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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Oct 2012 12:49:09 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/16/t1350410648hd9oq191z1626bi.htm/, Retrieved Tue, 30 Apr 2024 10:26:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179123, Retrieved Tue, 30 Apr 2024 10:26:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-16 16:49:09] [62859712c843b354ac43f7004f4dfb59] [Current]
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Dataseries X:
2,25
2,25
2,45
2,5
2,5
2,64
2,75
2,93
3
3,17
3,25
3,39
3,5
3,5
3,65
3,75
3,75
3,9
4
4
4
4
4
4
4
4
4
4
4
4
4,18
4,25
4,25
3,97
3,42
2,75
2,31
2
1,66
1,31
1,09
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1,14
1,25
1,25
1,4
1,5
1,5
1,5
1,32
1,11




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179123&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179123&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179123&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.337361111111110.1495776517622615.6264059742436
Geometric Mean1.98459205298409
Harmonic Mean1.6841637372883
Quadratic Mean2.65551757876146
Winsorized Mean ( 1 / 24 )2.337361111111110.1495776517622615.6264059742436
Winsorized Mean ( 2 / 24 )2.335416666666670.14923329583074615.6494343548868
Winsorized Mean ( 3 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 4 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 5 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 6 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 7 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 8 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 9 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 10 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 11 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 12 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 13 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 14 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 15 / 24 )2.321666666666670.14699254236775815.7944520808282
Winsorized Mean ( 16 / 24 )2.306111111111110.1445560842197915.9530546469755
Winsorized Mean ( 17 / 24 )2.270694444444440.13915269059012116.3180060321856
Winsorized Mean ( 18 / 24 )2.270694444444440.13915269059012116.3180060321856
Winsorized Mean ( 19 / 24 )2.244305555555560.1352449274124616.5943787947849
Winsorized Mean ( 20 / 24 )2.202638888888890.12924739913105517.042036464157
Winsorized Mean ( 21 / 24 )2.202638888888890.12924739913105517.042036464157
Winsorized Mean ( 22 / 24 )2.205694444444440.12223832298096718.0442138819909
Winsorized Mean ( 23 / 24 )2.20250.12008046174396918.3418681774899
Winsorized Mean ( 24 / 24 )2.165833333333330.11237369017760119.2734912407908
Trimmed Mean ( 1 / 24 )2.329142857142860.15017019231775415.5100211379798
Trimmed Mean ( 2 / 24 )2.320441176470590.1506936600674615.3983994776676
Trimmed Mean ( 3 / 24 )2.312272727272730.15133774812387315.2788894769339
Trimmed Mean ( 4 / 24 )2.306406250.15242880968894815.1310389073204
Trimmed Mean ( 5 / 24 )2.300161290322580.15349299674405514.9854477996676
Trimmed Mean ( 6 / 24 )2.29350.15451927000314.8428089257442
Trimmed Mean ( 7 / 24 )2.286379310344830.1554938074478214.7039894891768
Trimmed Mean ( 8 / 24 )2.278750.15639922744104514.5700847586282
Trimmed Mean ( 9 / 24 )2.270555555555560.15721355473882514.4424923113505
Trimmed Mean ( 10 / 24 )2.261730769230770.15790882709254714.3230167108088
Trimmed Mean ( 11 / 24 )2.25220.15844919098073414.2140201919608
Trimmed Mean ( 12 / 24 )2.2418750.15878825731287914.1186447785152
Trimmed Mean ( 13 / 24 )2.230652173913040.1588653615757414.0411487550706
Trimmed Mean ( 14 / 24 )2.218409090909090.15860016048910213.9874328252116
Trimmed Mean ( 15 / 24 )2.2050.1578846261306313.9658942991424
Trimmed Mean ( 16 / 24 )2.1910.15679105809144813.97401118833
Trimmed Mean ( 17 / 24 )2.177368421052630.15551487659900114.0010297964421
Trimmed Mean ( 18 / 24 )2.166388888888890.15466356358636814.0071057374746
Trimmed Mean ( 19 / 24 )2.154117647058820.15300560825708614.0786842495302
Trimmed Mean ( 20 / 24 )2.14343750.15124990627496414.1714963849521
Trimmed Mean ( 21 / 24 )2.136333333333330.14988231654288214.2534048219232
Trimmed Mean ( 22 / 24 )2.128214285714290.14724817402720514.4532473816693
Trimmed Mean ( 23 / 24 )2.118461538461540.14487415473458114.6227706545913
Trimmed Mean ( 24 / 24 )2.10750.14120245769097314.9253776064744
Median2.25
Midrange2.625
Midmean - Weighted Average at Xnp1.81345454545455
Midmean - Weighted Average at X(n+1)p1.81345454545455
Midmean - Empirical Distribution Function1.81345454545455
Midmean - Empirical Distribution Function - Averaging1.81345454545455
Midmean - Empirical Distribution Function - Interpolation1.81345454545455
