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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 computationMon, 17 Oct 2011 14:34:08 -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/2011/Oct/17/t1318876492yjwhg03g9chmu7m.htm/, Retrieved Wed, 15 May 2024 10:50:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130924, Retrieved Wed, 15 May 2024 10:50:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde consum...] [2011-10-17 18:34:08] [4f7490933b61503ca9688d4f22e6aac7] [Current]
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Dataseries X:
14,92
14,95
14,97
15,05
15,06
15,07
15,07
15,08
15,09
15,09
15,09
15,12
15,13
15,15
15,15
15,16
15,17
15,17
15,18
15,18
15,19
15,19
15,2
15,21
15,24
15,31
15,45
15,46
15,65
15,67
15,68
15,73
15,74
15,79
15,8
15,81
15,82
15,84
15,84
15,85
15,86
15,87
15,87
15,88
15,88
15,88
15,88
15,9
15,91
15,92
15,94
15,96
15,96
15,97
15,97
16
16,02
16,05
16,07
16,08
16,08
16,08
16,11
16,12
16,12
16,14
16,14
16,14
16,15
16,15
16,18
16,18
16,19
16,25




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=130924&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=130924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130924&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 Mean15.65162162162160.0490630566273764319.010324621485
Geometric Mean15.6459720121962
Harmonic Mean15.6402884173005
Quadratic Mean15.6572342316191
Winsorized Mean ( 1 / 24 )15.65121621621620.0488527973135354320.375026137547
Winsorized Mean ( 2 / 24 )15.65148648648650.0487073491959415321.337267267885
Winsorized Mean ( 3 / 24 )15.65472972972970.0481171680897259325.346032429377
Winsorized Mean ( 4 / 24 )15.65364864864860.047788010810303327.564348949083
Winsorized Mean ( 5 / 24 )15.65432432432430.0476737963481061328.363283889101
Winsorized Mean ( 6 / 24 )15.65351351351350.0475592471097994329.137117696049
Winsorized Mean ( 7 / 24 )15.65445945945950.0474012318655633330.254274906984
Winsorized Mean ( 8 / 24 )15.65554054054050.0472228138330636331.524940379117
Winsorized Mean ( 9 / 24 )15.65310810810810.0468859699199074333.854842607446
Winsorized Mean ( 10 / 24 )15.65310810810810.0468859699199074333.854842607446
Winsorized Mean ( 11 / 24 )15.65608108108110.0459608100398317340.639798722277
Winsorized Mean ( 12 / 24 )15.65283783783780.0450572552252854347.398831987744
Winsorized Mean ( 13 / 24 )15.65635135135140.0445041688076071351.795163707792
Winsorized Mean ( 14 / 24 )15.65635135135140.0445041688076071351.795163707792
Winsorized Mean ( 15 / 24 )15.65635135135140.0439264026887873356.422342668816
Winsorized Mean ( 16 / 24 )15.65418918918920.0430411006817807363.703272946633
Winsorized Mean ( 17 / 24 )15.64729729729730.0421898256487819370.878453671663
Winsorized Mean ( 18 / 24 )15.64486486486490.041232063401229379.43443947068
Winsorized Mean ( 19 / 24 )15.63716216216220.040342168621165387.613326120459
Winsorized Mean ( 20 / 24 )15.63986486486490.0399237950717382391.742940187974
Winsorized Mean ( 21 / 24 )15.6370270270270.0396045473109548394.829081222745
Winsorized Mean ( 22 / 24 )15.640.0391458223710748399.531777663113
Winsorized Mean ( 23 / 24 )15.63689189189190.037979283542036411.72161329965
Winsorized Mean ( 24 / 24 )15.64013513513510.0357826200747881437.087477173169
Trimmed Mean ( 1 / 24 )15.65347222222220.0486717791554709321.612903695605
Trimmed Mean ( 2 / 24 )15.65585714285710.0484263727308285323.291963861884
Trimmed Mean ( 3 / 24 )15.65823529411760.0481925012001435324.910201881595
Trimmed Mean ( 4 / 24 )15.65954545454550.0481331834410211325.337830059247
Trimmed Mean ( 5 / 24 )15.661250.048126868135252325.41593930415
Trimmed Mean ( 6 / 24 )15.66290322580650.0481005617982576325.628280424239
Trimmed Mean ( 7 / 24 )15.66483333333330.0480433488736799326.056232560324
Trimmed Mean ( 8 / 24 )15.6667241379310.0479554062433358326.69359651412
Trimmed Mean ( 9 / 24 )15.66857142857140.0478298041703693327.590122944265
Trimmed Mean ( 10 / 24 )15.67092592592590.0476830530824019328.647704224072
Trimmed Mean ( 11 / 24 )15.67346153846150.0474372528443591330.404072720778
Trimmed Mean ( 12 / 24 )15.67580.0472536274387739331.737495080372
Trimmed Mean ( 13 / 24 )15.678750.0471197217071458332.742839557609
Trimmed Mean ( 14 / 24 )15.68152173913040.046976165599435333.818683134901
Trimmed Mean ( 15 / 24 )15.68454545454550.0467002661321472335.855590419187
Trimmed Mean ( 16 / 24 )15.68785714285710.0463668847776307338.341840692856
Trimmed Mean ( 17 / 24 )15.691750.0460084823561694341.062108472175
Trimmed Mean ( 18 / 24 )15.69684210526320.0455815984169842344.367960984325
