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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 12:53:46 -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/Mar/05/t13625061227m7mkxwv8xdkta6.htm/, Retrieved Sat, 04 May 2024 15:36:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207427, Retrieved Sat, 04 May 2024 15:36:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 17:53:46] [4d26c4233714d8e4ecf99606d744931b] [Current]
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Dataseries X:
102,42
102,46
102,76
102,4
102,47
102,27
102,17
101,84
102,13
103,34
103,43
103,59
104,21
105,42
105,95
106,28
106,49
106,49
106,49
107,38
108,69
108,76
108,84
108,67
108,79
109,96
110,86
111
111,84
112,21
112,4
113,76
114,85
115,23
115,39
115,29
115,53
116,26
116,85
117,37
118,03
118,49
119,32
119,4
122,26
122,91
123,78
123,99
124,7
125,89
127,57
128,97
130,65
130,73
130,95
131,36
132,85
133,08
133,13
133,27
133,9
134,85
135,49
136,21
136,31
136,22
136,22
135,51
137,3
138,42
138,92
138,67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207427&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207427&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean118.0818055555561.4595965062736880.9003070698053
Geometric Mean117.449851420655
Harmonic Mean116.82939295817
Quadratic Mean118.720565878453
Winsorized Mean ( 1 / 24 )118.0823611111111.4582762764566880.9739299867291
Winsorized Mean ( 2 / 24 )118.0765277777781.4567318525143881.0557739737569
Winsorized Mean ( 3 / 24 )118.0340277777781.4471263638057681.5644236259805
Winsorized Mean ( 4 / 24 )117.986251.4359202340398482.1676909364634
Winsorized Mean ( 5 / 24 )117.9813888888891.4345867336837882.2406802730795
Winsorized Mean ( 6 / 24 )117.9847222222221.4340779806639882.2721803228546
Winsorized Mean ( 7 / 24 )117.9847222222221.4337556831101482.2906744936392
Winsorized Mean ( 8 / 24 )117.9391666666671.4151014655028283.3432580926343
Winsorized Mean ( 9 / 24 )118.0091666666671.4038514921915184.0610045457488
Winsorized Mean ( 10 / 24 )117.9327777777781.3865778911156685.0531214534851
Winsorized Mean ( 11 / 24 )117.8120833333331.3583958183948886.7288324492512
Winsorized Mean ( 12 / 24 )117.8104166666671.3259304678360888.8511272080004
Winsorized Mean ( 13 / 24 )118.0036111111111.2909810433185991.4061532675734
Winsorized Mean ( 14 / 24 )118.0969444444441.2753873976329992.5969196995538
Winsorized Mean ( 15 / 24 )118.1177777777781.2583060224972493.8704700334825
Winsorized Mean ( 16 / 24 )117.8333333333331.1984620426219798.3204550020955
Winsorized Mean ( 17 / 24 )117.7365277777781.1831534968769899.5107803751176
Winsorized Mean ( 18 / 24 )117.6815277777781.17452477087174100.195015632095
Winsorized Mean ( 19 / 24 )117.8952777777781.14018951030696103.399721460373
Winsorized Mean ( 20 / 24 )117.7869444444441.0215731991436115.299563989333
Winsorized Mean ( 21 / 24 )117.3844444444440.958777257640551122.431402610983
Winsorized Mean ( 22 / 24 )116.89250.880619263676809132.738976787703
Winsorized Mean ( 23 / 24 )116.5219444444440.825463417028082141.159428801774
Winsorized Mean ( 24 / 24 )116.3019444444440.790529047682876147.11912836769
Trimmed Mean ( 1 / 24 )118.0161428571431.4526614867715681.241324239569
Trimmed Mean ( 2 / 24 )117.9460294117651.4450046425598781.6232875230213
Trimmed Mean ( 3 / 24 )117.8748484848481.4358628448441582.0933899836673
Trimmed Mean ( 4 / 24 )117.815156251.4281420906064282.4954022606903
Trimmed Mean ( 5 / 24 )117.7654838709681.4216527328164482.8370256340044
Trimmed Mean ( 6 / 24 )117.7136666666671.4129718644198883.3092785715137
Trimmed Mean ( 7 / 24 )117.6575862068971.4013466496794283.9603721419053
Trimmed Mean ( 8 / 24 )117.59751.386059378471784.8430462839664
Trimmed Mean ( 9 / 24 )117.5405555555561.370548570250285.7616855811963
Trimmed Mean ( 10 / 24 )117.4684615384621.3525967814313486.8466221057798
Trimmed Mean ( 11 / 24 )117.40161.3328597568493788.0824853452812
Trimmed Mean ( 12 / 24 )117.3456251.3130135235272489.3712234469345
Trimmed Mean ( 13 / 24 )117.2851.2934346945937290.6771717893655
Trimmed Mean ( 14 / 24 )117.1945454545451.2739984855063491.9895484867606
Trimmed Mean ( 15 / 24 )117.0840476190481.2502153616811393.6511030080511
Trimmed Mean ( 16 / 24 )116.961.2209821603518495.7917353733465
Trimmed Mean ( 17 / 24 )116.8565789473681.195134950528197.7768902965583
Trimmed Mean ( 18 / 24 )116.7530555555561.16216149326148100.461989347023
Trimmed Mean ( 19 / 24 )116.6438235294121.1173120768752104.396816201639
