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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, 20 Apr 2008 12:49:12 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/20/t1208717637mtmbpxonlnb5fea.htm/, Retrieved Mon, 13 May 2024 20:16:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10427, Retrieved Mon, 13 May 2024 20:16:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Nietje Vant Santf...] [2008-04-20 18:49:12] [4c7a5669b420c0879a97a0998c00f1a1] [Current]
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Dataseries X:
71,42
71,47
71,64
71,55
71,62
71,65
71,65
71,65
71,6
71,7
71,73
71,83
71,83
71,87
71,91
71,99
72,1
72,12
72,12
72,12
72,25
72,59
72,72
72,76
72,76
72,91
73
73,16
73,16
73,11
73,11
73,33
73,51
73,66
73,65
73,65
73,65
73,65
73,71
73,73
73,85
73,77
73,77
73,78
73,88
74,3
74,53
74,71
74,71
74,78
74,9
74,65
74,65
74,53
74,53
74,53
74,65
74,85
74,96
74,96
74,96
75,19
74,98
75,54
75,61
75,59
75,58
75,44
75,37
75,22
75,33
75,33




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10427&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10427&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean73.51486111111110.158867519075477462.743180852373
Geometric Mean73.5026607561408
Harmonic Mean73.4904495270504
Quadratic Mean73.5270478482427
Winsorized Mean ( 1 / 24 )73.51527777777780.158688626846363463.267464334119
Winsorized Mean ( 2 / 24 )73.51722222222220.15824129054622464.589374672402
Winsorized Mean ( 3 / 24 )73.51763888888890.157576706245423466.551437966894
Winsorized Mean ( 4 / 24 )73.51319444444450.156402587640152470.02543598308
Winsorized Mean ( 5 / 24 )73.50972222222220.155334710070445473.234360748383
Winsorized Mean ( 6 / 24 )73.50722222222220.15463575028728475.3572319833
Winsorized Mean ( 7 / 24 )73.50722222222220.15463575028728475.3572319833
Winsorized Mean ( 8 / 24 )73.4950.152648244988161481.466393574982
Winsorized Mean ( 9 / 24 )73.49750.15099782227492486.745430448552
Winsorized Mean ( 10 / 24 )73.47250.14586994845507503.684965807954
Winsorized Mean ( 11 / 24 )73.48472222222220.142893879802682514.260808956234
Winsorized Mean ( 12 / 24 )73.48472222222220.142893879802682514.260808956234
Winsorized Mean ( 13 / 24 )73.49194444444440.141722805624749518.561173838421
Winsorized Mean ( 14 / 24 )73.48805555555560.138786045648334529.506084075374
Winsorized Mean ( 15 / 24 )73.49430555555560.134654956143332545.797255893984
Winsorized Mean ( 16 / 24 )73.50319444444440.12866304611731571.284425968176
Winsorized Mean ( 17 / 24 )73.49138888888890.125653270346652584.874461970954
Winsorized Mean ( 18 / 24 )73.49138888888890.125653270346652584.874461970954
Winsorized Mean ( 19 / 24 )73.47555555555560.123511463941277594.888548892021
Winsorized Mean ( 20 / 24 )73.51166666666670.117999761279300622.981486315618
Winsorized Mean ( 21 / 24 )73.61083333333330.103614404576202710.430500801628
Winsorized Mean ( 22 / 24 )73.61388888888890.0930319908032456791.275003934675
Winsorized Mean ( 23 / 24 )73.62666666666670.0913132324270442806.30884166204
Winsorized Mean ( 24 / 24 )73.62666666666670.0913132324270442806.30884166204
Trimmed Mean ( 1 / 24 )73.51485714285710.157781690370051465.927681281903
Trimmed Mean ( 2 / 24 )73.51441176470590.156618315834471469.385789095081
Trimmed Mean ( 3 / 24 )73.51287878787880.155422390882019472.987697401221
Trimmed Mean ( 4 / 24 )73.511093750.154191779998874476.751054761394
Trimmed Mean ( 5 / 24 )73.51048387096770.153027170922961480.375370122836
Trimmed Mean ( 6 / 24 )73.51066666666670.151832286798628484.157014404731
Trimmed Mean ( 7 / 24 )73.51137931034480.150453729630010488.597919713396
Trimmed Mean ( 8 / 24 )73.51214285714290.148655820187760494.51237606636
Trimmed Mean ( 9 / 24 )73.5150.146802336241376500.775409180989
Trimmed Mean ( 10 / 24 )73.51769230769230.144766055459557507.837918732483
Trimmed Mean ( 11 / 24 )73.52420.143202750515142513.427289179237
Trimmed Mean ( 12 / 24 )73.52958333333330.141717228669951518.847172100565
Trimmed Mean ( 13 / 24 )73.53543478260870.139655790286527526.547697247199
Trimmed Mean ( 14 / 24 )73.54090909090910.137110709030504536.361525740107
Trimmed Mean ( 15 / 24 )73.5473809523810.134301677991170547.628161110665
Trimmed Mean ( 16 / 24 )73.553750.131402048680513559.761059577058
Trimmed Mean ( 17 / 24 )73.55973684210530.128779414235671571.207263821592
Trimmed Mean ( 18 / 24 )73.56777777777780.125732842946521585.111861417698
Trimmed Mean ( 19 / 24 )73.57676470588240.121324920318284606.443956549576
