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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 09 Oct 2013 07:16:36 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/09/t1381317416g0lyw9z3hmqdopt.htm/, Retrieved Mon, 29 Apr 2024 02:03:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214409, Retrieved Mon, 29 Apr 2024 02:03:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-09 11:16:36] [8ac251e42bd40906c127555d6859e07b] [Current]
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Dataseries X:
28,53
28,48
28,68
28,89
29,2
29,21
29,15
29,22
29,34
29,13
28,84
28,76
28,75
28,89
28,82
29,12
29,21
29,3
29,32
29,52
29,64
29,54
29,54
29,34
29,34
29,54
29,94
30,17
30,23
30,34
30,34
30,36
30,3
30,28
29,89
29,58
29,68
29,73
30,07
30,32
30,55
30,62
30,67
30,79
30,8
30,5
30,07
29,41
29,42
29,99
30,14
30,41
30,78
30,88
30,92
30,93
31,62
31,48
31,3
31,11
31,16
31,22
31,66
32,11
32,27
32,36
32,42
32,52
32,41
31,87
31,04
30,58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214409&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214409&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean30.17416666666670.124685951346669242.001334879921
Geometric Mean30.1560738548745
Harmonic Mean30.1381798537074
Quadratic Mean30.1924517332837
Winsorized Mean ( 1 / 24 )30.17347222222220.124193825955269242.954687885127
Winsorized Mean ( 2 / 24 )30.17736111111110.123378527605743244.591678120387
Winsorized Mean ( 3 / 24 )30.17819444444440.12236236341615246.629711963061
Winsorized Mean ( 4 / 24 )30.173750.12103321455626249.301401360156
Winsorized Mean ( 5 / 24 )30.16680555555560.117706769820334256.287770037371
Winsorized Mean ( 6 / 24 )30.14847222222220.112961219355734266.892234292192
Winsorized Mean ( 7 / 24 )30.13291666666670.107941588109783279.159471287562
Winsorized Mean ( 8 / 24 )30.12847222222220.107062729283593281.409529010011
Winsorized Mean ( 9 / 24 )30.13972222222220.0992473578331592303.682867536775
Winsorized Mean ( 10 / 24 )30.11611111111110.0944563879035641318.836150519098
Winsorized Mean ( 11 / 24 )30.10694444444440.0918857047757256327.656456659166
Winsorized Mean ( 12 / 24 )30.10527777777780.0889892760112188338.302311550242
Winsorized Mean ( 13 / 24 )30.09805555555560.0872393589317725345.005464552925
Winsorized Mean ( 14 / 24 )30.08444444444440.0850501299494399353.726025607825
Winsorized Mean ( 15 / 24 )30.06361111111110.0812098716496169370.196510601836
Winsorized Mean ( 16 / 24 )30.07916666666670.0783280264909012384.015377562982
Winsorized Mean ( 17 / 24 )30.07444444444440.07625139853226394.411709468132
Winsorized Mean ( 18 / 24 )30.05944444444440.0726288959664076413.877204719559
Winsorized Mean ( 19 / 24 )30.05680555555560.0722508200723718416.006427684121
Winsorized Mean ( 20 / 24 )30.05402777777780.0718546665385995418.261321436
Winsorized Mean ( 21 / 24 )30.04236111111110.0645310800443353465.548710644094
Winsorized Mean ( 22 / 24 )30.03013888888890.0620387496454643484.054547528819
Winsorized Mean ( 23 / 24 )30.04930555555560.0559864330721398536.724772532595
Winsorized Mean ( 24 / 24 )30.04597222222220.0537730042202642558.755692710572
Trimmed Mean ( 1 / 24 )30.16485714285710.121323744790479248.631108402981
Trimmed Mean ( 2 / 24 )30.15573529411760.117900554101495255.772634182517
Trimmed Mean ( 3 / 24 )30.14393939393940.114315817965832263.69001184901
Trimmed Mean ( 4 / 24 )30.131093750.110461719736557272.774077950808
Trimmed Mean ( 5 / 24 )30.11870967741940.106297349886341283.34393763931
Trimmed Mean ( 6 / 24 )30.10716666666670.102336293871307294.19832913363
Trimmed Mean ( 7 / 24 )30.09862068965520.098929371090488304.243526041673
Trimmed Mean ( 8 / 24 )30.09232142857140.0961178224048953313.077436376033
Trimmed Mean ( 9 / 24 )30.08629629629630.0928500125392142324.03114952289
Trimmed Mean ( 10 / 24 )30.07807692307690.0906529184225044331.793807044276
Trimmed Mean ( 11 / 24 )30.07260.0889864974852583337.945652990578
Trimmed Mean ( 12 / 24 )30.06791666666670.0873968278944078344.038993074148
Trimmed Mean ( 13 / 24 )30.06304347826090.0859299060296388349.855421323184
Trimmed Mean ( 14 / 24 )30.05863636363640.0843458793826093356.373501392813
Trimmed Mean ( 15 / 24 )30.05547619047620.082697131797565363.440370145475
Trimmed Mean ( 16 / 24 )30.05450.0813097512050409369.629712975149
Trimmed Mean ( 17 / 24 )30.05157894736840.0799844635658629375.717703258991
Trimmed Mean ( 18 / 24 )30.04888888888890.0785440709146002382.573611718707
Trimmed Mean ( 19 / 24 )30.04764705882350.0773123152297914388.652790561432
