Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Jan 2013 18:32:02 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/15/t1358292775c0nxzynw5i0c3c9.htm/, Retrieved Sat, 27 Apr 2024 23:16:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205569, Retrieved Sat, 27 Apr 2024 23:16:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [Opdracht 1 (Frequ...] [2008-09-23 10:43:38] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2013-01-15 23:32:02] [dea6f921e04cc33dad49f75b9d343660] [Current]
Feedback Forum

Post a new message
Dataseries X:
106,68
109,73
108,06
111,33
105,66
103,65
100,34
100,56
102,67
101,5
102,35
104,98
106,31
103,73
106,62
108,54
105,12
105,29
104,62
104,34
108,23
107,6
106,87
107,96
108,34
109,04
106,95
105,59
108,08
108,48
106,84
105,6
106,9
106,84
106,81
106,98
107,53
107,37
106,98
108,94
106,38
109,02
106,53
105,02
109,7
108,39
110,18
109,54
109,1
110,85
112,23
110,58
110,77
108,08
108,05
108,87
109,61
111,27
107,61
110,98
106,63
106,83
108,77
106,12
106,8
106,34
105,16
107,97
106,76
108,78
105,58
109,22




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=205569&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=205569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205569&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 Mean107.1906944444440.28856461228159371.461675764472
Geometric Mean107.162854900535
Harmonic Mean107.134745278434
Quadratic Mean107.218268557648
Winsorized Mean ( 1 / 24 )107.181250.284731700956767376.428931656872
Winsorized Mean ( 2 / 24 )107.2056944444440.276307733286174387.993825469266
Winsorized Mean ( 3 / 24 )107.2290277777780.264075672612041406.054168932518
Winsorized Mean ( 4 / 24 )107.2395833333330.258111023343976415.478509766779
Winsorized Mean ( 5 / 24 )107.3020833333330.241219266734593444.832142912509
Winsorized Mean ( 6 / 24 )107.2929166666670.236649261865799453.383694589807
Winsorized Mean ( 7 / 24 )107.3133333333330.21719257229134494.093017091691
Winsorized Mean ( 8 / 24 )107.2944444444440.202395366898106530.123026474519
Winsorized Mean ( 9 / 24 )107.3356944444440.193706619797972554.114746085557
Winsorized Mean ( 10 / 24 )107.328750.190628945994203563.024410800991
Winsorized Mean ( 11 / 24 )107.3333333333330.1862534200041576.275771639363
Winsorized Mean ( 12 / 24 )107.2866666666670.17655867458498607.654463417644
Winsorized Mean ( 13 / 24 )107.2884722222220.169311602118639633.674661864244
Winsorized Mean ( 14 / 24 )107.3331944444440.158457182398629677.364022379417
Winsorized Mean ( 15 / 24 )107.3311111111110.157501963069411681.458878476394
Winsorized Mean ( 16 / 24 )107.3155555555560.154496112770088694.616541681255
Winsorized Mean ( 17 / 24 )107.3131944444440.149854366756101716.116565485905
Winsorized Mean ( 18 / 24 )107.4056944444440.129488554909152829.460908879549
Winsorized Mean ( 19 / 24 )107.4531944444440.122278483947496878.757987305298
Winsorized Mean ( 20 / 24 )107.3976388888890.11171771887706961.330395647221
Winsorized Mean ( 21 / 24 )107.3918055555560.107661573156181997.494300030023
Winsorized Mean ( 22 / 24 )107.4101388888890.0978196363822441098.04271270411
Winsorized Mean ( 23 / 24 )107.4229166666670.09198056317694191167.88713785127
Winsorized Mean ( 24 / 24 )107.3895833333330.08648374463940911241.73142341477
Trimmed Mean ( 1 / 24 )107.2165714285710.270457161142045396.427186382619
Trimmed Mean ( 2 / 24 )107.2539705882350.25315178653992423.674555310011
Trimmed Mean ( 3 / 24 )107.2803030303030.237848061204991451.045522451591
Trimmed Mean ( 4 / 24 )107.299531250.225304735180636476.241793870749
Trimmed Mean ( 5 / 24 )107.3169354838710.212397433947846505.264745854804
Trimmed Mean ( 6 / 24 )107.32050.202557995461605529.826037009448
Trimmed Mean ( 7 / 24 )107.3262068965520.191885733602595559.323535322483
Trimmed Mean ( 8 / 24 )107.3285714285710.184342888543568582.222467471021
Trimmed Mean ( 9 / 24 )107.3342592592590.178862506066252600.093678769669
Trimmed Mean ( 10 / 24 )107.3340384615380.174140046017861616.366200170461
Trimmed Mean ( 11 / 24 )107.33480.168893696792765635.516908198778
Trimmed Mean ( 12 / 24 )107.3350.163242575016055657.51841999211
Trimmed Mean ( 13 / 24 )107.3413043478260.15823989880703678.34538038176
Trimmed Mean ( 14 / 24 )107.3479545454550.153413788981386699.728200823456
Trimmed Mean ( 15 / 24 )107.3497619047620.149604390464883717.557563459079
Trimmed Mean ( 16 / 24 )107.3520.144679663837753741.997853412123
Trimmed Mean ( 17 / 24 )107.3563157894740.138736126548793773.816585917994