Trimmed Mean ( 20 / 24 )73.588750.115514932354108637.049674014572
Trimmed Mean ( 21 / 24 )73.5980.108891383191386675.884517608202
Trimmed Mean ( 22 / 24 )73.59642857142860.104102633379968706.960296602742
Trimmed Mean ( 23 / 24 )73.59423076923080.100408662018194732.947031560834
Trimmed Mean ( 24 / 24 )73.590.0949942790039393774.678230853758
Median73.65
Midrange73.515
Midmean - Weighted Average at Xnp73.5597368421053
Midmean - Weighted Average at X(n+1)p73.5597368421053
Midmean - Empirical Distribution Function73.5597368421053
Midmean - Empirical Distribution Function - Averaging73.5597368421053
Midmean - Empirical Distribution Function - Interpolation73.5597368421053
Midmean - Closest Observation73.5597368421053
Midmean - True Basic - Statistics Graphics Toolkit73.5597368421053
Midmean - MS Excel (old versions)73.5597368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 73.5148611111111 & 0.158867519075477 & 462.743180852373 \tabularnewline
Geometric Mean & 73.5026607561408 &  &  \tabularnewline
Harmonic Mean & 73.4904495270504 &  &  \tabularnewline
Quadratic Mean & 73.5270478482427 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 73.5152777777778 & 0.158688626846363 & 463.267464334119 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 73.5172222222222 & 0.15824129054622 & 464.589374672402 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 73.5176388888889 & 0.157576706245423 & 466.551437966894 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 73.5131944444445 & 0.156402587640152 & 470.02543598308 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 73.5097222222222 & 0.155334710070445 & 473.234360748383 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 73.5072222222222 & 0.15463575028728 & 475.3572319833 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 73.5072222222222 & 0.15463575028728 & 475.3572319833 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 73.495 & 0.152648244988161 & 481.466393574982 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 73.4975 & 0.15099782227492 & 486.745430448552 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 73.4725 & 0.14586994845507 & 503.684965807954 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 73.4847222222222 & 0.142893879802682 & 514.260808956234 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 73.4847222222222 & 0.142893879802682 & 514.260808956234 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 73.4919444444444 & 0.141722805624749 & 518.561173838421 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 73.4880555555556 & 0.138786045648334 & 529.506084075374 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 73.4943055555556 & 0.134654956143332 & 545.797255893984 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 73.5031944444444 & 0.12866304611731 & 571.284425968176 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 73.4913888888889 & 0.125653270346652 & 584.874461970954 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 73.4913888888889 & 0.125653270346652 & 584.874461970954 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 73.4755555555556 & 0.123511463941277 & 594.888548892021 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 73.5116666666667 & 0.117999761279300 & 622.981486315618 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 73.6108333333333 & 0.103614404576202 & 710.430500801628 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 73.6138888888889 & 0.0930319908032456 & 791.275003934675 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 73.6266666666667 & 0.0913132324270442 & 806.30884166204 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 73.6266666666667 & 0.0913132324270442 & 806.30884166204 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 73.5148571428571 & 0.157781690370051 & 465.927681281903 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 73.5144117647059 & 0.156618315834471 & 469.385789095081 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 73.5128787878788 & 0.155422390882019 & 472.987697401221 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 73.51109375 & 0.154191779998874 & 476.751054761394 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 73.5104838709677 & 0.153027170922961 & 480.375370122836 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 73.5106666666667 & 0.151832286798628 & 484.157014404731 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 73.5113793103448 & 0.150453729630010 & 