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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, 21 Oct 2007 22:11:30 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/tfo5mcvvo86gc6j1193029894.htm/, Retrieved Sun, 05 May 2024 23:56:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1598, Retrieved Sun, 05 May 2024 23:56:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordstime series
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [data analysis tim...] [2007-10-22 05:11:30] [079615521100262cd8b5675a0217a3b1] [Current]
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Dataseries X:
95,90
96,06
96,31
96,34
96,49
96,22
96,53
96,50
96,77
96,66
96,58
96,63
97,06
97,73
98,01
97,76
97,49
97,77
97,96
98,23
98,51
98,19
98,37
98,31
98,60
98,97
99,11
99,64
100,03
99,98
100,32
100,44
100,51
101,00
100,88
100,55
100,83
101,51
102,16
102,39
102,54
102,85
103,47
103,57
103,69
103,50
103,47
103,45
103,48
103,93
103,89
104,40
104,79
104,77
105,13
105,26
104,96
104,75
105,01
105,15
105,20
105,77
105,78
106,26
106,13
106,12
106,57
106,44
106,54




Summary of compuational 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 compuational 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=1598&T=0

[TABLE]
[ROW][C]Summary of compuational 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=1598&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1598&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 compuational 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 Mean101.1039130434780.420117316937905240.656380889964
Geometric Mean101.044576655596
Harmonic Mean100.985291343685
Quadratic Mean101.163249922008
Winsorized Mean ( 1 / 23 )101.1057971014490.419618092806564240.947182294299
Winsorized Mean ( 2 / 23 )101.1075362318840.418261809664206241.732651405722
Winsorized Mean ( 3 / 23 )101.1036231884060.416147432878657242.951452299085
Winsorized Mean ( 4 / 23 )101.0978260869570.414493953402063243.906636652165
Winsorized Mean ( 5 / 23 )101.1079710144930.412552436911511245.079078362539
Winsorized Mean ( 6 / 23 )101.0792753623190.407257860571736248.194780624779
Winsorized Mean ( 7 / 23 )101.0813043478260.406583603300037248.611364372295
Winsorized Mean ( 8 / 23 )101.0279710144930.3959619589846255.145649025395
Winsorized Mean ( 9 / 23 )101.0266666666670.393662587783935256.632633635269
Winsorized Mean ( 10 / 23 )101.0237681159420.391823512596441257.829775059955
Winsorized Mean ( 11 / 23 )101.0381159420290.38847688652276260.087844212346
Winsorized Mean ( 12 / 23 )101.0676811594200.377240628924230267.913033247859
Winsorized Mean ( 13 / 23 )101.1392753623190.363473012494214278.258005094474
Winsorized Mean ( 14 / 23 )101.1534782608700.351091273176781288.111627912599
Winsorized Mean ( 15 / 23 )101.1556521739130.349496012625994289.432922034972
Winsorized Mean ( 16 / 23 )101.1533333333330.348460177918998290.286637449996
Winsorized Mean ( 17 / 23 )101.1139130434780.32893173713985307.400903064846
Winsorized Mean ( 18 / 23 )101.0043478260870.309542499789052326.302035729891
Winsorized Mean ( 19 / 23 )101.0428985507250.301030632435479335.656533467176
Winsorized Mean ( 20 / 23 )100.9965217391300.2914410521443346.541851245872
Winsorized Mean ( 21 / 23 )100.9843478260870.283115543264687356.689522099731
Winsorized Mean ( 22 / 23 )100.9811594202900.277474416555457363.929621598492
Winsorized Mean ( 23 / 23 )101.0211594202900.270164259358278373.924958320710
Trimmed Mean ( 1 / 23 )101.10.417605383098403242.094580414394
Trimmed Mean ( 2 / 23 )101.0938461538460.414918243354807243.647628835154
Trimmed Mean ( 3 / 23 )101.0863492063490.412252954872604245.204668666565
Trimmed Mean ( 4 / 23 )101.0798360655740.409668564678113246.735641395856
Trimmed Mean ( 5 / 23 )101.0745762711860.406794953930337248.465658913987
Trimmed Mean ( 6 / 23 )101.0664912280700.403540680606075250.44932539708
Trimmed Mean ( 7 / 23 )101.0638181818180.400643883359449252.253490891675
Trimmed Mean ( 8 / 23 )101.0605660377360.396842985614978254.661338869640
Trimmed Mean ( 9 / 23 )101.0660784313730.394230258031469256.363067959398
Trimmed Mean ( 10 / 23 )101.0722448979590.390982895534908258.508098569584
Trimmed Mean ( 11 / 23 )101.0722448979590.386788217604948261.31159197096
Trimmed Mean ( 12 / 23 )101.0851111111110.38169380904179264.832985803141
Trimmed Mean ( 13 / 23 )101.0874418604650.377128524408909268.045070361368
Trimmed Mean ( 14 / 23 )101.0807317073170.373611150118889270.550629110378