Trimmed Mean ( 18 / 24 )107.3613888888890.131814656300126814.487492532244
Trimmed Mean ( 19 / 24 )107.3561764705880.127844473462829839.740456217706
Trimmed Mean ( 20 / 24 )107.34468750.123949606349978866.034920650791
Trimmed Mean ( 21 / 24 )107.3383333333330.121301451539517884.889108671259
Trimmed Mean ( 22 / 24 )107.3317857142860.118289231186375907.367345596958
Trimmed Mean ( 23 / 24 )107.3219230769230.116440832424117921.686326374072
Trimmed Mean ( 24 / 24 )107.308750.114838122520607934.434904060229
Median106.98
Midrange106.285
Midmean - Weighted Average at Xnp107.315405405405
Midmean - Weighted Average at X(n+1)p107.361388888889
Midmean - Empirical Distribution Function107.315405405405
Midmean - Empirical Distribution Function - Averaging107.361388888889
Midmean - Empirical Distribution Function - Interpolation107.361388888889
Midmean - Closest Observation107.315405405405
Midmean - True Basic - Statistics Graphics Toolkit107.361388888889
Midmean - MS Excel (old versions)107.356315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 107.190694444444 & 0.28856461228159 & 371.461675764472 \tabularnewline
Geometric Mean & 107.162854900535 &  &  \tabularnewline
Harmonic Mean & 107.134745278434 &  &  \tabularnewline
Quadratic Mean & 107.218268557648 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 107.18125 & 0.284731700956767 & 376.428931656872 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 107.205694444444 & 0.276307733286174 & 387.993825469266 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 107.229027777778 & 0.264075672612041 & 406.054168932518 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 107.239583333333 & 0.258111023343976 & 415.478509766779 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 107.302083333333 & 0.241219266734593 & 444.832142912509 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 107.292916666667 & 0.236649261865799 & 453.383694589807 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 107.313333333333 & 0.21719257229134 & 494.093017091691 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 107.294444444444 & 0.202395366898106 & 530.123026474519 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 107.335694444444 & 0.193706619797972 & 554.114746085557 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 107.32875 & 0.190628945994203 & 563.024410800991 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 107.333333333333 & 0.1862534200041 & 576.275771639363 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 107.286666666667 & 0.17655867458498 & 607.654463417644 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 107.288472222222 & 0.169311602118639 & 633.674661864244 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 107.333194444444 & 0.158457182398629 & 677.364022379417 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 107.331111111111 & 0.157501963069411 & 681.458878476394 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 107.315555555556 & 0.154496112770088 & 694.616541681255 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 107.313194444444 & 0.149854366756101 & 716.116565485905 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 107.405694444444 & 0.129488554909152 & 829.460908879549 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 107.453194444444 & 0.122278483947496 & 878.757987305298 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 107.397638888889 & 0.11171771887706 & 961.330395647221 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 107.391805555556 & 0.107661573156181 & 997.494300030023 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 107.410138888889 & 0.097819636382244 & 1098.04271270411 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 107.422916666667 & 0.0919805631769419 & 1167.88713785127 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 107.389583333333 & 0.0864837446394091 & 1241.73142341477 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 107.216571428571 & 0.270457161142045 & 396.427186382619 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 107.253970588235 & 0.25315178653992 & 423.674555310011 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 107.280303030303 & 0.237848061204991 & 451.045522451591 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 107.29953125 & 0.225304735180636 & 476.241793870749 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 107.316935483871 & 0.212397433947846 & 505.264745854804 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 107.3205 & 0.202557995461605 & 529.826037009448 