Trimmed Mean ( 20 / 24 )116.4956251.06160787380359109.735080037239
Trimmed Mean ( 21 / 24 )116.3406666666671.01733502809398114.358262965383
Trimmed Mean ( 22 / 24 )116.2128571428570.972734358146804119.470291318032
Trimmed Mean ( 23 / 24 )116.1273076923080.933112171951361124.451605265697
Trimmed Mean ( 24 / 24 )116.0758333333330.891346464923377130.225269186782
Median115.46
Midrange120.38
Midmean - Weighted Average at Xnp116.212894736842
Midmean - Weighted Average at X(n+1)p116.212894736842
Midmean - Empirical Distribution Function116.212894736842
Midmean - Empirical Distribution Function - Averaging116.212894736842
Midmean - Empirical Distribution Function - Interpolation116.212894736842
Midmean - Closest Observation116.212894736842
Midmean - True Basic - Statistics Graphics Toolkit116.212894736842
Midmean - MS Excel (old versions)116.590769230769
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 118.081805555556 & 1.45959650627368 & 80.9003070698053 \tabularnewline
Geometric Mean & 117.449851420655 &  &  \tabularnewline
Harmonic Mean & 116.82939295817 &  &  \tabularnewline
Quadratic Mean & 118.720565878453 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 118.082361111111 & 1.45827627645668 & 80.9739299867291 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 118.076527777778 & 1.45673185251438 & 81.0557739737569 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 118.034027777778 & 1.44712636380576 & 81.5644236259805 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 117.98625 & 1.43592023403984 & 82.1676909364634 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 117.981388888889 & 1.43458673368378 & 82.2406802730795 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 117.984722222222 & 1.43407798066398 & 82.2721803228546 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 117.984722222222 & 1.43375568311014 & 82.2906744936392 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 117.939166666667 & 1.41510146550282 & 83.3432580926343 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 118.009166666667 & 1.40385149219151 & 84.0610045457488 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 117.932777777778 & 1.38657789111566 & 85.0531214534851 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 117.812083333333 & 1.35839581839488 & 86.7288324492512 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 117.810416666667 & 1.32593046783608 & 88.8511272080004 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 118.003611111111 & 1.29098104331859 & 91.4061532675734 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 118.096944444444 & 1.27538739763299 & 92.5969196995538 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 118.117777777778 & 1.25830602249724 & 93.8704700334825 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 117.833333333333 & 1.19846204262197 & 98.3204550020955 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 117.736527777778 & 1.18315349687698 & 99.5107803751176 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 117.681527777778 & 1.17452477087174 & 100.195015632095 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 117.895277777778 & 1.14018951030696 & 103.399721460373 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 117.786944444444 & 1.0215731991436 & 115.299563989333 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 117.384444444444 & 0.958777257640551 & 122.431402610983 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 116.8925 & 0.880619263676809 & 132.738976787703 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 116.521944444444 & 0.825463417028082 & 141.159428801774 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 116.301944444444 & 0.790529047682876 & 147.11912836769 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 118.016142857143 & 1.45266148677156 & 81.241324239569 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 117.946029411765 & 1.44500464255987 & 81.6232875230213 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 117.874848484848 & 1.43586284484415 & 82.0933899836673 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 117.81515625 & 1.42814209060642 & 82.4954022606903 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 117.765483870968 & 1.42165273281644 & 82.8370256340044 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 117.713666666667 & 1.41297186441988 & 83.3092785715137 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 117.657586206897 & 1.40134664967942 & 83.9603721419053 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 117.5975 & 1.3860593784717 & 84.8430462839664 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 117.540555555556 & 1.3705485702502 & 85.7616855811963 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 117.468461538462 & 1.35259678143134 & 86.8466221057798 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 117.4016 & 1.33285975684937 & 88.0824853452812 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 117.345625 & 1.31301352352724 & 89.3712234469345 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 117.285 & 1.29343469459372 & 90.6771717893655 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 117.194545454545 & 1.27399848550634 & 91.9895484867606 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 117.084047619048 & 1.25021536168113 & 93.6511030080511 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 116.96 & 1.22098216035184 & 95.7917353733465 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 116.856578947368 & 1.1951349505281 & 97.7768902965583 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 116.753055555556 & 1.16216149326148 & 100.461989347023 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 116.643823529412 & 1.1173120768752 & 104.396816201639 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 116.495625 & 1.06160787380359 & 109.735080037239 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 116.340666666667 & 1.01733502809398 & 114.358262965383 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 116.212857142857 & 0.972734358146804 & 119.470291318032 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 116.127307692308 & 0.933112171951361 & 124.451605265697 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 116.075833333333 & 0.891346464923377 & 130.225269186782 \tabularnewline
Median & 115.46 &  &  \tabularnewline
Midrange & 120.38 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.212894736842 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.212894736842 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.212894736842 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.212894736842 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.212894736842 &  &  \tabularnewline
Midmean - Closest Observation & 116.212894736842 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.212894736842 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.590769230769 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207427&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]118.081805555556[/C][C]1.45959650627368[/C][C]80.9003070698053[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]117.449851420655[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]116.82939295817[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]118.720565878453[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]118.082361111111[/C][C]1.45827627645668[/C][C]80.9739299867291[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]118.076527777778[/C][C]1.45673185251438[/C][C]81.0557739737569[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]118.034027777778[/C][C]1.44712636380576[/C][C]81.5644236259805[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]117.98625[/C][C]1.43592023403984[/C][C]82.1676909364634[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]117.981388888889[/C][C]1.43458673368378[/C][C]82.2406802730795[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]117.984722222222[/C][C]1.43407798066398[/C][C]82.2721803228546[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]117.984722222222[/C][C]1.43375568311014[/C][C]82.2906744936392[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]117.939166666667[/C][C]1.41510146550282[/C][C]83.3432580926343[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]118.009166666667[/C][C]1.40385149219151[/C][C]84.0610045457488[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]117.932777777778[/C][C]1.38657789111566[/C][C]85.0531214534851[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]117.812083333333[/C][C]1.35839581839488[/C][C]86.7288324492512[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]117.810416666667[/C][C]1.32593046783608[/C][C]88.8511272080004[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]118.003611111111[/C][C]1.29098104331859[/C][C]91.4061532675734[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]118.096944444444[/C][C]1.27538