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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 computationWed, 07 Mar 2012 14:24:07 -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/2012/Mar/07/t133114840112cqrwosgsntzq1.htm/, Retrieved Sun, 19 May 2024 05:43:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163690, Retrieved Sun, 19 May 2024 05:43:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKEYWORD: KDG2011W52a
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 19:24:07] [118c7cedabc991c3d34fa0c13010a5e0] [Current]
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Dataseries X:
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,5751
1,5557
1,5553
1,577
1,4975
1,437
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614
1,4272
1,3686
1,3569
1,3406
1,2565
1,2209
1,277
1,2894
1,3067
1,3898
1,3661
1,322
1,336
1,3649
1,3999
1,4442
1,4349
1,4388
1,4264
1,4343
1,377
1,3706
1,3556
1,3179




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163690&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163690&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163690&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.36811250.010842153675013126.18457005945
Geometric Mean1.36509598511595
Harmonic Mean1.36211302379082
Quadratic Mean1.37115937282814
Winsorized Mean ( 1 / 24 )1.36820.0108097896930578126.570455008823
Winsorized Mean ( 2 / 24 )1.367891666666670.0106209362568387128.792004168738
Winsorized Mean ( 3 / 24 )1.368316666666670.010527058250008129.980915291851
Winsorized Mean ( 4 / 24 )1.368516666666670.0104241362889638131.283458766319
Winsorized Mean ( 5 / 24 )1.3667250.00918812549104134148.749056739875
Winsorized Mean ( 6 / 24 )1.36660.00902369750093715151.445679540795
Winsorized Mean ( 7 / 24 )1.366026388888890.00878057613071195155.573662656476
Winsorized Mean ( 8 / 24 )1.365648611111110.00858207976466497159.127932687587
Winsorized Mean ( 9 / 24 )1.365811111111110.00843058036389706162.006772031975
Winsorized Mean ( 10 / 24 )1.365408333333330.00833687547958636163.779384336094
Winsorized Mean ( 11 / 24 )1.364919444444440.00806387295910001169.263510395975
Winsorized Mean ( 12 / 24 )1.364186111111110.00794171853028195171.774673946129
Winsorized Mean ( 13 / 24 )1.36431250.00787624395557991173.218669672294
Winsorized Mean ( 14 / 24 )1.362484722222220.00742559326171506183.484965335623
Winsorized Mean ( 15 / 24 )1.362818055555560.00703095834853693193.831052325768
Winsorized Mean ( 16 / 24 )1.362706944444440.00692715402858878196.719596362441
Winsorized Mean ( 17 / 24 )1.364690277777780.00649263129927086210.190632252756
Winsorized Mean ( 18 / 24 )1.365815277777780.00629330215652657217.026807835905
Winsorized Mean ( 19 / 24 )1.364390277777780.00594913137875334229.342771391895
Winsorized Mean ( 20 / 24 )1.364473611111110.00590610145541252231.027797509416
Winsorized Mean ( 21 / 24 )1.367419444444440.00548497401103744249.302811953672
Winsorized Mean ( 22 / 24 )1.3666250.00527190628634641259.227862896461
Winsorized Mean ( 23 / 24 )1.362919444444440.00452694879696728301.068005310222
Winsorized Mean ( 24 / 24 )1.360752777777780.00415902490425749327.180723631833
Trimmed Mean ( 1 / 24 )1.367618571428570.0104444842730629130.941704317155
Trimmed Mean ( 2 / 24 )1.367002941176470.0100086398082011136.582289639032
Trimmed Mean ( 3 / 24 )1.366518181818180.00961023272365216142.194078032573
Trimmed Mean ( 4 / 24 )1.365843750.00917393323320275148.883114284795
Trimmed Mean ( 5 / 24 )1.365067741935480.00868289308543661157.21346888689
Trimmed Mean ( 6 / 24 )1.364670.00850058465918801160.53836938439
Trimmed Mean ( 7 / 24 )1.364270689655170.00832280702705299163.919538831149
Trimmed Mean ( 8 / 24 )1.363948214285710.00816583474513656167.031082168061
Trimmed Mean ( 9 / 24 )1.363664814814810.00801717067040503170.093025442094
Trimmed Mean ( 10 / 24 )1.363334615384620.00786340872119442173.377051063108
Trimmed Mean ( 11 / 24 )1.3630360.0076881619894166177.290229039962
Trimmed Mean ( 12 / 24 )1.362779166666670.00752458615431674181.110181838354
Trimmed Mean ( 13 / 24 )1.362595652173910.00733913404079862185.661638634637
Trimmed Mean ( 14 / 24 )1.362379545454550.00711058346739427191.598840193884
Trimmed Mean ( 15 / 24 )1.362366666666670.00691575795494367196.994555845147
Trimmed Mean ( 16 / 24 )1.36231250.00674639522691135201.931913885765
Trimmed Mean ( 17 / 24 )1.362265789473680.00653837917404254208.349157063558
Trimmed Mean ( 18 / 24 )1.361980555555560.006358278966808214.20585077589
