][C]0.0756438540385855[/C][C]29.7246204210841[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.25806451612903[/C][C]0.0712068308835707[/C][C]31.7113469046412[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.26896551724138[/C][C]0.0673391987739956[/C][C]33.6945725305776[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.27037037037037[/C][C]0.0661981000955656[/C][C]34.2966092243251[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.272[/C][C]0.0641664502160851[/C][C]35.4079116477361[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.26956521739130[/C][C]0.0623754989551901[/C][C]36.3855240504246[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.26666666666667[/C][C]0.0590936840285279[/C][C]38.3571730876081[/C][/ROW]
[ROW][C]Median[/C][C]2.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.25806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.25806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.25806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.25806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.25806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.17352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.25806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.25806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113253&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.216393442622950.20999844297977110.5543327425359
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.74924728893887
Winsorized Mean ( 1 / 20 )2.226229508196720.20624010675850910.7943578152016
Winsorized Mean ( 2 / 20 )2.216393442622950.20349649005268910.8915561248702
Winsorized Mean ( 3 / 20 )2.216393442622950.20090206852069811.0322081745744
Winsorized Mean ( 4 / 20 )2.209836065573770.19249164225746811.4801663057038
Winsorized Mean ( 5 / 20 )2.226229508196720.17654705156751212.6098368023179
Winsorized Mean ( 6 / 20 )2.206557377049180.16286151635885313.5486726783705
Winsorized Mean ( 7 / 20 )2.206557377049180.14771240800257114.9381992135066
Winsorized Mean ( 8 / 20 )2.180327868852460.12614112298461817.2848300162853
Winsorized Mean ( 9 / 20 )2.180327868852460.12035511372444418.1157891956663
Winsorized Mean ( 10 / 20 )2.147540983606560.10848198856764419.7962907203481
Winsorized Mean ( 11 / 20 )2.201639344262300.091421434611588324.082310167371
Winsorized Mean ( 12 / 20 )2.201639344262300.084720427510656925.9871132494622
Winsorized Mean ( 13 / 20 )2.180327868852460.08147612450346826.7603286501391
Winsorized Mean ( 14 / 20 )2.180327868852460.08147612450346826.7603286501391
Winsorized Mean ( 15 / 20 )2.180327868852460.073544888791698629.6462188559127
Winsorized Mean ( 16 / 20 )2.259016393442620.060434539810263237.3795581224727
Winsorized Mean ( 17 / 20 )2.259016393442620.060434539810263237.3795581224727
Winsorized Mean ( 18 / 20 )2.288524590163930.056010262557677740.8590227158332
Winsorized Mean ( 19 / 20 )2.288524590163930.056010262557677740.8590227158332
Winsorized Mean ( 20 / 20 )2.255737704918030.051135980198302444.1125347782601
Trimmed Mean ( 1 / 20 )2.220338983050850.19677082857300111.2838828760998
Trimmed Mean ( 2 / 20 )2.214035087719300.18505297278051911.9643313719972
Trimmed Mean ( 3 / 20 )2.212727272727270.17230961377617312.8415775779149
Trimmed Mean ( 4 / 20 )2.211320754716980.15746219343414514.0435028020984
Trimmed Mean ( 5 / 20 )2.211764705882350.14213076163356615.5614778986734
Trimmed Mean ( 6 / 20 )2.208163265306120.12876429762412817.1488782686635
Trimmed Mean ( 7 / 20 )2.208510638297870.11644716624978218.9657740022677
Trimmed Mean ( 8 / 20 )2.208888888888890.10564005124235420.9095779764568
Trimmed Mean ( 9 / 20 )2.213953488372090.098638651443946522.4450908032762
Trimmed Mean ( 10 / 20 )2.219512195121950.091145789956364924.3512311011240
Trimmed Mean ( 11 / 20 )2.230769230769230.084744105257506626.3235917588690
Trimmed Mean ( 12 / 20 )2.235135135135140.081393292790957927.4609253231175
Trimmed Mean ( 13 / 20 )2.240.078665337310137128.4750574597911
Trimmed Mean ( 14 / 20 )2.248484848484850.075643854038585529.7246204210841
Trimmed Mean ( 15 / 20 )2.258064516129030.071206830883570731.7113469046412
Trimmed Mean ( 16 / 20 )2.268965517241380.067339198773995633.6945725305776
Trimmed Mean ( 17 / 20 )2.270370370370370.066198100095565634.2966092243251
Trimmed Mean ( 18 / 20 )2.2720.064166450216085135.4079116477361
Trimmed Mean ( 19 / 20 )2.269565217391300.062375498955190136.3855240504246
Trimmed Mean ( 20 / 20 )2.266666666666670.059093684028527938.3571730876081
Median2.3
Midrange2.1
Midmean - Weighted Average at Xnp2.25806451612903
Midmean - Weighted Average at X(n+1)p2.25806451612903
Midmean - Empirical Distribution Function2.25806451612903
Midmean - Empirical Distribution Function - Averaging2.25806451612903
Midmean - Empirical Distribution Function - Interpolation2.25806451612903
Midmean - Closest Observation2.17352941176471
Midmean - True Basic - Statistics Graphics Toolkit2.25806451612903
Midmean - MS Excel (old versions)2.25806451612903
Number of observations61


Figures (Output of Computation)

Input Parameters & R Code

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')