Trimmed Mean ( 20 / 24 )30.04656250.0754991579943969397.972153573287
Trimmed Mean ( 21 / 24 )30.04566666666670.0728511051728402412.42568105704
Trimmed Mean ( 22 / 24 )30.04607142857140.0711160823269455422.493343916769
Trimmed Mean ( 23 / 24 )30.04807692307690.0690819340310291434.962879145514
Trimmed Mean ( 24 / 24 )30.04791666666670.0678365981303141442.945511638786
Median30.105
Midrange30.5
Midmean - Weighted Average at Xnp30.0291891891892
Midmean - Weighted Average at X(n+1)p30.0488888888889
Midmean - Empirical Distribution Function30.0291891891892
Midmean - Empirical Distribution Function - Averaging30.0488888888889
Midmean - Empirical Distribution Function - Interpolation30.0488888888889
Midmean - Closest Observation30.0291891891892
Midmean - True Basic - Statistics Graphics Toolkit30.0488888888889
Midmean - MS Excel (old versions)30.0515789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 30.1741666666667 & 0.124685951346669 & 242.001334879921 \tabularnewline
Geometric Mean & 30.1560738548745 &  &  \tabularnewline
Harmonic Mean & 30.1381798537074 &  &  \tabularnewline
Quadratic Mean & 30.1924517332837 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 30.1734722222222 & 0.124193825955269 & 242.954687885127 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 30.1773611111111 & 0.123378527605743 & 244.591678120387 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 30.1781944444444 & 0.12236236341615 & 246.629711963061 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 30.17375 & 0.12103321455626 & 249.301401360156 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 30.1668055555556 & 0.117706769820334 & 256.287770037371 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 30.1484722222222 & 0.112961219355734 & 266.892234292192 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 30.1329166666667 & 0.107941588109783 & 279.159471287562 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 30.1284722222222 & 0.107062729283593 & 281.409529010011 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 30.1397222222222 & 0.0992473578331592 & 303.682867536775 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 30.1161111111111 & 0.0944563879035641 & 318.836150519098 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 30.1069444444444 & 0.0918857047757256 & 327.656456659166 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 30.1052777777778 & 0.0889892760112188 & 338.302311550242 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 30.0980555555556 & 0.0872393589317725 & 345.005464552925 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 30.0844444444444 & 0.0850501299494399 & 353.726025607825 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 30.0636111111111 & 0.0812098716496169 & 370.196510601836 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 30.0791666666667 & 0.0783280264909012 & 384.015377562982 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 30.0744444444444 & 0.07625139853226 & 394.411709468132 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 30.0594444444444 & 0.0726288959664076 & 413.877204719559 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 30.0568055555556 & 0.0722508200723718 & 416.006427684121 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 30.0540277777778 & 0.0718546665385995 & 418.261321436 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 30.0423611111111 & 0.0645310800443353 & 465.548710644094 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 30.0301388888889 & 0.0620387496454643 & 484.054547528819 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 30.0493055555556 & 0.0559864330721398 & 536.724772532595 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 30.0459722222222 & 0.0537730042202642 & 558.755692710572 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 30.1648571428571 & 0.121323744790479 & 248.631108402981 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 30.1557352941176 & 0.117900554101495 & 255.772634182517 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 30.1439393939394 & 0.114315817965832 & 263.69001184901 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 30.13109375 & 0.110461719736557 & 272.774077950808 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 30.1187096774194 & 0.106297349886341 & 283.34393763931 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 30.1071666666667 & 0.102336293871307 & 294.19832913363 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 30.0986206896552 & 0.098929371090488 & 304.243526041673 