Midmean - Closest Observation1.81345454545455
Midmean - True Basic - Statistics Graphics Toolkit1.81345454545455
Midmean - MS Excel (old versions)1.81345454545455
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.33736111111111 & 0.14957765176226 & 15.6264059742436 \tabularnewline
Geometric Mean & 1.98459205298409 &  &  \tabularnewline
Harmonic Mean & 1.6841637372883 &  &  \tabularnewline
Quadratic Mean & 2.65551757876146 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.33736111111111 & 0.14957765176226 & 15.6264059742436 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.33541666666667 & 0.149233295830746 & 15.6494343548868 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.32791666666667 & 0.147983437286973 & 15.7309271182309 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.32166666666667 & 0.146992542367758 & 15.7944520808282 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.30611111111111 & 0.14455608421979 & 15.9530546469755 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.27069444444444 & 0.139152690590121 & 16.3180060321856 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.27069444444444 & 0.139152690590121 & 16.3180060321856 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.24430555555556 & 0.13524492741246 & 16.5943787947849 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.20263888888889 & 0.129247399131055 & 17.042036464157 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.20263888888889 & 0.129247399131055 & 17.042036464157 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.20569444444444 & 0.122238322980967 & 18.0442138819909 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.2025 & 0.120080461743969 & 18.3418681774899 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.16583333333333 & 0.112373690177601 & 19.2734912407908 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.32914285714286 & 0.150170192317754 & 15.5100211379798 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.32044117647059 & 0.15069366006746 & 15.3983994776676 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.31227272727273 & 0.151337748123873 & 15.2788894769339 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.30640625 & 0.152428809688948 & 15.1310389073204 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.30016129032258 & 0.153492996744055 & 14.9854477996676 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.2935 & 0.154519270003 & 14.8428089257442 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.28637931034483 & 0.15549380744782 & 14.7039894891768 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.27875 & 0.156399227441045 & 14.5700847586282 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.27055555555556 & 0.157213554738825 & 14.4424923113505 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.26173076923077 & 0.157908827092547 & 14.3230167108088 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.2522 & 0.158449190980734 & 14.2140201919608 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.241875 & 0.158788257312879 & 14.1186447785152 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.23065217391304 & 0.15886536157574 & 14.0411487550706 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.21840909090909 & 0.158600160489102 & 13.9874328252116 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.205 & 0.15788462613063 & 13.9658942991424 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.191 & 0.156791058091448 & 13.97401118833 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.17736842105263 & 0.155514876599001 & 14.0010297964421 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.16638888888889 & 0.154663563586368 & 14.0071057374746 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.15411764705882 & 0.153005608257086 & 14.0786842495302 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.1434375 & 0.151249906274964 & 14.1714963849521 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.13633333333333 & 0.149882316542882 & 14.2534048219232 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.12821428571429 & 0.147248174027205 & 14.4532473816693 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.11846153846154 & 0.144874154734581 & 14.6227706545913 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.1075 & 0.141202457690973 & 14.9253776064744 \tabularnewline
Median & 2.25 &  &  \tabularnewline
Midrange & 2.625 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.81345454545455 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.81345454545455 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.81345454545455 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.81345454545455 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.81345454545455 &  &  \tabularnewline