Trimmed Mean ( 19 / 24 )15.70277777777780.04508301181315348.308090924784
Trimmed Mean ( 20 / 24 )15.71029411764710.044424394091482353.641156822426
Trimmed Mean ( 21 / 24 )15.71843750.0434641801330371361.641182506798
Trimmed Mean ( 22 / 24 )15.7280.0419863141358305374.598254781739
Trimmed Mean ( 23 / 24 )15.73857142857140.0398067896076311395.374045073815
Trimmed Mean ( 24 / 24 )15.75115384615380.0366661735667041429.582700182743
Median15.83
Midrange15.585
Midmean - Weighted Average at Xnp15.6886486486487
Midmean - Weighted Average at X(n+1)p15.6968421052632
Midmean - Empirical Distribution Function15.6968421052632
Midmean - Empirical Distribution Function - Averaging15.6968421052632
Midmean - Empirical Distribution Function - Interpolation15.6886486486487
Midmean - Closest Observation15.6968421052632
Midmean - True Basic - Statistics Graphics Toolkit15.6968421052632
Midmean - MS Excel (old versions)15.6968421052632
Number of observations74

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.6516216216216 & 0.0490630566273764 & 319.010324621485 \tabularnewline
Geometric Mean & 15.6459720121962 &  &  \tabularnewline
Harmonic Mean & 15.6402884173005 &  &  \tabularnewline
Quadratic Mean & 15.6572342316191 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 15.6512162162162 & 0.0488527973135354 & 320.375026137547 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 15.6514864864865 & 0.0487073491959415 & 321.337267267885 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 15.6547297297297 & 0.0481171680897259 & 325.346032429377 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 15.6536486486486 & 0.047788010810303 & 327.564348949083 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 15.6543243243243 & 0.0476737963481061 & 328.363283889101 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 15.6535135135135 & 0.0475592471097994 & 329.137117696049 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 15.6544594594595 & 0.0474012318655633 & 330.254274906984 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 15.6555405405405 & 0.0472228138330636 & 331.524940379117 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 15.6531081081081 & 0.0468859699199074 & 333.854842607446 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 15.6531081081081 & 0.0468859699199074 & 333.854842607446 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 15.6560810810811 & 0.0459608100398317 & 340.639798722277 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 15.6528378378378 & 0.0450572552252854 & 347.398831987744 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 15.6563513513514 & 0.0445041688076071 & 351.795163707792 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 15.6563513513514 & 0.0445041688076071 & 351.795163707792 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 15.6563513513514 & 0.0439264026887873 & 356.422342668816 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 15.6541891891892 & 0.0430411006817807 & 363.703272946633 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 15.6472972972973 & 0.0421898256487819 & 370.878453671663 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 15.6448648648649 & 0.041232063401229 & 379.43443947068 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 15.6371621621622 & 0.040342168621165 & 387.613326120459 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 15.6398648648649 & 0.0399237950717382 & 391.742940187974 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 15.637027027027 & 0.0396045473109548 & 394.829081222745 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 15.64 & 0.0391458223710748 & 399.531777663113 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 15.6368918918919 & 0.037979283542036 & 411.72161329965 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 15.6401351351351 & 0.0357826200747881 & 437.087477173169 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 15.6534722222222 & 0.0486717791554709 & 321.612903695605 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 15.6558571428571 & 0.0484263727308285 & 323.291963861884 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 15.6582352941176 & 0.0481925012001435 & 324.910201881595 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 15.6595454545455 & 0.0481331834410211 & 325.337830059247 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 15.66125 & 0.048126868135252 & 325.41593930415 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 15.6629032258065 & 0.0481005617982576 & 325.628280424239 