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 30.0923214285714 & 0.0961178224048953 & 313.077436376033 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 30.0862962962963 & 0.0928500125392142 & 324.03114952289 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 30.0780769230769 & 0.0906529184225044 & 331.793807044276 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 30.0726 & 0.0889864974852583 & 337.945652990578 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 30.0679166666667 & 0.0873968278944078 & 344.038993074148 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 30.0630434782609 & 0.0859299060296388 & 349.855421323184 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 30.0586363636364 & 0.0843458793826093 & 356.373501392813 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 30.0554761904762 & 0.082697131797565 & 363.440370145475 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 30.0545 & 0.0813097512050409 & 369.629712975149 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 30.0515789473684 & 0.0799844635658629 & 375.717703258991 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 30.0488888888889 & 0.0785440709146002 & 382.573611718707 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 30.0476470588235 & 0.0773123152297914 & 388.652790561432 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 30.0465625 & 0.0754991579943969 & 397.972153573287 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 30.0456666666667 & 0.0728511051728402 & 412.42568105704 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 30.0460714285714 & 0.0711160823269455 & 422.493343916769 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 30.0480769230769 & 0.0690819340310291 & 434.962879145514 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 30.0479166666667 & 0.0678365981303141 & 442.945511638786 \tabularnewline
Median & 30.105 &  &  \tabularnewline
Midrange & 30.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 30.0291891891892 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 30.0488888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 30.0291891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 30.0488888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 30.0488888888889 &  &  \tabularnewline
Midmean - Closest Observation & 30.0291891891892 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 30.0488888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 30.0515789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214409&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]30.1741666666667[/C][C]0.124685951346669[/C][C]242.001334879921[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]30.1560738548745[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]30.1381798537074[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]30.1924517332837[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]30.1734722222222[/C][C]0.124193825955269[/C][C]242.954687885127[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]30.1773611111111[/C][C]0.123378527605743[/C][C]244.591678120387[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]30.1781944444444[/C][C]0.12236236341615[/C][C]246.629711963061[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]30.17375[/C][C]0.12103321455626[/C][C]249.301401360156[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]30.1668055555556[/C][C]0.117706769820334[/C][C]256.287770037371[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]30.1484722222222[/C][C]0.112961219355734[/C][C]266.892234292192[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]30.1329166666667[/C][C]0.107941588109783[/C][C]279.159471287562[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]30.1284722222222[/C][C]0.107062729283593[/C][C]281.409529010011[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]30.1397222222222[/C][C]0.0992473578331592[/C][C]303.682867536775[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]30.1161111111111[/C][C]0.0944563879035641[/C][C]318.836150519098[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]30.1069444444444[/C][C]0.0918857047757256[/C][C]327.656456659166[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]30.1052777777778[/C][C]0.0889892760112188[/C][C]338.302311550242[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]30.0980555555556[/C][C]0.0872393589317725[/C][C]345.005464552925[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]30.0844444444444[/C][C]0.0850501299494399[/C][C]353.726025607825[