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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, 14 Mar 2010 10:44:07 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/14/t1268585119wnjhfu2agtxrjek.htm/, Retrieved Wed, 19 Jan 2022 10:16:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74396, Retrieved Wed, 19 Jan 2022 10:16:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [maximumprijzen wijn] [2010-03-14 16:44:07] [590f55dfda8c59789c432bae20af0152] [Current]
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Dataseries X:
2,42
2,42
2,42
2,42
2,42
2,43
2,43
2,43
2,44
2,44
2,44
2,43
2,42
2,41
2,38
2,38
2,37
2,37
2,37
2,36
2,32
2,25
2,25
2,24
2,24
2,23
2,22
2,22
2,21
2,21
2,20
2,21
2,20
2,21
2,21
2,21
2,20
2,20
2,19
2,19
2,19
2,18
2,18
2,18
2,18
2,18
2,18
2,18
2,18
2,18
2,18
2,18
2,18
2,18
2,17
2,17
2,17
2,17
2,17
2,17
2,17
2,17
2,17
2,18
2,17
2,18
2,17
2,17
2,18
2,18
2,18
2,17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74396&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74396&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.253472222222220.0119845357487700188.031665928612
Geometric Mean2.25126702792253
Harmonic Mean2.24912030732528
Quadratic Mean2.25573374364578
Winsorized Mean ( 1 / 24 )2.253472222222220.0119845357487700188.031665928612
Winsorized Mean ( 2 / 24 )2.253472222222220.0119845357487700188.031665928612
Winsorized Mean ( 3 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 4 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 5 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 6 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 7 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 8 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 9 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 10 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 11 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 12 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 13 / 24 )2.252083333333330.0111609674686239201.782089201897
Winsorized Mean ( 14 / 24 )2.246250.0100301530919779223.949722342379
Winsorized Mean ( 15 / 24 )2.246250.0100301530919779223.949722342379
Winsorized Mean ( 16 / 24 )2.244027777777780.0096163896556189233.354497700349
Winsorized Mean ( 17 / 24 )2.244027777777780.0096163896556189233.354497700349
Winsorized Mean ( 18 / 24 )2.244027777777780.0096163896556189233.354497700349
Winsorized Mean ( 19 / 24 )2.241388888888890.00913150652448497245.456637727728
Winsorized Mean ( 20 / 24 )2.230277777777780.0071261059384449312.972863025452
Winsorized Mean ( 21 / 24 )2.209861111111110.00366588262827256602.818293763116
Winsorized Mean ( 22 / 24 )2.209861111111110.00366588262827256602.818293763116
Winsorized Mean ( 23 / 24 )2.206666666666670.00318324054138043693.213923981294
Winsorized Mean ( 24 / 24 )2.206666666666670.00318324054138043693.213923981294
Trimmed Mean ( 1 / 24 )2.2520.0119723629296845188.099877461646
Trimmed Mean ( 2 / 24 )2.250441176470590.0119452104190240188.396947188685
Trimmed Mean ( 3 / 24 )2.248787878787880.0118999620996344188.974373192077
Trimmed Mean ( 4 / 24 )2.24718750.0118720626066288189.283663206533
Trimmed Mean ( 5 / 24 )2.245483870967740.0118238378802595189.911591625990
Trimmed Mean ( 6 / 24 )2.243666666666670.0117506260601734190.940180989264
Trimmed Mean ( 7 / 24 )2.241724137931030.0116464813653418192.480807516859
Trimmed Mean ( 8 / 24 )2.239821428571430.0115558808085578193.825244970743
Trimmed Mean ( 9 / 24 )2.237777777777780.0114273650822505195.826226052198
Trimmed Mean ( 10 / 24 )2.235576923076920.0112506526089862198.706421820482
Trimmed Mean ( 11 / 24 )2.23320.0110118303729791202.800072681817
Trimmed Mean ( 12 / 24 )2.2306250.0106915417371075208.634550081593
Trimmed Mean ( 13 / 24 )2.227826086956520.0102618520777456217.097856223040
Trimmed Mean ( 14 / 24 )2.224772727272730.00981051252808991226.774362797321
Trimmed Mean ( 15 / 24 )2.222142857142860.00950906233377206233.686853566074
Trimmed Mean ( 16 / 24 )2.219250.0090821570633345244.35274401489
Trimmed Mean ( 17 / 24 )2.216315789473680.00860398740331222257.591705517896
Trimmed Mean ( 18 / 24 )2.213055555555560.00790639127084471279.907163678622
Trimmed Mean ( 19 / 24 )2.209411764705880.00684617301361633322.72216321609
Trimmed Mean ( 20 / 24 )2.2056250.00536824406625096410.865261113277
Trimmed Mean ( 21 / 24 )2.202666666666670.00409466525187398537.935711755335
Trimmed Mean ( 22 / 24 )2.201785714285710.00395254828484947557.054729154199
Trimmed Mean ( 23 / 24 )2.200769230769230.00371786029956756591.945111822844
Trimmed Mean ( 24 / 24 )2.20.00356106155805960617.793308015369
Median2.2
Midrange2.305
Midmean - Weighted Average at Xnp2.21651162790698
Midmean - Weighted Average at X(n+1)p2.21651162790698
Midmean - Empirical Distribution Function2.21651162790698
Midmean - Empirical Distribution Function - Averaging2.21651162790698
Midmean - Empirical Distribution Function - Interpolation2.21651162790698
Midmean - Closest Observation2.21651162790698
Midmean - True Basic - Statistics Graphics Toolkit2.21651162790698
Midmean - MS Excel (old versions)2.21651162790698
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.25347222222222 & 0.0119845357487700 & 188.031665928612 \tabularnewline
Geometric Mean & 2.25126702792253 &  &  \tabularnewline
Harmonic Mean & 2.24912030732528 &  &  \tabularnewline
