Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 07 May 2009 08:13:01 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/May/07/t1241705919mu74d7qu3xg0sxi.htm/, Retrieved Mon, 06 May 2024 13:54:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39585, Retrieved Mon, 06 May 2024 13:54:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2009-05-07 14:13:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
5,11
5,11
5,11
5,1
5,1
5,1
5,1
5,1
5,12
5,25
5,26
5,26
5,26
5,26
5,26
5,26
5,29
5,3
5,33
5,33
5,35
5,38
5,38
5,38
5,38
5,38
5,39
5,39
5,4
5,4
5,4
5,4
5,4
5,41
5,41
5,41
5,41
5,41
5,42
5,42
5,42
5,42
5,43
5,43
5,45
5,51
5,51
5,51
5,51
5,51
5,51
5,53
5,53
5,53
5,53
5,52
5,53
5,54
5,54
5,57
5,56
5,57
5,58
5,61
5,66
5,68
5,69
5,7
5,72
5,71
5,69
5,7
5,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39585&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]1 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=39585&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39585&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.418219178082190.0199546121837308271.527160146952
Geometric Mean5.41555835197629
Harmonic Mean5.41288232219603
Quadratic Mean5.42086418324151
Winsorized Mean ( 1 / 24 )5.418082191780820.0199262887613157271.906236865307
Winsorized Mean ( 2 / 24 )5.417808219178080.0198713964361343272.643557617636
Winsorized Mean ( 3 / 24 )5.417808219178080.0198713964361343272.643557617636
Winsorized Mean ( 4 / 24 )5.417808219178080.0198713964361343272.643557617636
Winsorized Mean ( 5 / 24 )5.417808219178080.0195869122109576276.603487105394
Winsorized Mean ( 6 / 24 )5.417808219178080.0195869122109576276.603487105394
Winsorized Mean ( 7 / 24 )5.416849315068490.0194040557282113279.160676043257
Winsorized Mean ( 8 / 24 )5.415753424657530.0187589834473486288.701860623636
Winsorized Mean ( 9 / 24 )5.425616438356160.0145008086445510374.159577672584
Winsorized Mean ( 10 / 24 )5.422876712328770.0135772207330195399.409924826547
Winsorized Mean ( 11 / 24 )5.42136986301370.0133394892588492406.41510014465
Winsorized Mean ( 12 / 24 )5.42136986301370.0133394892588492406.41510014465
Winsorized Mean ( 13 / 24 )5.419589041095890.0130687771396985414.697487237195
Winsorized Mean ( 14 / 24 )5.415753424657530.0125177466233282432.646033477358
Winsorized Mean ( 15 / 24 )5.415753424657530.0125177466233282432.646033477358
Winsorized Mean ( 16 / 24 )5.420136986301370.0111111945118948487.808667240859
Winsorized Mean ( 17 / 24 )5.422465753424660.0107372465531577505.014551596563
Winsorized Mean ( 18 / 24 )5.429863013698630.00961490857580248564.733712327103
Winsorized Mean ( 19 / 24 )5.429863013698630.00961490857580248564.733712327102
Winsorized Mean ( 20 / 24 )5.435342465753430.0088516485229935614.048609322241
Winsorized Mean ( 21 / 24 )5.441095890410960.00733925052845777741.36941766918
Winsorized Mean ( 22 / 24 )5.438082191780820.00689577091805431788.611201909708
Winsorized Mean ( 23 / 24 )5.438082191780820.00689577091805431788.611201909708
Winsorized Mean ( 24 / 24 )5.438082191780820.00689577091805431788.611201909708
Trimmed Mean ( 1 / 24 )5.418450704225350.0195550586140094277.086906829496
Trimmed Mean ( 2 / 24 )5.418840579710150.0191134900026214283.508693544033
Trimmed Mean ( 3 / 24 )5.419402985074630.0186215135998084291.029134448576
Trimmed Mean ( 4 / 24 )5.420.0180317561754043300.580816825429
Trimmed Mean ( 5 / 24 )5.420634920634920.0173203203780002312.963894566295
Trimmed Mean ( 6 / 24 )5.421311475409840.0165517493005747327.537070370055
Trimmed Mean ( 7 / 24 )5.422033898305080.0156072853498499347.40403451118
Trimmed Mean ( 8 / 24 )5.422982456140350.014483516065223374.424444431812
Trimmed Mean ( 9 / 24 )5.424181818181820.0132514935543230409.326073015544
Trimmed Mean ( 10 / 24 )5.423962264150940.0128724332277100421.362625713607
Trimmed Mean ( 11 / 24 )5.424117647058820.0126092915339171430.168311397098
Trimmed Mean ( 12 / 24 )5.424489795918370.0123237962683346440.163864916878
Trimmed Mean ( 13 / 24 )5.424893617021280.0119545560287741453.792981016089
Trimmed Mean ( 14 / 24 )5.425555555555560.0115363087577044470.302561201144
Trimmed Mean ( 15 / 24 )5.426744186046510.0111106432378936488.427543739161
Trimmed Mean ( 16 / 24 )5.42804878048780.0105415525780362514.919291091652
Trimmed Mean ( 17 / 24 )5.428974358974360.0101526465028314534.734894735115
Trimmed Mean ( 18 / 24 )5.429729729729730.0097220106183565558.498642192146
Trimmed Mean ( 19 / 24 )5.429714285714290.00943340848677037575.58350126882
Trimmed Mean ( 20 / 24 )5.429696969696970.00901897041599286602.030688566045