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]30.0636111111111[/C][C]0.0812098716496169[/C][C]370.196510601836[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]30.0791666666667[/C][C]0.0783280264909012[/C][C]384.015377562982[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]30.0744444444444[/C][C]0.07625139853226[/C][C]394.411709468132[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]30.0594444444444[/C][C]0.0726288959664076[/C][C]413.877204719559[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]30.0568055555556[/C][C]0.0722508200723718[/C][C]416.006427684121[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]30.0540277777778[/C][C]0.0718546665385995[/C][C]418.261321436[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]30.0423611111111[/C][C]0.0645310800443353[/C][C]465.548710644094[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]30.0301388888889[/C][C]0.0620387496454643[/C][C]484.054547528819[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]30.0493055555556[/C][C]0.0559864330721398[/C][C]536.724772532595[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]30.0459722222222[/C][C]0.0537730042202642[/C][C]558.755692710572[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]30.1648571428571[/C][C]0.121323744790479[/C][C]248.631108402981[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]30.1557352941176[/C][C]0.117900554101495[/C][C]255.772634182517[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]30.1439393939394[/C][C]0.114315817965832[/C][C]263.69001184901[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]30.13109375[/C][C]0.110461719736557[/C][C]272.774077950808[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]30.1187096774194[/C][C]0.106297349886341[/C][C]283.34393763931[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]30.1071666666667[/C][C]0.102336293871307[/C][C]294.19832913363[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]30.0986206896552[/C][C]0.098929371090488[/C][C]304.243526041673[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]30.0923214285714[/C][C]0.0961178224048953[/C][C]313.077436376033[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]30.0862962962963[/C][C]0.0928500125392142[/C][C]324.03114952289[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]30.0780769230769[/C][C]0.0906529184225044[/C][C]331.793807044276[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]30.0726[/C][C]0.0889864974852583[/C][C]337.945652990578[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]30.0679166666667[/C][C]0.0873968278944078[/C][C]344.038993074148[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]30.0630434782609[/C][C]0.0859299060296388[/C][C]349.855421323184[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]30.0586363636364[/C][C]0.0843458793826093[/C][C]356.373501392813[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]30.0554761904762[/C][C]0.082697131797565[/C][C]363.440370145475[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]30.0545[/C][C]0.0813097512050409[/C][C]369.629712975149[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]30.0515789473684[/C][C]0.0799844635658629[/C][C]375.717703258991[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]30.0488888888889[/C][C]0.0785440709146002[/C][C]382.573611718707[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]30.0476470588235[/C][C]0.0773123152297914[/C][C]388.652790561432[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]30.0465625[/C][C]0.0754991579943969[/C][C]397.972153573287[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]30.0456666666667[/C][C]0.0728511051728402[/C][C]412.42568105704[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]30.0460714285714[/C][C]0.0711160823269455[/C][C]422.493343916769[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]30.0480769230769[/C][C]0.0690819340310291[/C][C]434.962879145514[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]30.0479166666667[/C][C]0.0678365981303141[/C][C]442.945511638786[/C][/ROW]
[ROW][C]Median[/C][C]30.105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]30.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]30.0291891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]30.0488888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]30.0291891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]30.0488888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]30.0488888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]30.0291891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]30.0488888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]30.0515789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214409&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 Mean30.17416666666670.124685951346669242.001334879921
