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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 03 Mar 2013 14:02:09 -0500
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/Mar/03/t1362337378g8t4fkydm5y5k5q.htm/, Retrieved Fri, 03 May 2024 22:01:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207284, Retrieved Fri, 03 May 2024 22:01:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentrummaten indexcijfer braadkip
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten inde...] [2013-03-03 19:02:09] [d0c193e893cebff5c92468d6d00a5cdb] [Current]
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Dataseries X:
99,23
101,14
100,8
98,93
100,97
101,69
102,14
102,52
103,4
105,83
104,35
106,61
105,63
106,73
106,19
107,26
106,27
107,45
107,63
107,45
107,74
108,15
108,99
108,83
110,78
110,66
108,51
108,29
109,33
107,06
108,02
109,43
109,85
110,5
109,9
110,92
108,36
109,01
108,03
106,28
106,6
108,06
107,42
107,58
107,59
109,66
107,85
110,74
108,8
109,18
108,38
108,59
109,52
108,71
109,78
109,77
109,34
111,86
110,74
110,67
111,36
112,21
110,2
110,99
110,43
110,72
111,19
111,52
111,99
111,65
114,45
115,58




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=207284&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=207284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207284&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 Mean108.1109722222220.389890898011482277.285191251216
Geometric Mean108.060097850558
Harmonic Mean108.008230883566
Quadratic Mean108.160877278298
Winsorized Mean ( 1 / 24 )108.0994444444440.38457875298718281.085326749832
Winsorized Mean ( 2 / 24 )108.0808333333330.35888235863524301.159504591822
Winsorized Mean ( 3 / 24 )108.078750.355419308533902304.088009303217
Winsorized Mean ( 4 / 24 )108.0809722222220.351669901845376307.336430143924
Winsorized Mean ( 5 / 24 )108.1045833333330.339090940289453318.807052883966
Winsorized Mean ( 6 / 24 )108.131250.327677064959734329.993342723841
Winsorized Mean ( 7 / 24 )108.1526388888890.316035879845298342.216329809864
Winsorized Mean ( 8 / 24 )108.2315277777780.289529910107267373.818123791353
Winsorized Mean ( 9 / 24 )108.3252777777780.259071184064245418.129396246998
Winsorized Mean ( 10 / 24 )108.4933333333330.222030218304571488.64219547137
Winsorized Mean ( 11 / 24 )108.50250.213302314903135508.679430175305
Winsorized Mean ( 12 / 24 )108.5558333333330.202042557959745537.291917255185
Winsorized Mean ( 13 / 24 )108.5702777777780.199679513587171543.722667525333
Winsorized Mean ( 14 / 24 )108.5683333333330.198770083679321546.200571653874
Winsorized Mean ( 15 / 24 )108.6245833333330.186665716955582581.920371372644
Winsorized Mean ( 16 / 24 )108.6245833333330.185983716442301584.054267820983
Winsorized Mean ( 17 / 24 )108.6151388888890.175919893147394617.412487841192
Winsorized Mean ( 18 / 24 )108.6801388888890.161179690189428674.27936336868
Winsorized Mean ( 19 / 24 )108.6722222222220.144647488806698751.290071599156
Winsorized Mean ( 20 / 24 )108.6333333333330.12648909594428858.835558293401
Winsorized Mean ( 21 / 24 )108.62750.123262216204569881.271677118958
Winsorized Mean ( 22 / 24 )108.6061111111110.120298200747611902.807443803502
Winsorized Mean ( 23 / 24 )108.6444444444440.114321480806293950.341472820248
Winsorized Mean ( 24 / 24 )108.6111111111110.108850976281266997.796389354055
Trimmed Mean ( 1 / 24 )108.1354285714290.363153241540223297.768038949066
Trimmed Mean ( 2 / 24 )108.1735294117650.337091883425273320.902207174457
Trimmed Mean ( 3 / 24 )108.2240909090910.322747454964984335.321283697907
Trimmed Mean ( 4 / 24 )108.278593750.306945789380515352.761293675115
Trimmed Mean ( 5 / 24 )108.3359677419350.28900515546916374.858253189521
Trimmed Mean ( 6 / 24 )108.39150.271296825477417399.531029562388
Trimmed Mean ( 7 / 24 )108.4453448275860.252940387076147428.738747817836
Trimmed Mean ( 8 / 24 )108.4991071428570.233373937269085464.915270370381
Trimmed Mean ( 9 / 24 )108.5437037037040.216701383494445500.890681699253
Trimmed Mean ( 10 / 24 )108.5773076923080.204371367271761531.274557398874
Trimmed Mean ( 11 / 24 )108.58940.198551573519171546.90777854508
Trimmed Mean ( 12 / 24 )108.601250.193151730172925562.258748098045
Trimmed Mean ( 13 / 24 )108.6071739130430.188787041806262575.289346524636
Trimmed Mean ( 14 / 24 )108.6118181818180.18358028260531591.63117433112
Trimmed Mean ( 15 / 24 )108.6171428571430.176888609645542614.04260610559
Trimmed Mean ( 16 / 24 )108.616250.170965466410992635.311050121034