488.597919713396 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 73.5121428571429 & 0.148655820187760 & 494.51237606636 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 73.515 & 0.146802336241376 & 500.775409180989 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 73.5176923076923 & 0.144766055459557 & 507.837918732483 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 73.5242 & 0.143202750515142 & 513.427289179237 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 73.5295833333333 & 0.141717228669951 & 518.847172100565 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 73.5354347826087 & 0.139655790286527 & 526.547697247199 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 73.5409090909091 & 0.137110709030504 & 536.361525740107 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 73.547380952381 & 0.134301677991170 & 547.628161110665 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 73.55375 & 0.131402048680513 & 559.761059577058 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 73.5597368421053 & 0.128779414235671 & 571.207263821592 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 73.5677777777778 & 0.125732842946521 & 585.111861417698 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 73.5767647058824 & 0.121324920318284 & 606.443956549576 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 73.58875 & 0.115514932354108 & 637.049674014572 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 73.598 & 0.108891383191386 & 675.884517608202 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 73.5964285714286 & 0.104102633379968 & 706.960296602742 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 73.5942307692308 & 0.100408662018194 & 732.947031560834 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 73.59 & 0.0949942790039393 & 774.678230853758 \tabularnewline
Median & 73.65 &  &  \tabularnewline
Midrange & 73.515 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 73.5597368421053 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 73.5597368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 73.5597368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 73.5597368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 73.5597368421053 &  &  \tabularnewline
Midmean - Closest Observation & 73.5597368421053 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 73.5597368421053 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 73.5597368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10427&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]73.5148611111111[/C][C]0.158867519075477[/C][C]462.743180852373[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]73.5026607561408[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]73.4904495270504[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]73.5270478482427[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]73.5152777777778[/C][C]0.158688626846363[/C][C]463.267464334119[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]73.5172222222222[/C][C]0.15824129054622[/C][C]464.589374672402[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]73.5176388888889[/C][C]0.157576706245423[/C][C]466.551437966894[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]73.5131944444445[/C][C]0.156402587640152[/C][C]470.02543598308[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]73.5097222222222[/C][C]0.155334710070445[/C][C]473.234360748383[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]73.5072222222222[/C][C]0.15463575028728[/C][C]475.3572319833[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]73.5072222222222[/C][C]0.15463575028728[/C][C]475.3572319833[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]73.495[/C][C]0.152648244988161[/C][C]481.466393574982[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]73.4975[/C][C]0.15099782227492[/C][C]486.745430448552[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]73.4725[/C][C]0.14586994845507[/C][C]503.684965807954[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]73.4847222222222[/C][C]0.142893879802682[/C][C]514.260808956234[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]73.4847222222222[/C][C]0.142893879802682[/C][C]514.260808956234[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]73.4919444444444[/C][C]0.141722805624749[/C][C]518.561173838421[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]73.4880555555556[/C][C]0.138786045648334[/C][C]529.506084075374[