Geometric Mean30.1560738548745
Harmonic Mean30.1381798537074
Quadratic Mean30.1924517332837
Winsorized Mean ( 1 / 24 )30.17347222222220.124193825955269242.954687885127
Winsorized Mean ( 2 / 24 )30.17736111111110.123378527605743244.591678120387
Winsorized Mean ( 3 / 24 )30.17819444444440.12236236341615246.629711963061
Winsorized Mean ( 4 / 24 )30.173750.12103321455626249.301401360156
Winsorized Mean ( 5 / 24 )30.16680555555560.117706769820334256.287770037371
Winsorized Mean ( 6 / 24 )30.14847222222220.112961219355734266.892234292192
Winsorized Mean ( 7 / 24 )30.13291666666670.107941588109783279.159471287562
Winsorized Mean ( 8 / 24 )30.12847222222220.107062729283593281.409529010011
Winsorized Mean ( 9 / 24 )30.13972222222220.0992473578331592303.682867536775
Winsorized Mean ( 10 / 24 )30.11611111111110.0944563879035641318.836150519098
Winsorized Mean ( 11 / 24 )30.10694444444440.0918857047757256327.656456659166
Winsorized Mean ( 12 / 24 )30.10527777777780.0889892760112188338.302311550242
Winsorized Mean ( 13 / 24 )30.09805555555560.0872393589317725345.005464552925
Winsorized Mean ( 14 / 24 )30.08444444444440.0850501299494399353.726025607825
Winsorized Mean ( 15 / 24 )30.06361111111110.0812098716496169370.196510601836
Winsorized Mean ( 16 / 24 )30.07916666666670.0783280264909012384.015377562982
Winsorized Mean ( 17 / 24 )30.07444444444440.07625139853226394.411709468132
Winsorized Mean ( 18 / 24 )30.05944444444440.0726288959664076413.877204719559
Winsorized Mean ( 19 / 24 )30.05680555555560.0722508200723718416.006427684121
Winsorized Mean ( 20 / 24 )30.05402777777780.0718546665385995418.261321436
Winsorized Mean ( 21 / 24 )30.04236111111110.0645310800443353465.548710644094
Winsorized Mean ( 22 / 24 )30.03013888888890.0620387496454643484.054547528819
Winsorized Mean ( 23 / 24 )30.04930555555560.0559864330721398536.724772532595
Winsorized Mean ( 24 / 24 )30.04597222222220.0537730042202642558.755692710572
Trimmed Mean ( 1 / 24 )30.16485714285710.121323744790479248.631108402981
Trimmed Mean ( 2 / 24 )30.15573529411760.117900554101495255.772634182517
Trimmed Mean ( 3 / 24 )30.14393939393940.114315817965832263.69001184901
Trimmed Mean ( 4 / 24 )30.131093750.110461719736557272.774077950808
Trimmed Mean ( 5 / 24 )30.11870967741940.106297349886341283.34393763931
Trimmed Mean ( 6 / 24 )30.10716666666670.102336293871307294.19832913363
Trimmed Mean ( 7 / 24 )30.09862068965520.098929371090488304.243526041673
Trimmed Mean ( 8 / 24 )30.09232142857140.0961178224048953313.077436376033
Trimmed Mean ( 9 / 24 )30.08629629629630.0928500125392142324.03114952289
Trimmed Mean ( 10 / 24 )30.07807692307690.0906529184225044331.793807044276
Trimmed Mean ( 11 / 24 )30.07260.0889864974852583337.945652990578
Trimmed Mean ( 12 / 24 )30.06791666666670.0873968278944078344.038993074148
Trimmed Mean ( 13 / 24 )30.06304347826090.0859299060296388349.855421323184
Trimmed Mean ( 14 / 24 )30.05863636363640.0843458793826093356.373501392813
Trimmed Mean ( 15 / 24 )30.05547619047620.082697131797565363.440370145475
Trimmed Mean ( 16 / 24 )30.05450.0813097512050409369.629712975149
Trimmed Mean ( 17 / 24 )30.05157894736840.0799844635658629375.717703258991
Trimmed Mean ( 18 / 24 )30.04888888888890.0785440709146002382.573611718707
Trimmed Mean ( 19 / 24 )30.04764705882350.0773123152297914388.652790561432
Trimmed Mean ( 20 / 24 )30.04656250.0754991579943969397.972153573287
Trimmed Mean ( 21 / 24 )30.04566666666670.0728511051728402412.42568105704
Trimmed Mean ( 22 / 24 )30.04607142857140.0711160823269455422.493343916769
Trimmed Mean ( 23 / 24 )30.04807692307690.0690819340310291434.962879145514
Trimmed Mean ( 24 / 24 )30.04791666666670.0678365981303141442.945511638786
Median30.105
Midrange30.5
Midmean - Weighted Average at Xnp30.0291891891892
Midmean - Weighted Average at X(n+1)p30.0488888888889
Midmean - Empirical Distribution Function30.0291891891892
Midmean - Empirical Distribution Function - Averaging30.0488888888889
Midmean - Empirical Distribution Function - Interpolation30.0488888888889
Midmean - Closest Observation30.0291891891892
Midmean - True Basic - Statistics Graphics Toolkit30.0488888888889
Midmean - MS Excel (old versions)30.0515789473684
Number of observations72



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')