Trimmed Mean ( 17 / 24 )108.6152631578950.163086227549205665.998992006385
Trimmed Mean ( 18 / 24 )108.6152777777780.155045045226807700.540140569408
Trimmed Mean ( 19 / 24 )108.6076470588240.14799615716426733.854507710496
Trimmed Mean ( 20 / 24 )108.60.142774212680202760.64156097468
Trimmed Mean ( 21 / 24 )108.5960.140354723026559773.725298716529
Trimmed Mean ( 22 / 24 )108.5921428571430.137303353507311790.892138343586
Trimmed Mean ( 23 / 24 )108.5903846153850.133224484662578815.09329828083
Trimmed Mean ( 24 / 24 )108.5833333333330.128558996024927844.618709625575
Median108.55
Midrange107.255
Midmean - Weighted Average at Xnp108.564324324324
Midmean - Weighted Average at X(n+1)p108.615277777778
Midmean - Empirical Distribution Function108.564324324324
Midmean - Empirical Distribution Function - Averaging108.615277777778
Midmean - Empirical Distribution Function - Interpolation108.615277777778
Midmean - Closest Observation108.564324324324
Midmean - True Basic - Statistics Graphics Toolkit108.615277777778
Midmean - MS Excel (old versions)108.615263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.110972222222 & 0.389890898011482 & 277.285191251216 \tabularnewline
Geometric Mean & 108.060097850558 &  &  \tabularnewline
Harmonic Mean & 108.008230883566 &  &  \tabularnewline
Quadratic Mean & 108.160877278298 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 108.099444444444 & 0.38457875298718 & 281.085326749832 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 108.080833333333 & 0.35888235863524 & 301.159504591822 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 108.07875 & 0.355419308533902 & 304.088009303217 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 108.080972222222 & 0.351669901845376 & 307.336430143924 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 108.104583333333 & 0.339090940289453 & 318.807052883966 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 108.13125 & 0.327677064959734 & 329.993342723841 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 108.152638888889 & 0.316035879845298 & 342.216329809864 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 108.231527777778 & 0.289529910107267 & 373.818123791353 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 108.325277777778 & 0.259071184064245 & 418.129396246998 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 108.493333333333 & 0.222030218304571 & 488.64219547137 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 108.5025 & 0.213302314903135 & 508.679430175305 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 108.555833333333 & 0.202042557959745 & 537.291917255185 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 108.570277777778 & 0.199679513587171 & 543.722667525333 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 108.568333333333 & 0.198770083679321 & 546.200571653874 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 108.624583333333 & 0.186665716955582 & 581.920371372644 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 108.624583333333 & 0.185983716442301 & 584.054267820983 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 108.615138888889 & 0.175919893147394 & 617.412487841192 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.680138888889 & 0.161179690189428 & 674.27936336868 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.672222222222 & 0.144647488806698 & 751.290071599156 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.633333333333 & 0.12648909594428 & 858.835558293401 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.6275 & 0.123262216204569 & 881.271677118958 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.606111111111 & 0.120298200747611 & 902.807443803502 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.644444444444 & 0.114321480806293 & 950.341472820248 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.611111111111 & 0.108850976281266 & 997.796389354055 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 108.135428571429 & 0.363153241540223 & 297.768038949066 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 108.173529411765 & 0.337091883425273 & 320.902207174457 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 108.224090909091 & 0.322747454964984 & 335.321283697907 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 108.27859375 & 0.306945789380515 & 352.761293675115 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 108.335967741935 & 0.28900515546916 & 374.858253189521 