Quadratic Mean & 2.25573374364578 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.25347222222222 & 0.0119845357487700 & 188.031665928612 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.25347222222222 & 0.0119845357487700 & 188.031665928612 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.25305555555556 & 0.0118952109761127 & 189.408625040785 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.25305555555556 & 0.0118952109761127 & 189.408625040785 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.25305555555556 & 0.0118952109761127 & 189.408625040785 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.25305555555556 & 0.0118952109761127 & 189.408625040785 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.25208333333333 & 0.0116950317488083 & 192.567526254285 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.25208333333333 & 0.0116950317488083 & 192.567526254285 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.25208333333333 & 0.0116950317488083 & 192.567526254285 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.25208333333333 & 0.0116950317488083 & 192.567526254285 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.25208333333333 & 0.0116950317488083 & 192.567526254285 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.25208333333333 & 0.0116950317488083 & 192.567526254285 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.25208333333333 & 0.0111609674686239 & 201.782089201897 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.24625 & 0.0100301530919779 & 223.949722342379 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.24625 & 0.0100301530919779 & 223.949722342379 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.24402777777778 & 0.0096163896556189 & 233.354497700349 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.24402777777778 & 0.0096163896556189 & 233.354497700349 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.24402777777778 & 0.0096163896556189 & 233.354497700349 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.24138888888889 & 0.00913150652448497 & 245.456637727728 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.23027777777778 & 0.0071261059384449 & 312.972863025452 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.20986111111111 & 0.00366588262827256 & 602.818293763116 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.20986111111111 & 0.00366588262827256 & 602.818293763116 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.20666666666667 & 0.00318324054138043 & 693.213923981294 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.20666666666667 & 0.00318324054138043 & 693.213923981294 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.252 & 0.0119723629296845 & 188.099877461646 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.25044117647059 & 0.0119452104190240 & 188.396947188685 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.24878787878788 & 0.0118999620996344 & 188.974373192077 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.2471875 & 0.0118720626066288 & 189.283663206533 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.24548387096774 & 0.0118238378802595 & 189.911591625990 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.24366666666667 & 0.0117506260601734 & 190.940180989264 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.24172413793103 & 0.0116464813653418 & 192.480807516859 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.23982142857143 & 0.0115558808085578 & 193.825244970743 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.23777777777778 & 0.0114273650822505 & 195.826226052198 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.23557692307692 & 0.0112506526089862 & 198.706421820482 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.2332 & 0.0110118303729791 & 202.800072681817 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.230625 & 0.0106915417371075 & 208.634550081593 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.22782608695652 & 0.0102618520777456 & 217.097856223040 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.22477272727273 & 0.00981051252808991 & 226.774362797321 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.22214285714286 & 0.00950906233377206 & 233.686853566074 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.21925 & 0.0090821570633345 & 244.35274401489 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.21631578947368 & 0.00860398740331222 & 257.591705517896 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.21305555555556 & 0.00790639127084471 & 279.907163678622 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.20941176470588 & 0.00684617301361633 & 322.72216321609 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.205625 & 0.00536824406625096 & 410.865261113277 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.20266666666667 & 0.00409466525187398 & 537.935711755335 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.20178571428571 & 0.00395254828484947 & 557.054729154199 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.20076923076923 & 0.00371786029956756 & 591.945111822844 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.2 & 0.00356106155805960 & 617.793308015369 \tabularnewline
Median & 2.2 &  &  \tabularnewline
Midrange & 2.305 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.21651162790698 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.21651162790698 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.21651162790698 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.21651162790698 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.21651162790698 &  &  \tabularnewline