Trimmed Mean ( 21 / 24 )5.429032258064520.00864291416791286628.148348183301
Trimmed Mean ( 22 / 24 )5.427586206896550.00850463757019906638.191358784677
Trimmed Mean ( 23 / 24 )5.42629629629630.00840817923838956645.359255844742
Trimmed Mean ( 24 / 24 )5.42480.00820812605491248660.9060294284
Median5.41
Midrange5.41
Midmean - Weighted Average at Xnp5.4348717948718
Midmean - Weighted Average at X(n+1)p5.4348717948718
Midmean - Empirical Distribution Function5.4348717948718
Midmean - Empirical Distribution Function - Averaging5.4348717948718
Midmean - Empirical Distribution Function - Interpolation5.4348717948718
Midmean - Closest Observation5.4315
Midmean - True Basic - Statistics Graphics Toolkit5.4348717948718
Midmean - MS Excel (old versions)5.4348717948718
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.41821917808219 & 0.0199546121837308 & 271.527160146952 \tabularnewline
Geometric Mean & 5.41555835197629 &  &  \tabularnewline
Harmonic Mean & 5.41288232219603 &  &  \tabularnewline
Quadratic Mean & 5.42086418324151 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 5.41808219178082 & 0.0199262887613157 & 271.906236865307 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 5.41780821917808 & 0.0198713964361343 & 272.643557617636 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 5.41780821917808 & 0.0198713964361343 & 272.643557617636 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 5.41780821917808 & 0.0198713964361343 & 272.643557617636 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 5.41780821917808 & 0.0195869122109576 & 276.603487105394 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 5.41780821917808 & 0.0195869122109576 & 276.603487105394 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 5.41684931506849 & 0.0194040557282113 & 279.160676043257 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 5.41575342465753 & 0.0187589834473486 & 288.701860623636 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 5.42561643835616 & 0.0145008086445510 & 374.159577672584 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 5.42287671232877 & 0.0135772207330195 & 399.409924826547 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 5.4213698630137 & 0.0133394892588492 & 406.41510014465 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 5.4213698630137 & 0.0133394892588492 & 406.41510014465 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 5.41958904109589 & 0.0130687771396985 & 414.697487237195 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 5.41575342465753 & 0.0125177466233282 & 432.646033477358 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 5.41575342465753 & 0.0125177466233282 & 432.646033477358 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 5.42013698630137 & 0.0111111945118948 & 487.808667240859 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 5.42246575342466 & 0.0107372465531577 & 505.014551596563 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 5.42986301369863 & 0.00961490857580248 & 564.733712327103 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 5.42986301369863 & 0.00961490857580248 & 564.733712327102 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 5.43534246575343 & 0.0088516485229935 & 614.048609322241 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 5.44109589041096 & 0.00733925052845777 & 741.36941766918 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 5.43808219178082 & 0.00689577091805431 & 788.611201909708 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 5.43808219178082 & 0.00689577091805431 & 788.611201909708 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 5.43808219178082 & 0.00689577091805431 & 788.611201909708 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 5.41845070422535 & 0.0195550586140094 & 277.086906829496 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 5.41884057971015 & 0.0191134900026214 & 283.508693544033 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 5.41940298507463 & 0.0186215135998084 & 291.029134448576 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 5.42 & 0.0180317561754043 & 300.580816825429 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 5.42063492063492 & 0.0173203203780002 & 312.963894566295 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 5.42131147540984 & 0.0165517493005747 & 327.537070370055 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 5.42203389830508 & 0.0156072853498499 & 347.40403451118 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 