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 15.6648333333333 & 0.0480433488736799 & 326.056232560324 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 15.666724137931 & 0.0479554062433358 & 326.69359651412 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 15.6685714285714 & 0.0478298041703693 & 327.590122944265 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 15.6709259259259 & 0.0476830530824019 & 328.647704224072 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 15.6734615384615 & 0.0474372528443591 & 330.404072720778 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 15.6758 & 0.0472536274387739 & 331.737495080372 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 15.67875 & 0.0471197217071458 & 332.742839557609 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 15.6815217391304 & 0.046976165599435 & 333.818683134901 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 15.6845454545455 & 0.0467002661321472 & 335.855590419187 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 15.6878571428571 & 0.0463668847776307 & 338.341840692856 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 15.69175 & 0.0460084823561694 & 341.062108472175 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 15.6968421052632 & 0.0455815984169842 & 344.367960984325 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 15.7027777777778 & 0.04508301181315 & 348.308090924784 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 15.7102941176471 & 0.044424394091482 & 353.641156822426 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 15.7184375 & 0.0434641801330371 & 361.641182506798 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 15.728 & 0.0419863141358305 & 374.598254781739 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 15.7385714285714 & 0.0398067896076311 & 395.374045073815 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 15.7511538461538 & 0.0366661735667041 & 429.582700182743 \tabularnewline
Median & 15.83 &  &  \tabularnewline
Midrange & 15.585 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.6886486486487 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.6968421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.6968421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.6968421052632 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.6886486486487 &  &  \tabularnewline
Midmean - Closest Observation & 15.6968421052632 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.6968421052632 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.6968421052632 &  &  \tabularnewline
Number of observations & 74 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130924&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]15.6516216216216[/C][C]0.0490630566273764[/C][C]319.010324621485[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.6459720121962[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.6402884173005[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.6572342316191[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]15.6512162162162[/C][C]0.0488527973135354[/C][C]320.375026137547[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]15.6514864864865[/C][C]0.0487073491959415[/C][C]321.337267267885[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]15.6547297297297[/C][C]0.0481171680897259[/C][C]325.346032429377[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]15.6536486486486[/C][C]0.047788010810303[/C][C]327.564348949083[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]15.6543243243243[/C][C]0.0476737963481061[/C][C]328.363283889101[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]15.6535135135135[/C][C]0.0475592471097994[/C][C]329.137117696049[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]15.6544594594595[/C][C]0.0474012318655633[/C][C]330.254274906984[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]15.6555405405405[/C][C]0.0472228138330636[/C][C]331.524940379117[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]15.6531081081081[/C][C]0.0468859699199074[/C][C]333.854842607446[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]15.6531081081081[/C][C]0.0468859699199074[/C][C]333.854842607446[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]15.6560810810811[/C][C]0.0459608100398317[/C][C]340.639798722277[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]15.6528378378378[/C][C]0.0450572552252854[/C][C]347.398831987744[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]15.6563513513514[/C][C]0.0445041688076071[/C][C]351.795163707792[