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 108.3915 & 0.271296825477417 & 399.531029562388 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 108.445344827586 & 0.252940387076147 & 428.738747817836 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 108.499107142857 & 0.233373937269085 & 464.915270370381 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 108.543703703704 & 0.216701383494445 & 500.890681699253 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 108.577307692308 & 0.204371367271761 & 531.274557398874 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.5894 & 0.198551573519171 & 546.90777854508 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.60125 & 0.193151730172925 & 562.258748098045 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.607173913043 & 0.188787041806262 & 575.289346524636 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.611818181818 & 0.18358028260531 & 591.63117433112 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.617142857143 & 0.176888609645542 & 614.04260610559 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.61625 & 0.170965466410992 & 635.311050121034 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.615263157895 & 0.163086227549205 & 665.998992006385 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.615277777778 & 0.155045045226807 & 700.540140569408 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 108.607647058824 & 0.14799615716426 & 733.854507710496 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 108.6 & 0.142774212680202 & 760.64156097468 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 108.596 & 0.140354723026559 & 773.725298716529 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 108.592142857143 & 0.137303353507311 & 790.892138343586 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 108.590384615385 & 0.133224484662578 & 815.09329828083 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 108.583333333333 & 0.128558996024927 & 844.618709625575 \tabularnewline
Median & 108.55 &  &  \tabularnewline
Midrange & 107.255 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.564324324324 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.615277777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.564324324324 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.615277777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.615277777778 &  &  \tabularnewline
Midmean - Closest Observation & 108.564324324324 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.615277777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.615263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207284&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]108.110972222222[/C][C]0.389890898011482[/C][C]277.285191251216[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.060097850558[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.008230883566[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.160877278298[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]108.099444444444[/C][C]0.38457875298718[/C][C]281.085326749832[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]108.080833333333[/C][C]0.35888235863524[/C][C]301.159504591822[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]108.07875[/C][C]0.355419308533902[/C][C]304.088009303217[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]108.080972222222[/C][C]0.351669901845376[/C][C]307.336430143924[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]108.104583333333[/C][C]0.339090940289453[/C][C]318.807052883966[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]108.13125[/C][C]0.327677064959734[/C][C]329.993342723841[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]108.152638888889[/C][C]0.316035879845298[/C][C]342.216329809864[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]108.231527777778[/C][C]0.289529910107267[/C][C]373.818123791353[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]108.325277777778[/C][C]0.259071184064245[/C][C]418.129396246998[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]108.493333333333[/C][C]0.222030218304571[/C][C]488.64219547137[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]108.5025[/C][C]0.213302314903135[/C][C]508.679430175305[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]108.555833333333[/C][C]0.202042557959745[/C][C]537.291917255185[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]108.570277777778[/C][C]0.199679513587171[/C][C]543