Trimmed Mean ( 19 / 24 )1.361529411764710.00615132339341753221.339267127731
Trimmed Mean ( 20 / 24 )1.3611906250.00595112377462842228.728333764994
Trimmed Mean ( 21 / 24 )1.360796666666670.00566597727381896240.169806708291
Trimmed Mean ( 22 / 24 )1.359985714285710.00536591415971811253.449025423314
Trimmed Mean ( 23 / 24 )1.359150.00498250246053434272.784611902478
Trimmed Mean ( 24 / 24 )1.358658333333330.00470755604716481288.612247994711
Median1.35955
Midrange1.3854
Midmean - Weighted Average at Xnp1.3603027027027
Midmean - Weighted Average at X(n+1)p1.36198055555556
Midmean - Empirical Distribution Function1.3603027027027
Midmean - Empirical Distribution Function - Averaging1.36198055555556
Midmean - Empirical Distribution Function - Interpolation1.36198055555556
Midmean - Closest Observation1.3603027027027
Midmean - True Basic - Statistics Graphics Toolkit1.36198055555556
Midmean - MS Excel (old versions)1.36226578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.3681125 & 0.010842153675013 & 126.18457005945 \tabularnewline
Geometric Mean & 1.36509598511595 &  &  \tabularnewline
Harmonic Mean & 1.36211302379082 &  &  \tabularnewline
Quadratic Mean & 1.37115937282814 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.3682 & 0.0108097896930578 & 126.570455008823 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.36789166666667 & 0.0106209362568387 & 128.792004168738 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.36831666666667 & 0.010527058250008 & 129.980915291851 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.36851666666667 & 0.0104241362889638 & 131.283458766319 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.366725 & 0.00918812549104134 & 148.749056739875 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.3666 & 0.00902369750093715 & 151.445679540795 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.36602638888889 & 0.00878057613071195 & 155.573662656476 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.36564861111111 & 0.00858207976466497 & 159.127932687587 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.36581111111111 & 0.00843058036389706 & 162.006772031975 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.36540833333333 & 0.00833687547958636 & 163.779384336094 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.36491944444444 & 0.00806387295910001 & 169.263510395975 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.36418611111111 & 0.00794171853028195 & 171.774673946129 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.3643125 & 0.00787624395557991 & 173.218669672294 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.36248472222222 & 0.00742559326171506 & 183.484965335623 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.36281805555556 & 0.00703095834853693 & 193.831052325768 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.36270694444444 & 0.00692715402858878 & 196.719596362441 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.36469027777778 & 0.00649263129927086 & 210.190632252756 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.36581527777778 & 0.00629330215652657 & 217.026807835905 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.36439027777778 & 0.00594913137875334 & 229.342771391895 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.36447361111111 & 0.00590610145541252 & 231.027797509416 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.36741944444444 & 0.00548497401103744 & 249.302811953672 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.366625 & 0.00527190628634641 & 259.227862896461 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.36291944444444 & 0.00452694879696728 & 301.068005310222 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.36075277777778 & 0.00415902490425749 & 327.180723631833 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.36761857142857 & 0.0104444842730629 & 130.941704317155 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.36700294117647 & 0.0100086398082011 & 136.582289639032 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.36651818181818 & 0.00961023272365216 & 142.194078032573 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.36584375 & 0.00917393323320275 & 148.883114284795 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.36506774193548 & 0.00868289308543661 & 157.21346888689 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.36467 & 0.00850058465918801 & 160.53836938439 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.36427068965517 & 