5.42298245614035 & 0.014483516065223 & 374.424444431812 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 5.42418181818182 & 0.0132514935543230 & 409.326073015544 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 5.42396226415094 & 0.0128724332277100 & 421.362625713607 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 5.42411764705882 & 0.0126092915339171 & 430.168311397098 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 5.42448979591837 & 0.0123237962683346 & 440.163864916878 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 5.42489361702128 & 0.0119545560287741 & 453.792981016089 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 5.42555555555556 & 0.0115363087577044 & 470.302561201144 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 5.42674418604651 & 0.0111106432378936 & 488.427543739161 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 5.4280487804878 & 0.0105415525780362 & 514.919291091652 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 5.42897435897436 & 0.0101526465028314 & 534.734894735115 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 5.42972972972973 & 0.0097220106183565 & 558.498642192146 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 5.42971428571429 & 0.00943340848677037 & 575.58350126882 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 5.42969696969697 & 0.00901897041599286 & 602.030688566045 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 5.42903225806452 & 0.00864291416791286 & 628.148348183301 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 5.42758620689655 & 0.00850463757019906 & 638.191358784677 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 5.4262962962963 & 0.00840817923838956 & 645.359255844742 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 5.4248 & 0.00820812605491248 & 660.9060294284 \tabularnewline
Median & 5.41 &  &  \tabularnewline
Midrange & 5.41 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.4348717948718 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.4348717948718 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.4348717948718 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.4348717948718 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.4348717948718 &  &  \tabularnewline
Midmean - Closest Observation & 5.4315 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.4348717948718 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.4348717948718 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39585&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]5.41821917808219[/C][C]0.0199546121837308[/C][C]271.527160146952[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.41555835197629[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5.41288232219603[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.42086418324151[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]5.41808219178082[/C][C]0.0199262887613157[/C][C]271.906236865307[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]5.41780821917808[/C][C]0.0198713964361343[/C][C]272.643557617636[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]5.41780821917808[/C][C]0.0198713964361343[/C][C]272.643557617636[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]5.41780821917808[/C][C]0.0198713964361343[/C][C]272.643557617636[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]5.41780821917808[/C][C]0.0195869122109576[/C][C]276.603487105394[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]5.41780821917808[/C][C]0.0195869122109576[/C][C]276.603487105394[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]5.41684931506849[/C][C]0.0194040557282113[/C][C]279.160676043257[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]5.41575342465753[/C][C]0.0187589834473486[/C][C]288.701860623636[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]5.42561643835616[/C][C]0.0145008086445510[/C][C]374.159577672584[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]5.42287671232877[/C][C]0.0135772207330195[/C][C]399.409924826547[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]5.4213698630137[/C][C]0.0133394892588492[/C][C]406.41510014465[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]5.4213698630137[/C][C]0.0133394892588492[/C][C]406.41510014465[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]5.41958904109589[/C][C]0.0130687771396985[/C][C]414.697487237195[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]5.41575342465753[/C][C]0.0125177466233282[/C][C]432.646033477358[