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]15.6563513513514[/C][C]0.0445041688076071[/C][C]351.795163707792[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]15.6563513513514[/C][C]0.0439264026887873[/C][C]356.422342668816[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]15.6541891891892[/C][C]0.0430411006817807[/C][C]363.703272946633[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]15.6472972972973[/C][C]0.0421898256487819[/C][C]370.878453671663[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]15.6448648648649[/C][C]0.041232063401229[/C][C]379.43443947068[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]15.6371621621622[/C][C]0.040342168621165[/C][C]387.613326120459[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]15.6398648648649[/C][C]0.0399237950717382[/C][C]391.742940187974[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]15.637027027027[/C][C]0.0396045473109548[/C][C]394.829081222745[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]15.64[/C][C]0.0391458223710748[/C][C]399.531777663113[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]15.6368918918919[/C][C]0.037979283542036[/C][C]411.72161329965[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]15.6401351351351[/C][C]0.0357826200747881[/C][C]437.087477173169[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]15.6534722222222[/C][C]0.0486717791554709[/C][C]321.612903695605[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]15.6558571428571[/C][C]0.0484263727308285[/C][C]323.291963861884[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]15.6582352941176[/C][C]0.0481925012001435[/C][C]324.910201881595[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]15.6595454545455[/C][C]0.0481331834410211[/C][C]325.337830059247[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]15.66125[/C][C]0.048126868135252[/C][C]325.41593930415[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]15.6629032258065[/C][C]0.0481005617982576[/C][C]325.628280424239[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]15.6648333333333[/C][C]0.0480433488736799[/C][C]326.056232560324[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]15.666724137931[/C][C]0.0479554062433358[/C][C]326.69359651412[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]15.6685714285714[/C][C]0.0478298041703693[/C][C]327.590122944265[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]15.6709259259259[/C][C]0.0476830530824019[/C][C]328.647704224072[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]15.6734615384615[/C][C]0.0474372528443591[/C][C]330.404072720778[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]15.6758[/C][C]0.0472536274387739[/C][C]331.737495080372[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]15.67875[/C][C]0.0471197217071458[/C][C]332.742839557609[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]15.6815217391304[/C][C]0.046976165599435[/C][C]333.818683134901[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]15.6845454545455[/C][C]0.0467002661321472[/C][C]335.855590419187[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]15.6878571428571[/C][C]0.0463668847776307[/C][C]338.341840692856[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]15.69175[/C][C]0.0460084823561694[/C][C]341.062108472175[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]15.6968421052632[/C][C]0.0455815984169842[/C][C]344.367960984325[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]15.7027777777778[/C][C]0.04508301181315[/C][C]348.308090924784[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]15.7102941176471[/C][C]0.044424394091482[/C][C]353.641156822426[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]15.7184375[/C][C]0.0434641801330371[/C][C]361.641182506798[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]15.728[/C][C]0.0419863141358305[/C][C]374.598254781739[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]15.7385714285714[/C][C]0.0398067896076311[/C][C]395.374045073815[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]15.7511538461538[/C][C]0.0366661735667041[/C][C]429.582700182743[/C][/ROW]
[ROW][C]Median[/C][C]15.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.6886486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.6968421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.6968421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.6968421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.6886486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.6968421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.6968421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.6968421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]74[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130924&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 Mean15.65162162162160.0490630566273764319.010324621485