Trimmed Mean ( 15 / 23 )101.0715384615380.370951386257646272.465725175478
Trimmed Mean ( 16 / 23 )101.0610810810810.366872952574728275.466153533071
Trimmed Mean ( 17 / 23 )101.0497142857140.360715555368429280.136835747224
Trimmed Mean ( 18 / 23 )101.0418181818180.356307997550514283.57998943735
Trimmed Mean ( 19 / 23 )101.0464516129030.353979997122460285.458083604499
Trimmed Mean ( 20 / 23 )101.0468965517240.351432011884814287.529004571284
Trimmed Mean ( 21 / 23 )101.0533333333330.348712732489896289.789628878152
Trimmed Mean ( 22 / 23 )101.0533333333330.345210216148557292.729845775614
Trimmed Mean ( 23 / 23 )101.0734782608700.339461098550499297.746866113537
Median100.83
Midrange101.235
Midmean - Weighted Average at Xnp100.951176470588
Midmean - Weighted Average at X(n+1)p101.049714285714
Midmean - Empirical Distribution Function101.049714285714
Midmean - Empirical Distribution Function - Averaging101.049714285714
Midmean - Empirical Distribution Function - Interpolation101.049714285714
Midmean - Closest Observation100.958611111111
Midmean - True Basic - Statistics Graphics Toolkit101.049714285714
Midmean - MS Excel (old versions)101.049714285714
Number of observations69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.103913043478 & 0.420117316937905 & 240.656380889964 \tabularnewline
Geometric Mean & 101.044576655596 &  &  \tabularnewline
Harmonic Mean & 100.985291343685 &  &  \tabularnewline
Quadratic Mean & 101.163249922008 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 101.105797101449 & 0.419618092806564 & 240.947182294299 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 101.107536231884 & 0.418261809664206 & 241.732651405722 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 101.103623188406 & 0.416147432878657 & 242.951452299085 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 101.097826086957 & 0.414493953402063 & 243.906636652165 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 101.107971014493 & 0.412552436911511 & 245.079078362539 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 101.079275362319 & 0.407257860571736 & 248.194780624779 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 101.081304347826 & 0.406583603300037 & 248.611364372295 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 101.027971014493 & 0.3959619589846 & 255.145649025395 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 101.026666666667 & 0.393662587783935 & 256.632633635269 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 101.023768115942 & 0.391823512596441 & 257.829775059955 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 101.038115942029 & 0.38847688652276 & 260.087844212346 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 101.067681159420 & 0.377240628924230 & 267.913033247859 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 101.139275362319 & 0.363473012494214 & 278.258005094474 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 101.153478260870 & 0.351091273176781 & 288.111627912599 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 101.155652173913 & 0.349496012625994 & 289.432922034972 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 101.153333333333 & 0.348460177918998 & 290.286637449996 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 101.113913043478 & 0.32893173713985 & 307.400903064846 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 101.004347826087 & 0.309542499789052 & 326.302035729891 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 101.042898550725 & 0.301030632435479 & 335.656533467176 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 100.996521739130 & 0.2914410521443 & 346.541851245872 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 100.984347826087 & 0.283115543264687 & 356.689522099731 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 100.981159420290 & 0.277474416555457 & 363.929621598492 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 101.021159420290 & 0.270164259358278 & 373.924958320710 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 101.1 & 0.417605383098403 & 242.094580414394 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 101.093846153846 & 0.414918243354807 & 243.647628835154 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 101.086349206349 & 0.412252954872604 & 245.204668666565 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 101.079836065574 & 0.409668564678113 & 246.735641395856 