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]5.41575342465753[/C][C]0.0125177466233282[/C][C]432.646033477358[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]5.42013698630137[/C][C]0.0111111945118948[/C][C]487.808667240859[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]5.42246575342466[/C][C]0.0107372465531577[/C][C]505.014551596563[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]5.42986301369863[/C][C]0.00961490857580248[/C][C]564.733712327103[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]5.42986301369863[/C][C]0.00961490857580248[/C][C]564.733712327102[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]5.43534246575343[/C][C]0.0088516485229935[/C][C]614.048609322241[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]5.44109589041096[/C][C]0.00733925052845777[/C][C]741.36941766918[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]5.43808219178082[/C][C]0.00689577091805431[/C][C]788.611201909708[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]5.43808219178082[/C][C]0.00689577091805431[/C][C]788.611201909708[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]5.43808219178082[/C][C]0.00689577091805431[/C][C]788.611201909708[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]5.41845070422535[/C][C]0.0195550586140094[/C][C]277.086906829496[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]5.41884057971015[/C][C]0.0191134900026214[/C][C]283.508693544033[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]5.41940298507463[/C][C]0.0186215135998084[/C][C]291.029134448576[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]5.42[/C][C]0.0180317561754043[/C][C]300.580816825429[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]5.42063492063492[/C][C]0.0173203203780002[/C][C]312.963894566295[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]5.42131147540984[/C][C]0.0165517493005747[/C][C]327.537070370055[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]5.42203389830508[/C][C]0.0156072853498499[/C][C]347.40403451118[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]5.42298245614035[/C][C]0.014483516065223[/C][C]374.424444431812[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]5.42418181818182[/C][C]0.0132514935543230[/C][C]409.326073015544[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]5.42396226415094[/C][C]0.0128724332277100[/C][C]421.362625713607[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]5.42411764705882[/C][C]0.0126092915339171[/C][C]430.168311397098[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]5.42448979591837[/C][C]0.0123237962683346[/C][C]440.163864916878[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]5.42489361702128[/C][C]0.0119545560287741[/C][C]453.792981016089[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]5.42555555555556[/C][C]0.0115363087577044[/C][C]470.302561201144[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]5.42674418604651[/C][C]0.0111106432378936[/C][C]488.427543739161[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]5.4280487804878[/C][C]0.0105415525780362[/C][C]514.919291091652[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]5.42897435897436[/C][C]0.0101526465028314[/C][C]534.734894735115[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]5.42972972972973[/C][C]0.0097220106183565[/C][C]558.498642192146[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]5.42971428571429[/C][C]0.00943340848677037[/C][C]575.58350126882[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]5.42969696969697[/C][C]0.00901897041599286[/C][C]602.030688566045[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]5.42903225806452[/C][C]0.00864291416791286[/C][C]628.148348183301[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]5.42758620689655[/C][C]0.00850463757019906[/C][C]638.191358784677[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]5.4262962962963[/C][C]0.00840817923838956[/C][C]645.359255844742[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]5.4248[/C][C]0.00820812605491248[/C][C]660.9060294284[/C][/ROW]
[ROW][C]Median[/C][C]5.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.4348717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.4348717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.4348717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.4348717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.4348717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.4315[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.4348717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.4348717948718[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39585&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39585&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 Mean5.418219178082190.0199546121837308271.527160146952