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]73.4943055555556[/C][C]0.134654956143332[/C][C]545.797255893984[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]73.5031944444444[/C][C]0.12866304611731[/C][C]571.284425968176[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]73.4913888888889[/C][C]0.125653270346652[/C][C]584.874461970954[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]73.4913888888889[/C][C]0.125653270346652[/C][C]584.874461970954[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]73.4755555555556[/C][C]0.123511463941277[/C][C]594.888548892021[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]73.5116666666667[/C][C]0.117999761279300[/C][C]622.981486315618[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]73.6108333333333[/C][C]0.103614404576202[/C][C]710.430500801628[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]73.6138888888889[/C][C]0.0930319908032456[/C][C]791.275003934675[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]73.6266666666667[/C][C]0.0913132324270442[/C][C]806.30884166204[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]73.6266666666667[/C][C]0.0913132324270442[/C][C]806.30884166204[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]73.5148571428571[/C][C]0.157781690370051[/C][C]465.927681281903[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]73.5144117647059[/C][C]0.156618315834471[/C][C]469.385789095081[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]73.5128787878788[/C][C]0.155422390882019[/C][C]472.987697401221[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]73.51109375[/C][C]0.154191779998874[/C][C]476.751054761394[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]73.5104838709677[/C][C]0.153027170922961[/C][C]480.375370122836[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]73.5106666666667[/C][C]0.151832286798628[/C][C]484.157014404731[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]73.5113793103448[/C][C]0.150453729630010[/C][C]488.597919713396[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]73.5121428571429[/C][C]0.148655820187760[/C][C]494.51237606636[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]73.515[/C][C]0.146802336241376[/C][C]500.775409180989[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]73.5176923076923[/C][C]0.144766055459557[/C][C]507.837918732483[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]73.5242[/C][C]0.143202750515142[/C][C]513.427289179237[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]73.5295833333333[/C][C]0.141717228669951[/C][C]518.847172100565[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]73.5354347826087[/C][C]0.139655790286527[/C][C]526.547697247199[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]73.5409090909091[/C][C]0.137110709030504[/C][C]536.361525740107[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]73.547380952381[/C][C]0.134301677991170[/C][C]547.628161110665[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]73.55375[/C][C]0.131402048680513[/C][C]559.761059577058[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]73.5597368421053[/C][C]0.128779414235671[/C][C]571.207263821592[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]73.5677777777778[/C][C]0.125732842946521[/C][C]585.111861417698[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]73.5767647058824[/C][C]0.121324920318284[/C][C]606.443956549576[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]73.58875[/C][C]0.115514932354108[/C][C]637.049674014572[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]73.598[/C][C]0.108891383191386[/C][C]675.884517608202[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]73.5964285714286[/C][C]0.104102633379968[/C][C]706.960296602742[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]73.5942307692308[/C][C]0.100408662018194[/C][C]732.947031560834[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]73.59[/C][C]0.0949942790039393[/C][C]774.678230853758[/C][/ROW]
[ROW][C]Median[/C][C]73.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]73.515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]73.5597368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]73.5597368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]73.5597368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]73.5597368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]73.5597368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]73.5597368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]73.5597368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]73.5597368421053[/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=10427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10427&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 Mean73.51486111111110.158867519075477462.743180852373