Midmean - Closest Observation & 2.21651162790698 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.21651162790698 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.21651162790698 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74396&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]2.25347222222222[/C][C]0.0119845357487700[/C][C]188.031665928612[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.25126702792253[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.24912030732528[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.25573374364578[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.25347222222222[/C][C]0.0119845357487700[/C][C]188.031665928612[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.25347222222222[/C][C]0.0119845357487700[/C][C]188.031665928612[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.25305555555556[/C][C]0.0118952109761127[/C][C]189.408625040785[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.25305555555556[/C][C]0.0118952109761127[/C][C]189.408625040785[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.25305555555556[/C][C]0.0118952109761127[/C][C]189.408625040785[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.25305555555556[/C][C]0.0118952109761127[/C][C]189.408625040785[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.25208333333333[/C][C]0.0116950317488083[/C][C]192.567526254285[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.25208333333333[/C][C]0.0116950317488083[/C][C]192.567526254285[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.25208333333333[/C][C]0.0116950317488083[/C][C]192.567526254285[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.25208333333333[/C][C]0.0116950317488083[/C][C]192.567526254285[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.25208333333333[/C][C]0.0116950317488083[/C][C]192.567526254285[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.25208333333333[/C][C]0.0116950317488083[/C][C]192.567526254285[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.25208333333333[/C][C]0.0111609674686239[/C][C]201.782089201897[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.24625[/C][C]0.0100301530919779[/C][C]223.949722342379[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.24625[/C][C]0.0100301530919779[/C][C]223.949722342379[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.24402777777778[/C][C]0.0096163896556189[/C][C]233.354497700349[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.24402777777778[/C][C]0.0096163896556189[/C][C]233.354497700349[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.24402777777778[/C][C]0.0096163896556189[/C][C]233.354497700349[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.24138888888889[/C][C]0.00913150652448497[/C][C]245.456637727728[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.23027777777778[/C][C]0.0071261059384449[/C][C]312.972863025452[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.20986111111111[/C][C]0.00366588262827256[/C][C]602.818293763116[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.20986111111111[/C][C]0.00366588262827256[/C][C]602.818293763116[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.20666666666667[/C][C]0.00318324054138043[/C][C]693.213923981294[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.20666666666667[/C][C]0.00318324054138043[/C][C]693.213923981294[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.252[/C][C]0.0119723629296845[/C][C]188.099877461646[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.25044117647059[/C][C]0.0119452104190240[/C][C]188.396947188685[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.24878787878788[/C][C]0.0118999620996344[/C][C]188.974373192077[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.2471875[/C][C]0.0118720626066288[/C][C]189.283663206533[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.24548387096774[/C][C]0.0118238378802595[/C][C]189.911591625990[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.24366666666667[/C][C]0.0117506260601734[/C][C]190.940180989264[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.24172413793103[/C][C]0.0116464813653418[/C][C]192.480807516859[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.23982142857143[/C][C]0.0115558808085578[/C][C]193.825244970743[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.23777777777778[/C][C]0.0114273650822505[/C][C]195.826226052198[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.23557692307692[/C][C]0.0112506526089862[/C][C]198.706421820482[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.2332[/C][C]0.0110118303729791[/C][C]202.800072681817[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.230625[/C][C]0.0106915417371075[/C][C]208.634550081593[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.22782608695652[/C][C]0.0102618520777456[/C][C]217.097856223040[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.22477272727273[/C][C]0.00981051252808991[/C][C]226.774362797321[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.22214285714286[/C][C]0.00950906233377206[/C][C]233.686853566074[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.21925[/C][C]0.0090821570633345[/C][C]244.35274401489[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.21631578947368[/C][C]0.00860398740331222[/C][C]257.591705517896[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.21305555555556[/C][C]0.00790639127084471[/C][C]279.907163678622[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.20941176470588[/C][C]0.00684617301361633[/C][C]322.72216321609[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.205625[/C][C]0.00536824406625096[/C][C]410.865261113277[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.20266666666667[/C][C]0.00409466525187398[/C][C]537.935711755335[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.20178571428571[/C][C]0.00395254828484947[/C][C]557.054729154199[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.20076923076923[/C][C]0.00371786029956756[/C][C]591.945111822844[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.2[/C][C]0.00356106155805960[/C][C]617.793308015369[/C][/ROW]