Midmean - Closest Observation & 1.81345454545455 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.81345454545455 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.81345454545455 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179123&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]2.33736111111111[/C][C]0.14957765176226[/C][C]15.6264059742436[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.98459205298409[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.6841637372883[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.65551757876146[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.33736111111111[/C][C]0.14957765176226[/C][C]15.6264059742436[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.33541666666667[/C][C]0.149233295830746[/C][C]15.6494343548868[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.32791666666667[/C][C]0.147983437286973[/C][C]15.7309271182309[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.32166666666667[/C][C]0.146992542367758[/C][C]15.7944520808282[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.30611111111111[/C][C]0.14455608421979[/C][C]15.9530546469755[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.27069444444444[/C][C]0.139152690590121[/C][C]16.3180060321856[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.27069444444444[/C][C]0.139152690590121[/C][C]16.3180060321856[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.24430555555556[/C][C]0.13524492741246[/C][C]16.5943787947849[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.20263888888889[/C][C]0.129247399131055[/C][C]17.042036464157[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.20263888888889[/C][C]0.129247399131055[/C][C]17.042036464157[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.20569444444444[/C][C]0.122238322980967[/C][C]18.0442138819909[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.2025[/C][C]0.120080461743969[/C][C]18.3418681774899[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.16583333333333[/C][C]0.112373690177601[/C][C]19.2734912407908[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.32914285714286[/C][C]0.150170192317754[/C][C]15.5100211379798[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.32044117647059[/C][C]0.15069366006746[/C][C]15.3983994776676[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.31227272727273[/C][C]0.151337748123873[/C][C]15.2788894769339[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.30640625[/C][C]0.152428809688948[/C][C]15.1310389073204[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.30016129032258[/C][C]0.153492996744055[/C][C]14.9854477996676[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.2935[/C][C]0.154519270003[/C][C]14.8428089257442[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.28637931034483[/C][C]0.15549380744782[/C][C]14.7039894891768[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.27875[/C][C]0.156399227441045[/C][C]14.5700847586282[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.27055555555556[/C][C]0.157213554738825[/C][C]14.4424923113505[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.26173076923077[/C][C]0.157908827092547[/C][C]14.3230167108088[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.2522[/C][C]0.158449190980734[/C][C]14.2140201919608[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.241875[/C][C]0.158788257312879[/C][C]14.1186447785152[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.23065217391304[/C][C]0.15886536157574[/C][C]14.0411487550706[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.21840909090909[/C][C]0.158600160489102[/C][C]13.9874328252116[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.205[/C][C]0.15788462613063[/C][C]13.9658942991424[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.191[/C][C]0.156791058091448[/C][C]13.97401118833[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.17736842105263[/C][C]0.155514876599001[/C][C]14.0010297964421[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.16638888888889[/C][C]0.154663563586368[/C][C]14.0071057374746[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.15411764705882[/C][C]0.153005608257086[/C][C]14.0786842495302[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.1434375[/C][C]0.151249906274964[/C][C]14.1714963849521[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.13633333333333[/C][C]0.149882316542882[/C][C]14.2534048219232[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.12821428571429[/C][C]0.147248174027205[/C][C]14.4532473816693[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.11846153846154[/C][C]0.144874154734581[/C][C]14.6227706545913[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.1075[/C][C]0.141202457690973[/C][C]14.9253776064744[/C][/ROW]