Geometric Mean73.5026607561408
Harmonic Mean73.4904495270504
Quadratic Mean73.5270478482427
Winsorized Mean ( 1 / 24 )73.51527777777780.158688626846363463.267464334119
Winsorized Mean ( 2 / 24 )73.51722222222220.15824129054622464.589374672402
Winsorized Mean ( 3 / 24 )73.51763888888890.157576706245423466.551437966894
Winsorized Mean ( 4 / 24 )73.51319444444450.156402587640152470.02543598308
Winsorized Mean ( 5 / 24 )73.50972222222220.155334710070445473.234360748383
Winsorized Mean ( 6 / 24 )73.50722222222220.15463575028728475.3572319833
Winsorized Mean ( 7 / 24 )73.50722222222220.15463575028728475.3572319833
Winsorized Mean ( 8 / 24 )73.4950.152648244988161481.466393574982
Winsorized Mean ( 9 / 24 )73.49750.15099782227492486.745430448552
Winsorized Mean ( 10 / 24 )73.47250.14586994845507503.684965807954
Winsorized Mean ( 11 / 24 )73.48472222222220.142893879802682514.260808956234
Winsorized Mean ( 12 / 24 )73.48472222222220.142893879802682514.260808956234
Winsorized Mean ( 13 / 24 )73.49194444444440.141722805624749518.561173838421
Winsorized Mean ( 14 / 24 )73.48805555555560.138786045648334529.506084075374
Winsorized Mean ( 15 / 24 )73.49430555555560.134654956143332545.797255893984
Winsorized Mean ( 16 / 24 )73.50319444444440.12866304611731571.284425968176
Winsorized Mean ( 17 / 24 )73.49138888888890.125653270346652584.874461970954
Winsorized Mean ( 18 / 24 )73.49138888888890.125653270346652584.874461970954
Winsorized Mean ( 19 / 24 )73.47555555555560.123511463941277594.888548892021
Winsorized Mean ( 20 / 24 )73.51166666666670.117999761279300622.981486315618
Winsorized Mean ( 21 / 24 )73.61083333333330.103614404576202710.430500801628
Winsorized Mean ( 22 / 24 )73.61388888888890.0930319908032456791.275003934675
Winsorized Mean ( 23 / 24 )73.62666666666670.0913132324270442806.30884166204
Winsorized Mean ( 24 / 24 )73.62666666666670.0913132324270442806.30884166204
Trimmed Mean ( 1 / 24 )73.51485714285710.157781690370051465.927681281903
Trimmed Mean ( 2 / 24 )73.51441176470590.156618315834471469.385789095081
Trimmed Mean ( 3 / 24 )73.51287878787880.155422390882019472.987697401221
Trimmed Mean ( 4 / 24 )73.511093750.154191779998874476.751054761394
Trimmed Mean ( 5 / 24 )73.51048387096770.153027170922961480.375370122836
Trimmed Mean ( 6 / 24 )73.51066666666670.151832286798628484.157014404731
Trimmed Mean ( 7 / 24 )73.51137931034480.150453729630010488.597919713396
Trimmed Mean ( 8 / 24 )73.51214285714290.148655820187760494.51237606636
Trimmed Mean ( 9 / 24 )73.5150.146802336241376500.775409180989
Trimmed Mean ( 10 / 24 )73.51769230769230.144766055459557507.837918732483
Trimmed Mean ( 11 / 24 )73.52420.143202750515142513.427289179237
Trimmed Mean ( 12 / 24 )73.52958333333330.141717228669951518.847172100565
Trimmed Mean ( 13 / 24 )73.53543478260870.139655790286527526.547697247199
Trimmed Mean ( 14 / 24 )73.54090909090910.137110709030504536.361525740107
Trimmed Mean ( 15 / 24 )73.5473809523810.134301677991170547.628161110665
Trimmed Mean ( 16 / 24 )73.553750.131402048680513559.761059577058
Trimmed Mean ( 17 / 24 )73.55973684210530.128779414235671571.207263821592
Trimmed Mean ( 18 / 24 )73.56777777777780.125732842946521585.111861417698
Trimmed Mean ( 19 / 24 )73.57676470588240.121324920318284606.443956549576
Trimmed Mean ( 20 / 24 )73.588750.115514932354108637.049674014572
Trimmed Mean ( 21 / 24 )73.5980.108891383191386675.884517608202
Trimmed Mean ( 22 / 24 )73.59642857142860.104102633379968706.960296602742
Trimmed Mean ( 23 / 24 )73.59423076923080.100408662018194732.947031560834
Trimmed Mean ( 24 / 24 )73.590.0949942790039393774.678230853758
Median73.65
Midrange73.515
Midmean - Weighted Average at Xnp73.5597368421053
Midmean - Weighted Average at X(n+1)p73.5597368421053
Midmean - Empirical Distribution Function73.5597368421053
Midmean - Empirical Distribution Function - Averaging73.5597368421053
Midmean - Empirical Distribution Function - Interpolation73.5597368421053
Midmean - Closest Observation73.5597368421053
Midmean - True Basic - Statistics Graphics Toolkit73.5597368421053
Midmean - MS Excel (old versions)73.5597368421053
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')