Geometric Mean15.6459720121962
Harmonic Mean15.6402884173005
Quadratic Mean15.6572342316191
Winsorized Mean ( 1 / 24 )15.65121621621620.0488527973135354320.375026137547
Winsorized Mean ( 2 / 24 )15.65148648648650.0487073491959415321.337267267885
Winsorized Mean ( 3 / 24 )15.65472972972970.0481171680897259325.346032429377
Winsorized Mean ( 4 / 24 )15.65364864864860.047788010810303327.564348949083
Winsorized Mean ( 5 / 24 )15.65432432432430.0476737963481061328.363283889101
Winsorized Mean ( 6 / 24 )15.65351351351350.0475592471097994329.137117696049
Winsorized Mean ( 7 / 24 )15.65445945945950.0474012318655633330.254274906984
Winsorized Mean ( 8 / 24 )15.65554054054050.0472228138330636331.524940379117
Winsorized Mean ( 9 / 24 )15.65310810810810.0468859699199074333.854842607446
Winsorized Mean ( 10 / 24 )15.65310810810810.0468859699199074333.854842607446
Winsorized Mean ( 11 / 24 )15.65608108108110.0459608100398317340.639798722277
Winsorized Mean ( 12 / 24 )15.65283783783780.0450572552252854347.398831987744
Winsorized Mean ( 13 / 24 )15.65635135135140.0445041688076071351.795163707792
Winsorized Mean ( 14 / 24 )15.65635135135140.0445041688076071351.795163707792
Winsorized Mean ( 15 / 24 )15.65635135135140.0439264026887873356.422342668816
Winsorized Mean ( 16 / 24 )15.65418918918920.0430411006817807363.703272946633
Winsorized Mean ( 17 / 24 )15.64729729729730.0421898256487819370.878453671663
Winsorized Mean ( 18 / 24 )15.64486486486490.041232063401229379.43443947068
Winsorized Mean ( 19 / 24 )15.63716216216220.040342168621165387.613326120459
Winsorized Mean ( 20 / 24 )15.63986486486490.0399237950717382391.742940187974
Winsorized Mean ( 21 / 24 )15.6370270270270.0396045473109548394.829081222745
Winsorized Mean ( 22 / 24 )15.640.0391458223710748399.531777663113
Winsorized Mean ( 23 / 24 )15.63689189189190.037979283542036411.72161329965
Winsorized Mean ( 24 / 24 )15.64013513513510.0357826200747881437.087477173169
Trimmed Mean ( 1 / 24 )15.65347222222220.0486717791554709321.612903695605
Trimmed Mean ( 2 / 24 )15.65585714285710.0484263727308285323.291963861884
Trimmed Mean ( 3 / 24 )15.65823529411760.0481925012001435324.910201881595
Trimmed Mean ( 4 / 24 )15.65954545454550.0481331834410211325.337830059247
Trimmed Mean ( 5 / 24 )15.661250.048126868135252325.41593930415
Trimmed Mean ( 6 / 24 )15.66290322580650.0481005617982576325.628280424239
Trimmed Mean ( 7 / 24 )15.66483333333330.0480433488736799326.056232560324
Trimmed Mean ( 8 / 24 )15.6667241379310.0479554062433358326.69359651412
Trimmed Mean ( 9 / 24 )15.66857142857140.0478298041703693327.590122944265
Trimmed Mean ( 10 / 24 )15.67092592592590.0476830530824019328.647704224072
Trimmed Mean ( 11 / 24 )15.67346153846150.0474372528443591330.404072720778
Trimmed Mean ( 12 / 24 )15.67580.0472536274387739331.737495080372
Trimmed Mean ( 13 / 24 )15.678750.0471197217071458332.742839557609
Trimmed Mean ( 14 / 24 )15.68152173913040.046976165599435333.818683134901
Trimmed Mean ( 15 / 24 )15.68454545454550.0467002661321472335.855590419187
Trimmed Mean ( 16 / 24 )15.68785714285710.0463668847776307338.341840692856
Trimmed Mean ( 17 / 24 )15.691750.0460084823561694341.062108472175
Trimmed Mean ( 18 / 24 )15.69684210526320.0455815984169842344.367960984325
Trimmed Mean ( 19 / 24 )15.70277777777780.04508301181315348.308090924784
Trimmed Mean ( 20 / 24 )15.71029411764710.044424394091482353.641156822426
Trimmed Mean ( 21 / 24 )15.71843750.0434641801330371361.641182506798
Trimmed Mean ( 22 / 24 )15.7280.0419863141358305374.598254781739
Trimmed Mean ( 23 / 24 )15.73857142857140.0398067896076311395.374045073815
Trimmed Mean ( 24 / 24 )15.75115384615380.0366661735667041429.582700182743
Median15.83
Midrange15.585
Midmean - Weighted Average at Xnp15.6886486486487
Midmean - Weighted Average at X(n+1)p15.6968421052632
Midmean - Empirical Distribution Function15.6968421052632
Midmean - Empirical Distribution Function - Averaging15.6968421052632
Midmean - Empirical Distribution Function - Interpolation15.6886486486487
Midmean - Closest Observation15.6968421052632
Midmean - True Basic - Statistics Graphics Toolkit15.6968421052632
Midmean - MS Excel (old versions)15.6968421052632
Number of observations74



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')