0.00832280702705299 & 163.919538831149 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.36394821428571 & 0.00816583474513656 & 167.031082168061 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.36366481481481 & 0.00801717067040503 & 170.093025442094 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.36333461538462 & 0.00786340872119442 & 173.377051063108 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.363036 & 0.0076881619894166 & 177.290229039962 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.36277916666667 & 0.00752458615431674 & 181.110181838354 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.36259565217391 & 0.00733913404079862 & 185.661638634637 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.36237954545455 & 0.00711058346739427 & 191.598840193884 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.36236666666667 & 0.00691575795494367 & 196.994555845147 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.3623125 & 0.00674639522691135 & 201.931913885765 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.36226578947368 & 0.00653837917404254 & 208.349157063558 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.36198055555556 & 0.006358278966808 & 214.20585077589 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.36152941176471 & 0.00615132339341753 & 221.339267127731 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.361190625 & 0.00595112377462842 & 228.728333764994 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.36079666666667 & 0.00566597727381896 & 240.169806708291 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.35998571428571 & 0.00536591415971811 & 253.449025423314 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.35915 & 0.00498250246053434 & 272.784611902478 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.35865833333333 & 0.00470755604716481 & 288.612247994711 \tabularnewline
Median & 1.35955 &  &  \tabularnewline
Midrange & 1.3854 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.3603027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.36198055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.3603027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.36198055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.36198055555556 &  &  \tabularnewline
Midmean - Closest Observation & 1.3603027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.36198055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.36226578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163690&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]1.3681125[/C][C]0.010842153675013[/C][C]126.18457005945[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.36509598511595[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.36211302379082[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.37115937282814[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.3682[/C][C]0.0108097896930578[/C][C]126.570455008823[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.36789166666667[/C][C]0.0106209362568387[/C][C]128.792004168738[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.36831666666667[/C][C]0.010527058250008[/C][C]129.980915291851[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.36851666666667[/C][C]0.0104241362889638[/C][C]131.283458766319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.366725[/C][C]0.00918812549104134[/C][C]148.749056739875[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.3666[/C][C]0.00902369750093715[/C][C]151.445679540795[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.36602638888889[/C][C]0.00878057613071195[/C][C]155.573662656476[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.36564861111111[/C][C]0.00858207976466497[/C][C]159.127932687587[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.36581111111111[/C][C]0.00843058036389706[/C][C]162.006772031975[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.36540833333333[/C][C]0.00833687547958636[/C][C]163.779384336094[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.36491944444444[/C][C]0.00806387295910001[/C][C]169.263510395975[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.36418611111111[/C][C]0.00794171853028195[/C][C]171.774673946129[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.3643125[/C][C]0.00787624395557991[/C][C]173.218669672294[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.36248472222222[/C][C]0.00742559326171506[/C][C]183.484965335623[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