[ROW][C]Median[/C][C]2.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.21651162790698[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.21651162790698[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.21651162790698[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.21651162790698[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.21651162790698[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.21651162790698[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.21651162790698[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.21651162790698[/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=74396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74396&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 Mean2.253472222222220.0119845357487700188.031665928612
Geometric Mean2.25126702792253
Harmonic Mean2.24912030732528
Quadratic Mean2.25573374364578
Winsorized Mean ( 1 / 24 )2.253472222222220.0119845357487700188.031665928612
Winsorized Mean ( 2 / 24 )2.253472222222220.0119845357487700188.031665928612
Winsorized Mean ( 3 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 4 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 5 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 6 / 24 )2.253055555555560.0118952109761127189.408625040785
Winsorized Mean ( 7 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 8 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 9 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 10 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 11 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 12 / 24 )2.252083333333330.0116950317488083192.567526254285
Winsorized Mean ( 13 / 24 )2.252083333333330.0111609674686239201.782089201897
Winsorized Mean ( 14 / 24 )2.246250.0100301530919779223.949722342379
Winsorized Mean ( 15 / 24 )2.246250.0100301530919779223.949722342379
Winsorized Mean ( 16 / 24 )2.244027777777780.0096163896556189233.354497700349
Winsorized Mean ( 17 / 24 )2.244027777777780.0096163896556189233.354497700349
Winsorized Mean ( 18 / 24 )2.244027777777780.0096163896556189233.354497700349
Winsorized Mean ( 19 / 24 )2.241388888888890.00913150652448497245.456637727728
Winsorized Mean ( 20 / 24 )2.230277777777780.0071261059384449312.972863025452
Winsorized Mean ( 21 / 24 )2.209861111111110.00366588262827256602.818293763116
Winsorized Mean ( 22 / 24 )2.209861111111110.00366588262827256602.818293763116
Winsorized Mean ( 23 / 24 )2.206666666666670.00318324054138043693.213923981294
Winsorized Mean ( 24 / 24 )2.206666666666670.00318324054138043693.213923981294
Trimmed Mean ( 1 / 24 )2.2520.0119723629296845188.099877461646
Trimmed Mean ( 2 / 24 )2.250441176470590.0119452104190240188.396947188685
Trimmed Mean ( 3 / 24 )2.248787878787880.0118999620996344188.974373192077
Trimmed Mean ( 4 / 24 )2.24718750.0118720626066288189.283663206533
Trimmed Mean ( 5 / 24 )2.245483870967740.0118238378802595189.911591625990
Trimmed Mean ( 6 / 24 )2.243666666666670.0117506260601734190.940180989264
Trimmed Mean ( 7 / 24 )2.241724137931030.0116464813653418192.480807516859
Trimmed Mean ( 8 / 24 )2.239821428571430.0115558808085578193.825244970743
Trimmed Mean ( 9 / 24 )2.237777777777780.0114273650822505195.826226052198
Trimmed Mean ( 10 / 24 )2.235576923076920.0112506526089862198.706421820482
Trimmed Mean ( 11 / 24 )2.23320.0110118303729791202.800072681817
Trimmed Mean ( 12 / 24 )2.2306250.0106915417371075208.634550081593
Trimmed Mean ( 13 / 24 )2.227826086956520.0102618520777456217.097856223040
Trimmed Mean ( 14 / 24 )2.224772727272730.00981051252808991226.774362797321
Trimmed Mean ( 15 / 24 )2.222142857142860.00950906233377206233.686853566074
Trimmed Mean ( 16 / 24 )2.219250.0090821570633345244.35274401489
Trimmed Mean ( 17 / 24 )2.216315789473680.00860398740331222257.591705517896
Trimmed Mean ( 18 / 24 )2.213055555555560.00790639127084471279.907163678622
Trimmed Mean ( 19 / 24 )2.209411764705880.00684617301361633322.72216321609
Trimmed Mean ( 20 / 24 )2.2056250.00536824406625096410.865261113277
Trimmed Mean ( 21 / 24 )2.202666666666670.00409466525187398537.935711755335
Trimmed Mean ( 22 / 24 )2.201785714285710.00395254828484947557.054729154199
Trimmed Mean ( 23 / 24 )2.200769230769230.00371786029956756591.945111822844
Trimmed Mean ( 24 / 24 )2.20.00356106155805960617.793308015369
Median2.2
Midrange2.305
Midmean - Weighted Average at Xnp2.21651162790698
Midmean - Weighted Average at X(n+1)p2.21651162790698
Midmean - Empirical Distribution Function2.21651162790698
Midmean - Empirical Distribution Function - Averaging2.21651162790698
Midmean - Empirical Distribution Function - Interpolation2.21651162790698
Midmean - Closest Observation2.21651162790698
Midmean - True Basic - Statistics Graphics Toolkit2.21651162790698
Midmean - MS Excel (old versions)2.21651162790698
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')