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 107.326206896552 & 0.191885733602595 & 559.323535322483 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 107.328571428571 & 0.184342888543568 & 582.222467471021 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 107.334259259259 & 0.178862506066252 & 600.093678769669 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 107.334038461538 & 0.174140046017861 & 616.366200170461 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 107.3348 & 0.168893696792765 & 635.516908198778 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 107.335 & 0.163242575016055 & 657.51841999211 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 107.341304347826 & 0.15823989880703 & 678.34538038176 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 107.347954545455 & 0.153413788981386 & 699.728200823456 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 107.349761904762 & 0.149604390464883 & 717.557563459079 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 107.352 & 0.144679663837753 & 741.997853412123 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 107.356315789474 & 0.138736126548793 & 773.816585917994 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 107.361388888889 & 0.131814656300126 & 814.487492532244 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 107.356176470588 & 0.127844473462829 & 839.740456217706 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 107.3446875 & 0.123949606349978 & 866.034920650791 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 107.338333333333 & 0.121301451539517 & 884.889108671259 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 107.331785714286 & 0.118289231186375 & 907.367345596958 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 107.321923076923 & 0.116440832424117 & 921.686326374072 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 107.30875 & 0.114838122520607 & 934.434904060229 \tabularnewline
Median & 106.98 &  &  \tabularnewline
Midrange & 106.285 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.315405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.361388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 107.315405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.361388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.361388888889 &  &  \tabularnewline
Midmean - Closest Observation & 107.315405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.361388888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.356315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205569&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]107.190694444444[/C][C]0.28856461228159[/C][C]371.461675764472[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107.162854900535[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.134745278434[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]107.218268557648[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]107.18125[/C][C]0.284731700956767[/C][C]376.428931656872[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]107.205694444444[/C][C]0.276307733286174[/C][C]387.993825469266[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]107.229027777778[/C][C]0.264075672612041[/C][C]406.054168932518[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]107.239583333333[/C][C]0.258111023343976[/C][C]415.478509766779[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]107.302083333333[/C][C]0.241219266734593[/C][C]444.832142912509[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]107.292916666667[/C][C]0.236649261865799[/C][C]453.383694589807[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]107.313333333333[/C][C]0.21719257229134[/C][C]494.093017091691[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]107.294444444444[/C][C]0.202395366898106[/C][C]530.123026474519[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]107.335694444444[/C][C]0.193706619797972[/C][C]554.114746085557[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]107.32875[/C][C]0.190628945994203[/C][C]563.024410800991[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]107.333333333333[/C][C]0.1862534200041[/C][C]576.275771639363[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]107.286666666667[/C][C]0.17655867458498[/C][C]607.654463417644[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]107.288472222222[/C][C]0.169311602118639[/C][C]633.674661864244[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]107.333194444444[/C][C]