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 101.074576271186 & 0.406794953930337 & 248.465658913987 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 101.066491228070 & 0.403540680606075 & 250.44932539708 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 101.063818181818 & 0.400643883359449 & 252.253490891675 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 101.060566037736 & 0.396842985614978 & 254.661338869640 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 101.066078431373 & 0.394230258031469 & 256.363067959398 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 101.072244897959 & 0.390982895534908 & 258.508098569584 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 101.072244897959 & 0.386788217604948 & 261.31159197096 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 101.085111111111 & 0.38169380904179 & 264.832985803141 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 101.087441860465 & 0.377128524408909 & 268.045070361368 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 101.080731707317 & 0.373611150118889 & 270.550629110378 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 101.071538461538 & 0.370951386257646 & 272.465725175478 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 101.061081081081 & 0.366872952574728 & 275.466153533071 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 101.049714285714 & 0.360715555368429 & 280.136835747224 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 101.041818181818 & 0.356307997550514 & 283.57998943735 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 101.046451612903 & 0.353979997122460 & 285.458083604499 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 101.046896551724 & 0.351432011884814 & 287.529004571284 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 101.053333333333 & 0.348712732489896 & 289.789628878152 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 101.053333333333 & 0.345210216148557 & 292.729845775614 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 101.073478260870 & 0.339461098550499 & 297.746866113537 \tabularnewline
Median & 100.83 &  &  \tabularnewline
Midrange & 101.235 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.951176470588 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.049714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.049714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.049714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.049714285714 &  &  \tabularnewline
Midmean - Closest Observation & 100.958611111111 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.049714285714 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.049714285714 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1598&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]101.103913043478[/C][C]0.420117316937905[/C][C]240.656380889964[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.044576655596[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.985291343685[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.163249922008[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]101.105797101449[/C][C]0.419618092806564[/C][C]240.947182294299[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]101.107536231884[/C][C]0.418261809664206[/C][C]241.732651405722[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]101.103623188406[/C][C]0.416147432878657[/C][C]242.951452299085[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]101.097826086957[/C][C]0.414493953402063[/C][C]243.906636652165[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]101.107971014493[/C][C]0.412552436911511[/C][C]245.079078362539[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]101.079275362319[/C][C]0.407257860571736[/C][C]248.194780624779[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]101.081304347826[/C][C]0.406583603300037[/C][C]248.611364372295[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]101.027971014493[/C][C]0.3959619589846[/C][C]255.145649025395[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]101.026666666667[/C][C]0.393662587783935[/C][C]256.632633635269[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]101.023768115942[/C][C]0.391823512596441[/C][C]257.829775059955[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]101.038115942029[/C][C]0.38847688652276[/C][C]260.087844212346[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]101.067681159420[/C][C]0.377240628924230[/C][C]267