.36281805555556[/C][C]0.00703095834853693[/C][C]193.831052325768[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.36270694444444[/C][C]0.00692715402858878[/C][C]196.719596362441[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.36469027777778[/C][C]0.00649263129927086[/C][C]210.190632252756[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.36581527777778[/C][C]0.00629330215652657[/C][C]217.026807835905[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.36439027777778[/C][C]0.00594913137875334[/C][C]229.342771391895[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.36447361111111[/C][C]0.00590610145541252[/C][C]231.027797509416[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.36741944444444[/C][C]0.00548497401103744[/C][C]249.302811953672[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.366625[/C][C]0.00527190628634641[/C][C]259.227862896461[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.36291944444444[/C][C]0.00452694879696728[/C][C]301.068005310222[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.36075277777778[/C][C]0.00415902490425749[/C][C]327.180723631833[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.36761857142857[/C][C]0.0104444842730629[/C][C]130.941704317155[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.36700294117647[/C][C]0.0100086398082011[/C][C]136.582289639032[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.36651818181818[/C][C]0.00961023272365216[/C][C]142.194078032573[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.36584375[/C][C]0.00917393323320275[/C][C]148.883114284795[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.36506774193548[/C][C]0.00868289308543661[/C][C]157.21346888689[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.36467[/C][C]0.00850058465918801[/C][C]160.53836938439[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.36427068965517[/C][C]0.00832280702705299[/C][C]163.919538831149[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.36394821428571[/C][C]0.00816583474513656[/C][C]167.031082168061[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.36366481481481[/C][C]0.00801717067040503[/C][C]170.093025442094[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.36333461538462[/C][C]0.00786340872119442[/C][C]173.377051063108[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.363036[/C][C]0.0076881619894166[/C][C]177.290229039962[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.36277916666667[/C][C]0.00752458615431674[/C][C]181.110181838354[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.36259565217391[/C][C]0.00733913404079862[/C][C]185.661638634637[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.36237954545455[/C][C]0.00711058346739427[/C][C]191.598840193884[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.36236666666667[/C][C]0.00691575795494367[/C][C]196.994555845147[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.3623125[/C][C]0.00674639522691135[/C][C]201.931913885765[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.36226578947368[/C][C]0.00653837917404254[/C][C]208.349157063558[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.36198055555556[/C][C]0.006358278966808[/C][C]214.20585077589[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.36152941176471[/C][C]0.00615132339341753[/C][C]221.339267127731[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.361190625[/C][C]0.00595112377462842[/C][C]228.728333764994[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.36079666666667[/C][C]0.00566597727381896[/C][C]240.169806708291[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.35998571428571[/C][C]0.00536591415971811[/C][C]253.449025423314[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.35915[/C][C]0.00498250246053434[/C][C]272.784611902478[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.35865833333333[/C][C]0.00470755604716481[/C][C]288.612247994711[/C][/ROW]
[ROW][C]Median[/C][C]1.35955[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.3854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.3603027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.36198055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.3603027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.36198055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.36198055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.3603027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.36198055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.36226578947368[/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=163690&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163690&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 Mean1.36811250.010842153675013126.18457005945