739763299[/C][C]92.5969196995538[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]118.117777777778[/C][C]1.25830602249724[/C][C]93.8704700334825[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]117.833333333333[/C][C]1.19846204262197[/C][C]98.3204550020955[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]117.736527777778[/C][C]1.18315349687698[/C][C]99.5107803751176[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]117.681527777778[/C][C]1.17452477087174[/C][C]100.195015632095[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]117.895277777778[/C][C]1.14018951030696[/C][C]103.399721460373[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]117.786944444444[/C][C]1.0215731991436[/C][C]115.299563989333[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]117.384444444444[/C][C]0.958777257640551[/C][C]122.431402610983[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]116.8925[/C][C]0.880619263676809[/C][C]132.738976787703[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]116.521944444444[/C][C]0.825463417028082[/C][C]141.159428801774[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]116.301944444444[/C][C]0.790529047682876[/C][C]147.11912836769[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]118.016142857143[/C][C]1.45266148677156[/C][C]81.241324239569[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]117.946029411765[/C][C]1.44500464255987[/C][C]81.6232875230213[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]117.874848484848[/C][C]1.43586284484415[/C][C]82.0933899836673[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]117.81515625[/C][C]1.42814209060642[/C][C]82.4954022606903[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]117.765483870968[/C][C]1.42165273281644[/C][C]82.8370256340044[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]117.713666666667[/C][C]1.41297186441988[/C][C]83.3092785715137[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]117.657586206897[/C][C]1.40134664967942[/C][C]83.9603721419053[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]117.5975[/C][C]1.3860593784717[/C][C]84.8430462839664[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]117.540555555556[/C][C]1.3705485702502[/C][C]85.7616855811963[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]117.468461538462[/C][C]1.35259678143134[/C][C]86.8466221057798[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]117.4016[/C][C]1.33285975684937[/C][C]88.0824853452812[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]117.345625[/C][C]1.31301352352724[/C][C]89.3712234469345[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]117.285[/C][C]1.29343469459372[/C][C]90.6771717893655[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]117.194545454545[/C][C]1.27399848550634[/C][C]91.9895484867606[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]117.084047619048[/C][C]1.25021536168113[/C][C]93.6511030080511[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]116.96[/C][C]1.22098216035184[/C][C]95.7917353733465[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]116.856578947368[/C][C]1.1951349505281[/C][C]97.7768902965583[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]116.753055555556[/C][C]1.16216149326148[/C][C]100.461989347023[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]116.643823529412[/C][C]1.1173120768752[/C][C]104.396816201639[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]116.495625[/C][C]1.06160787380359[/C][C]109.735080037239[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]116.340666666667[/C][C]1.01733502809398[/C][C]114.358262965383[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]116.212857142857[/C][C]0.972734358146804[/C][C]119.470291318032[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]116.127307692308[/C][C]0.933112171951361[/C][C]124.451605265697[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]116.075833333333[/C][C]0.891346464923377[/C][C]130.225269186782[/C][/ROW]
[ROW][C]Median[/C][C]115.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]120.38[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.212894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.212894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.212894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.212894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.212894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.212894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.212894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.590769230769[/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=207427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207427&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 Mean118.0818055555561.4595965062736880.9003070698053