.913033247859[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]101.139275362319[/C][C]0.363473012494214[/C][C]278.258005094474[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]101.153478260870[/C][C]0.351091273176781[/C][C]288.111627912599[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]101.155652173913[/C][C]0.349496012625994[/C][C]289.432922034972[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]101.153333333333[/C][C]0.348460177918998[/C][C]290.286637449996[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]101.113913043478[/C][C]0.32893173713985[/C][C]307.400903064846[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]101.004347826087[/C][C]0.309542499789052[/C][C]326.302035729891[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]101.042898550725[/C][C]0.301030632435479[/C][C]335.656533467176[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]100.996521739130[/C][C]0.2914410521443[/C][C]346.541851245872[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]100.984347826087[/C][C]0.283115543264687[/C][C]356.689522099731[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]100.981159420290[/C][C]0.277474416555457[/C][C]363.929621598492[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]101.021159420290[/C][C]0.270164259358278[/C][C]373.924958320710[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]101.1[/C][C]0.417605383098403[/C][C]242.094580414394[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]101.093846153846[/C][C]0.414918243354807[/C][C]243.647628835154[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]101.086349206349[/C][C]0.412252954872604[/C][C]245.204668666565[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]101.079836065574[/C][C]0.409668564678113[/C][C]246.735641395856[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]101.074576271186[/C][C]0.406794953930337[/C][C]248.465658913987[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]101.066491228070[/C][C]0.403540680606075[/C][C]250.44932539708[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]101.063818181818[/C][C]0.400643883359449[/C][C]252.253490891675[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]101.060566037736[/C][C]0.396842985614978[/C][C]254.661338869640[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]101.066078431373[/C][C]0.394230258031469[/C][C]256.363067959398[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]101.072244897959[/C][C]0.390982895534908[/C][C]258.508098569584[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]101.072244897959[/C][C]0.386788217604948[/C][C]261.31159197096[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]101.085111111111[/C][C]0.38169380904179[/C][C]264.832985803141[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]101.087441860465[/C][C]0.377128524408909[/C][C]268.045070361368[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]101.080731707317[/C][C]0.373611150118889[/C][C]270.550629110378[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]101.071538461538[/C][C]0.370951386257646[/C][C]272.465725175478[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]101.061081081081[/C][C]0.366872952574728[/C][C]275.466153533071[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]101.049714285714[/C][C]0.360715555368429[/C][C]280.136835747224[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]101.041818181818[/C][C]0.356307997550514[/C][C]283.57998943735[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]101.046451612903[/C][C]0.353979997122460[/C][C]285.458083604499[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]101.046896551724[/C][C]0.351432011884814[/C][C]287.529004571284[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]101.053333333333[/C][C]0.348712732489896[/C][C]289.789628878152[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]101.053333333333[/C][C]0.345210216148557[/C][C]292.729845775614[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]101.073478260870[/C][C]0.339461098550499[/C][C]297.746866113537[/C][/ROW]
[ROW][C]Median[/C][C]100.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.951176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.049714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.049714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.049714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.049714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.958611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.049714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.049714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1598&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1598&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 Mean101.1039130434780.420117316937905240.656380889964