0.158457182398629[/C][C]677.364022379417[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]107.331111111111[/C][C]0.157501963069411[/C][C]681.458878476394[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]107.315555555556[/C][C]0.154496112770088[/C][C]694.616541681255[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]107.313194444444[/C][C]0.149854366756101[/C][C]716.116565485905[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]107.405694444444[/C][C]0.129488554909152[/C][C]829.460908879549[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]107.453194444444[/C][C]0.122278483947496[/C][C]878.757987305298[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]107.397638888889[/C][C]0.11171771887706[/C][C]961.330395647221[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]107.391805555556[/C][C]0.107661573156181[/C][C]997.494300030023[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]107.410138888889[/C][C]0.097819636382244[/C][C]1098.04271270411[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]107.422916666667[/C][C]0.0919805631769419[/C][C]1167.88713785127[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]107.389583333333[/C][C]0.0864837446394091[/C][C]1241.73142341477[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]107.216571428571[/C][C]0.270457161142045[/C][C]396.427186382619[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]107.253970588235[/C][C]0.25315178653992[/C][C]423.674555310011[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]107.280303030303[/C][C]0.237848061204991[/C][C]451.045522451591[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]107.29953125[/C][C]0.225304735180636[/C][C]476.241793870749[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]107.316935483871[/C][C]0.212397433947846[/C][C]505.264745854804[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]107.3205[/C][C]0.202557995461605[/C][C]529.826037009448[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]107.326206896552[/C][C]0.191885733602595[/C][C]559.323535322483[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]107.328571428571[/C][C]0.184342888543568[/C][C]582.222467471021[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]107.334259259259[/C][C]0.178862506066252[/C][C]600.093678769669[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]107.334038461538[/C][C]0.174140046017861[/C][C]616.366200170461[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]107.3348[/C][C]0.168893696792765[/C][C]635.516908198778[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]107.335[/C][C]0.163242575016055[/C][C]657.51841999211[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]107.341304347826[/C][C]0.15823989880703[/C][C]678.34538038176[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]107.347954545455[/C][C]0.153413788981386[/C][C]699.728200823456[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]107.349761904762[/C][C]0.149604390464883[/C][C]717.557563459079[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]107.352[/C][C]0.144679663837753[/C][C]741.997853412123[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]107.356315789474[/C][C]0.138736126548793[/C][C]773.816585917994[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]107.361388888889[/C][C]0.131814656300126[/C][C]814.487492532244[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]107.356176470588[/C][C]0.127844473462829[/C][C]839.740456217706[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]107.3446875[/C][C]0.123949606349978[/C][C]866.034920650791[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]107.338333333333[/C][C]0.121301451539517[/C][C]884.889108671259[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]107.331785714286[/C][C]0.118289231186375[/C][C]907.367345596958[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]107.321923076923[/C][C]0.116440832424117[/C][C]921.686326374072[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]107.30875[/C][C]0.114838122520607[/C][C]934.434904060229[/C][/ROW]
[ROW][C]Median[/C][C]106.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.285[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.315405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.361388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]107.315405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.361388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.361388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.315405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.361388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.356315789474[/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=205569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205569&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 Mean107.1906944444440.28856461228159371.461675764472