Geometric Mean5.41555835197629
Harmonic Mean5.41288232219603
Quadratic Mean5.42086418324151
Winsorized Mean ( 1 / 24 )5.418082191780820.0199262887613157271.906236865307
Winsorized Mean ( 2 / 24 )5.417808219178080.0198713964361343272.643557617636
Winsorized Mean ( 3 / 24 )5.417808219178080.0198713964361343272.643557617636
Winsorized Mean ( 4 / 24 )5.417808219178080.0198713964361343272.643557617636
Winsorized Mean ( 5 / 24 )5.417808219178080.0195869122109576276.603487105394
Winsorized Mean ( 6 / 24 )5.417808219178080.0195869122109576276.603487105394
Winsorized Mean ( 7 / 24 )5.416849315068490.0194040557282113279.160676043257
Winsorized Mean ( 8 / 24 )5.415753424657530.0187589834473486288.701860623636
Winsorized Mean ( 9 / 24 )5.425616438356160.0145008086445510374.159577672584
Winsorized Mean ( 10 / 24 )5.422876712328770.0135772207330195399.409924826547
Winsorized Mean ( 11 / 24 )5.42136986301370.0133394892588492406.41510014465
Winsorized Mean ( 12 / 24 )5.42136986301370.0133394892588492406.41510014465
Winsorized Mean ( 13 / 24 )5.419589041095890.0130687771396985414.697487237195
Winsorized Mean ( 14 / 24 )5.415753424657530.0125177466233282432.646033477358
Winsorized Mean ( 15 / 24 )5.415753424657530.0125177466233282432.646033477358
Winsorized Mean ( 16 / 24 )5.420136986301370.0111111945118948487.808667240859
Winsorized Mean ( 17 / 24 )5.422465753424660.0107372465531577505.014551596563
Winsorized Mean ( 18 / 24 )5.429863013698630.00961490857580248564.733712327103
Winsorized Mean ( 19 / 24 )5.429863013698630.00961490857580248564.733712327102
Winsorized Mean ( 20 / 24 )5.435342465753430.0088516485229935614.048609322241
Winsorized Mean ( 21 / 24 )5.441095890410960.00733925052845777741.36941766918
Winsorized Mean ( 22 / 24 )5.438082191780820.00689577091805431788.611201909708
Winsorized Mean ( 23 / 24 )5.438082191780820.00689577091805431788.611201909708
Winsorized Mean ( 24 / 24 )5.438082191780820.00689577091805431788.611201909708
Trimmed Mean ( 1 / 24 )5.418450704225350.0195550586140094277.086906829496
Trimmed Mean ( 2 / 24 )5.418840579710150.0191134900026214283.508693544033
Trimmed Mean ( 3 / 24 )5.419402985074630.0186215135998084291.029134448576
Trimmed Mean ( 4 / 24 )5.420.0180317561754043300.580816825429
Trimmed Mean ( 5 / 24 )5.420634920634920.0173203203780002312.963894566295
Trimmed Mean ( 6 / 24 )5.421311475409840.0165517493005747327.537070370055
Trimmed Mean ( 7 / 24 )5.422033898305080.0156072853498499347.40403451118
Trimmed Mean ( 8 / 24 )5.422982456140350.014483516065223374.424444431812
Trimmed Mean ( 9 / 24 )5.424181818181820.0132514935543230409.326073015544
Trimmed Mean ( 10 / 24 )5.423962264150940.0128724332277100421.362625713607
Trimmed Mean ( 11 / 24 )5.424117647058820.0126092915339171430.168311397098
Trimmed Mean ( 12 / 24 )5.424489795918370.0123237962683346440.163864916878
Trimmed Mean ( 13 / 24 )5.424893617021280.0119545560287741453.792981016089
Trimmed Mean ( 14 / 24 )5.425555555555560.0115363087577044470.302561201144
Trimmed Mean ( 15 / 24 )5.426744186046510.0111106432378936488.427543739161
Trimmed Mean ( 16 / 24 )5.42804878048780.0105415525780362514.919291091652
Trimmed Mean ( 17 / 24 )5.428974358974360.0101526465028314534.734894735115
Trimmed Mean ( 18 / 24 )5.429729729729730.0097220106183565558.498642192146
Trimmed Mean ( 19 / 24 )5.429714285714290.00943340848677037575.58350126882
Trimmed Mean ( 20 / 24 )5.429696969696970.00901897041599286602.030688566045
Trimmed Mean ( 21 / 24 )5.429032258064520.00864291416791286628.148348183301
Trimmed Mean ( 22 / 24 )5.427586206896550.00850463757019906638.191358784677
Trimmed Mean ( 23 / 24 )5.42629629629630.00840817923838956645.359255844742
Trimmed Mean ( 24 / 24 )5.42480.00820812605491248660.9060294284
Median5.41
Midrange5.41
Midmean - Weighted Average at Xnp5.4348717948718
Midmean - Weighted Average at X(n+1)p5.4348717948718
Midmean - Empirical Distribution Function5.4348717948718
Midmean - Empirical Distribution Function - Averaging5.4348717948718
Midmean - Empirical Distribution Function - Interpolation5.4348717948718
Midmean - Closest Observation5.4315
Midmean - True Basic - Statistics Graphics Toolkit5.4348717948718
Midmean - MS Excel (old versions)5.4348717948718
Number of observations73



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')