Geometric Mean1.36509598511595
Harmonic Mean1.36211302379082
Quadratic Mean1.37115937282814
Winsorized Mean ( 1 / 24 )1.36820.0108097896930578126.570455008823
Winsorized Mean ( 2 / 24 )1.367891666666670.0106209362568387128.792004168738
Winsorized Mean ( 3 / 24 )1.368316666666670.010527058250008129.980915291851
Winsorized Mean ( 4 / 24 )1.368516666666670.0104241362889638131.283458766319
Winsorized Mean ( 5 / 24 )1.3667250.00918812549104134148.749056739875
Winsorized Mean ( 6 / 24 )1.36660.00902369750093715151.445679540795
Winsorized Mean ( 7 / 24 )1.366026388888890.00878057613071195155.573662656476
Winsorized Mean ( 8 / 24 )1.365648611111110.00858207976466497159.127932687587
Winsorized Mean ( 9 / 24 )1.365811111111110.00843058036389706162.006772031975
Winsorized Mean ( 10 / 24 )1.365408333333330.00833687547958636163.779384336094
Winsorized Mean ( 11 / 24 )1.364919444444440.00806387295910001169.263510395975
Winsorized Mean ( 12 / 24 )1.364186111111110.00794171853028195171.774673946129
Winsorized Mean ( 13 / 24 )1.36431250.00787624395557991173.218669672294
Winsorized Mean ( 14 / 24 )1.362484722222220.00742559326171506183.484965335623
Winsorized Mean ( 15 / 24 )1.362818055555560.00703095834853693193.831052325768
Winsorized Mean ( 16 / 24 )1.362706944444440.00692715402858878196.719596362441
Winsorized Mean ( 17 / 24 )1.364690277777780.00649263129927086210.190632252756
Winsorized Mean ( 18 / 24 )1.365815277777780.00629330215652657217.026807835905
Winsorized Mean ( 19 / 24 )1.364390277777780.00594913137875334229.342771391895
Winsorized Mean ( 20 / 24 )1.364473611111110.00590610145541252231.027797509416
Winsorized Mean ( 21 / 24 )1.367419444444440.00548497401103744249.302811953672
Winsorized Mean ( 22 / 24 )1.3666250.00527190628634641259.227862896461
Winsorized Mean ( 23 / 24 )1.362919444444440.00452694879696728301.068005310222
Winsorized Mean ( 24 / 24 )1.360752777777780.00415902490425749327.180723631833
Trimmed Mean ( 1 / 24 )1.367618571428570.0104444842730629130.941704317155
Trimmed Mean ( 2 / 24 )1.367002941176470.0100086398082011136.582289639032
Trimmed Mean ( 3 / 24 )1.366518181818180.00961023272365216142.194078032573
Trimmed Mean ( 4 / 24 )1.365843750.00917393323320275148.883114284795
Trimmed Mean ( 5 / 24 )1.365067741935480.00868289308543661157.21346888689
Trimmed Mean ( 6 / 24 )1.364670.00850058465918801160.53836938439
Trimmed Mean ( 7 / 24 )1.364270689655170.00832280702705299163.919538831149
Trimmed Mean ( 8 / 24 )1.363948214285710.00816583474513656167.031082168061
Trimmed Mean ( 9 / 24 )1.363664814814810.00801717067040503170.093025442094
Trimmed Mean ( 10 / 24 )1.363334615384620.00786340872119442173.377051063108
Trimmed Mean ( 11 / 24 )1.3630360.0076881619894166177.290229039962
Trimmed Mean ( 12 / 24 )1.362779166666670.00752458615431674181.110181838354
Trimmed Mean ( 13 / 24 )1.362595652173910.00733913404079862185.661638634637
Trimmed Mean ( 14 / 24 )1.362379545454550.00711058346739427191.598840193884
Trimmed Mean ( 15 / 24 )1.362366666666670.00691575795494367196.994555845147
Trimmed Mean ( 16 / 24 )1.36231250.00674639522691135201.931913885765
Trimmed Mean ( 17 / 24 )1.362265789473680.00653837917404254208.349157063558
Trimmed Mean ( 18 / 24 )1.361980555555560.006358278966808214.20585077589
Trimmed Mean ( 19 / 24 )1.361529411764710.00615132339341753221.339267127731
Trimmed Mean ( 20 / 24 )1.3611906250.00595112377462842228.728333764994
Trimmed Mean ( 21 / 24 )1.360796666666670.00566597727381896240.169806708291
Trimmed Mean ( 22 / 24 )1.359985714285710.00536591415971811253.449025423314
Trimmed Mean ( 23 / 24 )1.359150.00498250246053434272.784611902478
Trimmed Mean ( 24 / 24 )1.358658333333330.00470755604716481288.612247994711
Median1.35955
Midrange1.3854
Midmean - Weighted Average at Xnp1.3603027027027
Midmean - Weighted Average at X(n+1)p1.36198055555556
Midmean - Empirical Distribution Function1.3603027027027
Midmean - Empirical Distribution Function - Averaging1.36198055555556
Midmean - Empirical Distribution Function - Interpolation1.36198055555556
Midmean - Closest Observation1.3603027027027
Midmean - True Basic - Statistics Graphics Toolkit1.36198055555556
Midmean - MS Excel (old versions)1.36226578947368
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')