[ROW][C]Median[/C][C]2.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.81345454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.81345454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.81345454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.81345454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.81345454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.81345454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.81345454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.81345454545455[/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=179123&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179123&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 Mean2.337361111111110.1495776517622615.6264059742436
Geometric Mean1.98459205298409
Harmonic Mean1.6841637372883
Quadratic Mean2.65551757876146
Winsorized Mean ( 1 / 24 )2.337361111111110.1495776517622615.6264059742436
Winsorized Mean ( 2 / 24 )2.335416666666670.14923329583074615.6494343548868
Winsorized Mean ( 3 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 4 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 5 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 6 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 7 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 8 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 9 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 10 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 11 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 12 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 13 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 14 / 24 )2.327916666666670.14798343728697315.7309271182309
Winsorized Mean ( 15 / 24 )2.321666666666670.14699254236775815.7944520808282
Winsorized Mean ( 16 / 24 )2.306111111111110.1445560842197915.9530546469755
Winsorized Mean ( 17 / 24 )2.270694444444440.13915269059012116.3180060321856
Winsorized Mean ( 18 / 24 )2.270694444444440.13915269059012116.3180060321856
Winsorized Mean ( 19 / 24 )2.244305555555560.1352449274124616.5943787947849
Winsorized Mean ( 20 / 24 )2.202638888888890.12924739913105517.042036464157
Winsorized Mean ( 21 / 24 )2.202638888888890.12924739913105517.042036464157
Winsorized Mean ( 22 / 24 )2.205694444444440.12223832298096718.0442138819909
Winsorized Mean ( 23 / 24 )2.20250.12008046174396918.3418681774899
Winsorized Mean ( 24 / 24 )2.165833333333330.11237369017760119.2734912407908
Trimmed Mean ( 1 / 24 )2.329142857142860.15017019231775415.5100211379798
Trimmed Mean ( 2 / 24 )2.320441176470590.1506936600674615.3983994776676
Trimmed Mean ( 3 / 24 )2.312272727272730.15133774812387315.2788894769339
Trimmed Mean ( 4 / 24 )2.306406250.15242880968894815.1310389073204
Trimmed Mean ( 5 / 24 )2.300161290322580.15349299674405514.9854477996676
Trimmed Mean ( 6 / 24 )2.29350.15451927000314.8428089257442
Trimmed Mean ( 7 / 24 )2.286379310344830.1554938074478214.7039894891768
Trimmed Mean ( 8 / 24 )2.278750.15639922744104514.5700847586282
Trimmed Mean ( 9 / 24 )2.270555555555560.15721355473882514.4424923113505
Trimmed Mean ( 10 / 24 )2.261730769230770.15790882709254714.3230167108088
Trimmed Mean ( 11 / 24 )2.25220.15844919098073414.2140201919608
Trimmed Mean ( 12 / 24 )2.2418750.15878825731287914.1186447785152
Trimmed Mean ( 13 / 24 )2.230652173913040.1588653615757414.0411487550706
Trimmed Mean ( 14 / 24 )2.218409090909090.15860016048910213.9874328252116
Trimmed Mean ( 15 / 24 )2.2050.1578846261306313.9658942991424
Trimmed Mean ( 16 / 24 )2.1910.15679105809144813.97401118833
Trimmed Mean ( 17 / 24 )2.177368421052630.15551487659900114.0010297964421
Trimmed Mean ( 18 / 24 )2.166388888888890.15466356358636814.0071057374746
Trimmed Mean ( 19 / 24 )2.154117647058820.15300560825708614.0786842495302
Trimmed Mean ( 20 / 24 )2.14343750.15124990627496414.1714963849521
Trimmed Mean ( 21 / 24 )2.136333333333330.14988231654288214.2534048219232
Trimmed Mean ( 22 / 24 )2.128214285714290.14724817402720514.4532473816693
Trimmed Mean ( 23 / 24 )2.118461538461540.14487415473458114.6227706545913
Trimmed Mean ( 24 / 24 )2.10750.14120245769097314.9253776064744
Median2.25
Midrange2.625
Midmean - Weighted Average at Xnp1.81345454545455
Midmean - Weighted Average at X(n+1)p1.81345454545455
Midmean - Empirical Distribution Function1.81345454545455
Midmean - Empirical Distribution Function - Averaging1.81345454545455
Midmean - Empirical Distribution Function - Interpolation1.81345454545455
Midmean - Closest Observation1.81345454545455
Midmean - True Basic - Statistics Graphics Toolkit1.81345454545455
Midmean - MS Excel (old versions)1.81345454545455
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')