Geometric Mean101.044576655596
Harmonic Mean100.985291343685
Quadratic Mean101.163249922008
Winsorized Mean ( 1 / 23 )101.1057971014490.419618092806564240.947182294299
Winsorized Mean ( 2 / 23 )101.1075362318840.418261809664206241.732651405722
Winsorized Mean ( 3 / 23 )101.1036231884060.416147432878657242.951452299085
Winsorized Mean ( 4 / 23 )101.0978260869570.414493953402063243.906636652165
Winsorized Mean ( 5 / 23 )101.1079710144930.412552436911511245.079078362539
Winsorized Mean ( 6 / 23 )101.0792753623190.407257860571736248.194780624779
Winsorized Mean ( 7 / 23 )101.0813043478260.406583603300037248.611364372295
Winsorized Mean ( 8 / 23 )101.0279710144930.3959619589846255.145649025395
Winsorized Mean ( 9 / 23 )101.0266666666670.393662587783935256.632633635269
Winsorized Mean ( 10 / 23 )101.0237681159420.391823512596441257.829775059955
Winsorized Mean ( 11 / 23 )101.0381159420290.38847688652276260.087844212346
Winsorized Mean ( 12 / 23 )101.0676811594200.377240628924230267.913033247859
Winsorized Mean ( 13 / 23 )101.1392753623190.363473012494214278.258005094474
Winsorized Mean ( 14 / 23 )101.1534782608700.351091273176781288.111627912599
Winsorized Mean ( 15 / 23 )101.1556521739130.349496012625994289.432922034972
Winsorized Mean ( 16 / 23 )101.1533333333330.348460177918998290.286637449996
Winsorized Mean ( 17 / 23 )101.1139130434780.32893173713985307.400903064846
Winsorized Mean ( 18 / 23 )101.0043478260870.309542499789052326.302035729891
Winsorized Mean ( 19 / 23 )101.0428985507250.301030632435479335.656533467176
Winsorized Mean ( 20 / 23 )100.9965217391300.2914410521443346.541851245872
Winsorized Mean ( 21 / 23 )100.9843478260870.283115543264687356.689522099731
Winsorized Mean ( 22 / 23 )100.9811594202900.277474416555457363.929621598492
Winsorized Mean ( 23 / 23 )101.0211594202900.270164259358278373.924958320710
Trimmed Mean ( 1 / 23 )101.10.417605383098403242.094580414394
Trimmed Mean ( 2 / 23 )101.0938461538460.414918243354807243.647628835154
Trimmed Mean ( 3 / 23 )101.0863492063490.412252954872604245.204668666565
Trimmed Mean ( 4 / 23 )101.0798360655740.409668564678113246.735641395856
Trimmed Mean ( 5 / 23 )101.0745762711860.406794953930337248.465658913987
Trimmed Mean ( 6 / 23 )101.0664912280700.403540680606075250.44932539708
Trimmed Mean ( 7 / 23 )101.0638181818180.400643883359449252.253490891675
Trimmed Mean ( 8 / 23 )101.0605660377360.396842985614978254.661338869640
Trimmed Mean ( 9 / 23 )101.0660784313730.394230258031469256.363067959398
Trimmed Mean ( 10 / 23 )101.0722448979590.390982895534908258.508098569584
Trimmed Mean ( 11 / 23 )101.0722448979590.386788217604948261.31159197096
Trimmed Mean ( 12 / 23 )101.0851111111110.38169380904179264.832985803141
Trimmed Mean ( 13 / 23 )101.0874418604650.377128524408909268.045070361368
Trimmed Mean ( 14 / 23 )101.0807317073170.373611150118889270.550629110378
Trimmed Mean ( 15 / 23 )101.0715384615380.370951386257646272.465725175478
Trimmed Mean ( 16 / 23 )101.0610810810810.366872952574728275.466153533071
Trimmed Mean ( 17 / 23 )101.0497142857140.360715555368429280.136835747224
Trimmed Mean ( 18 / 23 )101.0418181818180.356307997550514283.57998943735
Trimmed Mean ( 19 / 23 )101.0464516129030.353979997122460285.458083604499
Trimmed Mean ( 20 / 23 )101.0468965517240.351432011884814287.529004571284
Trimmed Mean ( 21 / 23 )101.0533333333330.348712732489896289.789628878152
Trimmed Mean ( 22 / 23 )101.0533333333330.345210216148557292.729845775614
Trimmed Mean ( 23 / 23 )101.0734782608700.339461098550499297.746866113537
Median100.83
Midrange101.235
Midmean - Weighted Average at Xnp100.951176470588
Midmean - Weighted Average at X(n+1)p101.049714285714
Midmean - Empirical Distribution Function101.049714285714
Midmean - Empirical Distribution Function - Averaging101.049714285714
Midmean - Empirical Distribution Function - Interpolation101.049714285714
Midmean - Closest Observation100.958611111111
Midmean - True Basic - Statistics Graphics Toolkit101.049714285714
Midmean - MS Excel (old versions)101.049714285714
Number of observations69



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')