Geometric Mean107.162854900535
Harmonic Mean107.134745278434
Quadratic Mean107.218268557648
Winsorized Mean ( 1 / 24 )107.181250.284731700956767376.428931656872
Winsorized Mean ( 2 / 24 )107.2056944444440.276307733286174387.993825469266
Winsorized Mean ( 3 / 24 )107.2290277777780.264075672612041406.054168932518
Winsorized Mean ( 4 / 24 )107.2395833333330.258111023343976415.478509766779
Winsorized Mean ( 5 / 24 )107.3020833333330.241219266734593444.832142912509
Winsorized Mean ( 6 / 24 )107.2929166666670.236649261865799453.383694589807
Winsorized Mean ( 7 / 24 )107.3133333333330.21719257229134494.093017091691
Winsorized Mean ( 8 / 24 )107.2944444444440.202395366898106530.123026474519
Winsorized Mean ( 9 / 24 )107.3356944444440.193706619797972554.114746085557
Winsorized Mean ( 10 / 24 )107.328750.190628945994203563.024410800991
Winsorized Mean ( 11 / 24 )107.3333333333330.1862534200041576.275771639363
Winsorized Mean ( 12 / 24 )107.2866666666670.17655867458498607.654463417644
Winsorized Mean ( 13 / 24 )107.2884722222220.169311602118639633.674661864244
Winsorized Mean ( 14 / 24 )107.3331944444440.158457182398629677.364022379417
Winsorized Mean ( 15 / 24 )107.3311111111110.157501963069411681.458878476394
Winsorized Mean ( 16 / 24 )107.3155555555560.154496112770088694.616541681255
Winsorized Mean ( 17 / 24 )107.3131944444440.149854366756101716.116565485905
Winsorized Mean ( 18 / 24 )107.4056944444440.129488554909152829.460908879549
Winsorized Mean ( 19 / 24 )107.4531944444440.122278483947496878.757987305298
Winsorized Mean ( 20 / 24 )107.3976388888890.11171771887706961.330395647221
Winsorized Mean ( 21 / 24 )107.3918055555560.107661573156181997.494300030023
Winsorized Mean ( 22 / 24 )107.4101388888890.0978196363822441098.04271270411
Winsorized Mean ( 23 / 24 )107.4229166666670.09198056317694191167.88713785127
Winsorized Mean ( 24 / 24 )107.3895833333330.08648374463940911241.73142341477
Trimmed Mean ( 1 / 24 )107.2165714285710.270457161142045396.427186382619
Trimmed Mean ( 2 / 24 )107.2539705882350.25315178653992423.674555310011
Trimmed Mean ( 3 / 24 )107.2803030303030.237848061204991451.045522451591
Trimmed Mean ( 4 / 24 )107.299531250.225304735180636476.241793870749
Trimmed Mean ( 5 / 24 )107.3169354838710.212397433947846505.264745854804
Trimmed Mean ( 6 / 24 )107.32050.202557995461605529.826037009448
Trimmed Mean ( 7 / 24 )107.3262068965520.191885733602595559.323535322483
Trimmed Mean ( 8 / 24 )107.3285714285710.184342888543568582.222467471021
Trimmed Mean ( 9 / 24 )107.3342592592590.178862506066252600.093678769669
Trimmed Mean ( 10 / 24 )107.3340384615380.174140046017861616.366200170461
Trimmed Mean ( 11 / 24 )107.33480.168893696792765635.516908198778
Trimmed Mean ( 12 / 24 )107.3350.163242575016055657.51841999211
Trimmed Mean ( 13 / 24 )107.3413043478260.15823989880703678.34538038176
Trimmed Mean ( 14 / 24 )107.3479545454550.153413788981386699.728200823456
Trimmed Mean ( 15 / 24 )107.3497619047620.149604390464883717.557563459079
Trimmed Mean ( 16 / 24 )107.3520.144679663837753741.997853412123
Trimmed Mean ( 17 / 24 )107.3563157894740.138736126548793773.816585917994
Trimmed Mean ( 18 / 24 )107.3613888888890.131814656300126814.487492532244
Trimmed Mean ( 19 / 24 )107.3561764705880.127844473462829839.740456217706
Trimmed Mean ( 20 / 24 )107.34468750.123949606349978866.034920650791
Trimmed Mean ( 21 / 24 )107.3383333333330.121301451539517884.889108671259
Trimmed Mean ( 22 / 24 )107.3317857142860.118289231186375907.367345596958
Trimmed Mean ( 23 / 24 )107.3219230769230.116440832424117921.686326374072
Trimmed Mean ( 24 / 24 )107.308750.114838122520607934.434904060229
Median106.98
Midrange106.285
Midmean - Weighted Average at Xnp107.315405405405
Midmean - Weighted Average at X(n+1)p107.361388888889
Midmean - Empirical Distribution Function107.315405405405
Midmean - Empirical Distribution Function - Averaging107.361388888889
Midmean - Empirical Distribution Function - Interpolation107.361388888889
Midmean - Closest Observation107.315405405405
Midmean - True Basic - Statistics Graphics Toolkit107.361388888889
Midmean - MS Excel (old versions)107.356315789474
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')