.722667525333[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]108.568333333333[/C][C]0.198770083679321[/C][C]546.200571653874[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]108.624583333333[/C][C]0.186665716955582[/C][C]581.920371372644[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]108.624583333333[/C][C]0.185983716442301[/C][C]584.054267820983[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]108.615138888889[/C][C]0.175919893147394[/C][C]617.412487841192[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.680138888889[/C][C]0.161179690189428[/C][C]674.27936336868[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.672222222222[/C][C]0.144647488806698[/C][C]751.290071599156[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.633333333333[/C][C]0.12648909594428[/C][C]858.835558293401[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.6275[/C][C]0.123262216204569[/C][C]881.271677118958[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.606111111111[/C][C]0.120298200747611[/C][C]902.807443803502[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.644444444444[/C][C]0.114321480806293[/C][C]950.341472820248[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.611111111111[/C][C]0.108850976281266[/C][C]997.796389354055[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]108.135428571429[/C][C]0.363153241540223[/C][C]297.768038949066[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]108.173529411765[/C][C]0.337091883425273[/C][C]320.902207174457[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]108.224090909091[/C][C]0.322747454964984[/C][C]335.321283697907[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]108.27859375[/C][C]0.306945789380515[/C][C]352.761293675115[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]108.335967741935[/C][C]0.28900515546916[/C][C]374.858253189521[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]108.3915[/C][C]0.271296825477417[/C][C]399.531029562388[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]108.445344827586[/C][C]0.252940387076147[/C][C]428.738747817836[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]108.499107142857[/C][C]0.233373937269085[/C][C]464.915270370381[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]108.543703703704[/C][C]0.216701383494445[/C][C]500.890681699253[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]108.577307692308[/C][C]0.204371367271761[/C][C]531.274557398874[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.5894[/C][C]0.198551573519171[/C][C]546.90777854508[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.60125[/C][C]0.193151730172925[/C][C]562.258748098045[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.607173913043[/C][C]0.188787041806262[/C][C]575.289346524636[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.611818181818[/C][C]0.18358028260531[/C][C]591.63117433112[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.617142857143[/C][C]0.176888609645542[/C][C]614.04260610559[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.61625[/C][C]0.170965466410992[/C][C]635.311050121034[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.615263157895[/C][C]0.163086227549205[/C][C]665.998992006385[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.615277777778[/C][C]0.155045045226807[/C][C]700.540140569408[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]108.607647058824[/C][C]0.14799615716426[/C][C]733.854507710496[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]108.6[/C][C]0.142774212680202[/C][C]760.64156097468[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]108.596[/C][C]0.140354723026559[/C][C]773.725298716529[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]108.592142857143[/C][C]0.137303353507311[/C][C]790.892138343586[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]108.590384615385[/C][C]0.133224484662578[/C][C]815.09329828083[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]108.583333333333[/C][C]0.128558996024927[/C][C]844.618709625575[/C][/ROW]
[ROW][C]Median[/C][C]108.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.564324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.615277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.564324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.615277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.615277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.564324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.615277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.615263157895[/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=207284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207284&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 Mean108.1109722222220.389890898011482277.285191251216