Geometric Mean117.449851420655
Harmonic Mean116.82939295817
Quadratic Mean118.720565878453
Winsorized Mean ( 1 / 24 )118.0823611111111.4582762764566880.9739299867291
Winsorized Mean ( 2 / 24 )118.0765277777781.4567318525143881.0557739737569
Winsorized Mean ( 3 / 24 )118.0340277777781.4471263638057681.5644236259805
Winsorized Mean ( 4 / 24 )117.986251.4359202340398482.1676909364634
Winsorized Mean ( 5 / 24 )117.9813888888891.4345867336837882.2406802730795
Winsorized Mean ( 6 / 24 )117.9847222222221.4340779806639882.2721803228546
Winsorized Mean ( 7 / 24 )117.9847222222221.4337556831101482.2906744936392
Winsorized Mean ( 8 / 24 )117.9391666666671.4151014655028283.3432580926343
Winsorized Mean ( 9 / 24 )118.0091666666671.4038514921915184.0610045457488
Winsorized Mean ( 10 / 24 )117.9327777777781.3865778911156685.0531214534851
Winsorized Mean ( 11 / 24 )117.8120833333331.3583958183948886.7288324492512
Winsorized Mean ( 12 / 24 )117.8104166666671.3259304678360888.8511272080004
Winsorized Mean ( 13 / 24 )118.0036111111111.2909810433185991.4061532675734
Winsorized Mean ( 14 / 24 )118.0969444444441.2753873976329992.5969196995538
Winsorized Mean ( 15 / 24 )118.1177777777781.2583060224972493.8704700334825
Winsorized Mean ( 16 / 24 )117.8333333333331.1984620426219798.3204550020955
Winsorized Mean ( 17 / 24 )117.7365277777781.1831534968769899.5107803751176
Winsorized Mean ( 18 / 24 )117.6815277777781.17452477087174100.195015632095
Winsorized Mean ( 19 / 24 )117.8952777777781.14018951030696103.399721460373
Winsorized Mean ( 20 / 24 )117.7869444444441.0215731991436115.299563989333
Winsorized Mean ( 21 / 24 )117.3844444444440.958777257640551122.431402610983
Winsorized Mean ( 22 / 24 )116.89250.880619263676809132.738976787703
Winsorized Mean ( 23 / 24 )116.5219444444440.825463417028082141.159428801774
Winsorized Mean ( 24 / 24 )116.3019444444440.790529047682876147.11912836769
Trimmed Mean ( 1 / 24 )118.0161428571431.4526614867715681.241324239569
Trimmed Mean ( 2 / 24 )117.9460294117651.4450046425598781.6232875230213
Trimmed Mean ( 3 / 24 )117.8748484848481.4358628448441582.0933899836673
Trimmed Mean ( 4 / 24 )117.815156251.4281420906064282.4954022606903
Trimmed Mean ( 5 / 24 )117.7654838709681.4216527328164482.8370256340044
Trimmed Mean ( 6 / 24 )117.7136666666671.4129718644198883.3092785715137
Trimmed Mean ( 7 / 24 )117.6575862068971.4013466496794283.9603721419053
Trimmed Mean ( 8 / 24 )117.59751.386059378471784.8430462839664
Trimmed Mean ( 9 / 24 )117.5405555555561.370548570250285.7616855811963
Trimmed Mean ( 10 / 24 )117.4684615384621.3525967814313486.8466221057798
Trimmed Mean ( 11 / 24 )117.40161.3328597568493788.0824853452812
Trimmed Mean ( 12 / 24 )117.3456251.3130135235272489.3712234469345
Trimmed Mean ( 13 / 24 )117.2851.2934346945937290.6771717893655
Trimmed Mean ( 14 / 24 )117.1945454545451.2739984855063491.9895484867606
Trimmed Mean ( 15 / 24 )117.0840476190481.2502153616811393.6511030080511
Trimmed Mean ( 16 / 24 )116.961.2209821603518495.7917353733465
Trimmed Mean ( 17 / 24 )116.8565789473681.195134950528197.7768902965583
Trimmed Mean ( 18 / 24 )116.7530555555561.16216149326148100.461989347023
Trimmed Mean ( 19 / 24 )116.6438235294121.1173120768752104.396816201639
Trimmed Mean ( 20 / 24 )116.4956251.06160787380359109.735080037239
Trimmed Mean ( 21 / 24 )116.3406666666671.01733502809398114.358262965383
Trimmed Mean ( 22 / 24 )116.2128571428570.972734358146804119.470291318032
Trimmed Mean ( 23 / 24 )116.1273076923080.933112171951361124.451605265697
Trimmed Mean ( 24 / 24 )116.0758333333330.891346464923377130.225269186782
Median115.46
Midrange120.38
Midmean - Weighted Average at Xnp116.212894736842
Midmean - Weighted Average at X(n+1)p116.212894736842
Midmean - Empirical Distribution Function116.212894736842
Midmean - Empirical Distribution Function - Averaging116.212894736842
Midmean - Empirical Distribution Function - Interpolation116.212894736842
Midmean - Closest Observation116.212894736842
Midmean - True Basic - Statistics Graphics Toolkit116.212894736842
Midmean - MS Excel (old versions)116.590769230769
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')