Geometric Mean108.060097850558
Harmonic Mean108.008230883566
Quadratic Mean108.160877278298
Winsorized Mean ( 1 / 24 )108.0994444444440.38457875298718281.085326749832
Winsorized Mean ( 2 / 24 )108.0808333333330.35888235863524301.159504591822
Winsorized Mean ( 3 / 24 )108.078750.355419308533902304.088009303217
Winsorized Mean ( 4 / 24 )108.0809722222220.351669901845376307.336430143924
Winsorized Mean ( 5 / 24 )108.1045833333330.339090940289453318.807052883966
Winsorized Mean ( 6 / 24 )108.131250.327677064959734329.993342723841
Winsorized Mean ( 7 / 24 )108.1526388888890.316035879845298342.216329809864
Winsorized Mean ( 8 / 24 )108.2315277777780.289529910107267373.818123791353
Winsorized Mean ( 9 / 24 )108.3252777777780.259071184064245418.129396246998
Winsorized Mean ( 10 / 24 )108.4933333333330.222030218304571488.64219547137
Winsorized Mean ( 11 / 24 )108.50250.213302314903135508.679430175305
Winsorized Mean ( 12 / 24 )108.5558333333330.202042557959745537.291917255185
Winsorized Mean ( 13 / 24 )108.5702777777780.199679513587171543.722667525333
Winsorized Mean ( 14 / 24 )108.5683333333330.198770083679321546.200571653874
Winsorized Mean ( 15 / 24 )108.6245833333330.186665716955582581.920371372644
Winsorized Mean ( 16 / 24 )108.6245833333330.185983716442301584.054267820983
Winsorized Mean ( 17 / 24 )108.6151388888890.175919893147394617.412487841192
Winsorized Mean ( 18 / 24 )108.6801388888890.161179690189428674.27936336868
Winsorized Mean ( 19 / 24 )108.6722222222220.144647488806698751.290071599156
Winsorized Mean ( 20 / 24 )108.6333333333330.12648909594428858.835558293401
Winsorized Mean ( 21 / 24 )108.62750.123262216204569881.271677118958
Winsorized Mean ( 22 / 24 )108.6061111111110.120298200747611902.807443803502
Winsorized Mean ( 23 / 24 )108.6444444444440.114321480806293950.341472820248
Winsorized Mean ( 24 / 24 )108.6111111111110.108850976281266997.796389354055
Trimmed Mean ( 1 / 24 )108.1354285714290.363153241540223297.768038949066
Trimmed Mean ( 2 / 24 )108.1735294117650.337091883425273320.902207174457
Trimmed Mean ( 3 / 24 )108.2240909090910.322747454964984335.321283697907
Trimmed Mean ( 4 / 24 )108.278593750.306945789380515352.761293675115
Trimmed Mean ( 5 / 24 )108.3359677419350.28900515546916374.858253189521
Trimmed Mean ( 6 / 24 )108.39150.271296825477417399.531029562388
Trimmed Mean ( 7 / 24 )108.4453448275860.252940387076147428.738747817836
Trimmed Mean ( 8 / 24 )108.4991071428570.233373937269085464.915270370381
Trimmed Mean ( 9 / 24 )108.5437037037040.216701383494445500.890681699253
Trimmed Mean ( 10 / 24 )108.5773076923080.204371367271761531.274557398874
Trimmed Mean ( 11 / 24 )108.58940.198551573519171546.90777854508
Trimmed Mean ( 12 / 24 )108.601250.193151730172925562.258748098045
Trimmed Mean ( 13 / 24 )108.6071739130430.188787041806262575.289346524636
Trimmed Mean ( 14 / 24 )108.6118181818180.18358028260531591.63117433112
Trimmed Mean ( 15 / 24 )108.6171428571430.176888609645542614.04260610559
Trimmed Mean ( 16 / 24 )108.616250.170965466410992635.311050121034
Trimmed Mean ( 17 / 24 )108.6152631578950.163086227549205665.998992006385
Trimmed Mean ( 18 / 24 )108.6152777777780.155045045226807700.540140569408
Trimmed Mean ( 19 / 24 )108.6076470588240.14799615716426733.854507710496
Trimmed Mean ( 20 / 24 )108.60.142774212680202760.64156097468
Trimmed Mean ( 21 / 24 )108.5960.140354723026559773.725298716529
Trimmed Mean ( 22 / 24 )108.5921428571430.137303353507311790.892138343586
Trimmed Mean ( 23 / 24 )108.5903846153850.133224484662578815.09329828083
Trimmed Mean ( 24 / 24 )108.5833333333330.128558996024927844.618709625575
Median108.55
Midrange107.255
Midmean - Weighted Average at Xnp108.564324324324
Midmean - Weighted Average at X(n+1)p108.615277777778
Midmean - Empirical Distribution Function108.564324324324
Midmean - Empirical Distribution Function - Averaging108.615277777778
Midmean - Empirical Distribution Function - Interpolation108.615277777778
Midmean - Closest Observation108.564324324324
Midmean - True Basic - Statistics Graphics Toolkit108.615277777778
Midmean - MS Excel (old versions)108.615263157895
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')