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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 21 Apr 2008 11:22:27 -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/21/t1208798600gakzjhd0xd1w2ap.htm/, Retrieved Thu, 16 May 2024 13:15:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10551, Retrieved Thu, 16 May 2024 13:15:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact211
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [Maximuprijzen Stu...] [-0001-11-30 00:00:00] [54b77ee6776d034ae64561dfe3b58da8]
- RM D    [Central Tendency] [Centrummaten prij...] [2008-04-21 17:22:27] [f12139c84a7390b2232de02c02cfb50d] [Current]
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Dataseries X:
11.98
11.79
11.66
11.96
11.83
12.36
12.53
12.55
12.53
12.24
12.34
12.05
12.22
12.23
11.92
12.13
12.1
12.15
12.23
12.08
12.02
11.93
12.16
11.87
11.93
11.79
11.43
11.63
11.93
11.89
11.83
11.59
12.04
11.81
11.9
11.72
11.91
11.94
11.91
11.84
12.01
11.89
11.8
11.7
11.5
11.76
11.61
11.27
11.64
11.39
11.54
11.62
11.59
11.44
11.31
11.56
11.4
11.51
11.5
11.24
11.8
11.87
11.86
12.11
11.92
12.61
13.34
13.31
13.47
13.24
13.18
13.3




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10551&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10551&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11.98944444444440.0590813505394759202.931116756269
Geometric Mean11.9794592783188
Harmonic Mean11.9698081265545
Quadratic Mean11.9997754608622
Winsorized Mean ( 1 / 24 )11.98805555555560.0583948833190362205.292910511691
Winsorized Mean ( 2 / 24 )11.98833333333330.0579372873413637206.919134178627
Winsorized Mean ( 3 / 24 )11.991250.0572819187183013209.337436110862
Winsorized Mean ( 4 / 24 )11.98847222222220.0561400759426589213.545707249616
Winsorized Mean ( 5 / 24 )11.98638888888890.0545400835912082219.772103371347
Winsorized Mean ( 6 / 24 )11.93972222222220.0414156628486726288.290018823274
Winsorized Mean ( 7 / 24 )11.93972222222220.0391517913127579304.959794223555
Winsorized Mean ( 8 / 24 )11.93750.0386680376557983308.717502198097
Winsorized Mean ( 9 / 24 )11.938750.0384703295523777310.336566879296
Winsorized Mean ( 10 / 24 )11.91930555555560.0330056228842194361.129544422396
Winsorized Mean ( 11 / 24 )11.91930555555560.0319454778018886373.114017247565
Winsorized Mean ( 12 / 24 )11.90763888888890.0282146735480936422.037096002249
Winsorized Mean ( 13 / 24 )11.90583333333330.0279172359972778426.468914562111
Winsorized Mean ( 14 / 24 )11.90972222222220.0273067059571049436.146426483325
Winsorized Mean ( 15 / 24 )11.90972222222220.0266431617523533447.008592032824
Winsorized Mean ( 16 / 24 )11.89861111111110.024187343878462491.9354175845
Winsorized Mean ( 17 / 24 )11.89861111111110.0234615070781932507.154594607034
Winsorized Mean ( 18 / 24 )11.89861111111110.0219414728282553542.288624115906
Winsorized Mean ( 19 / 24 )11.90388888888890.0195734597580415608.164782110037
Winsorized Mean ( 20 / 24 )11.90666666666670.0183557268272123648.662228346909
Winsorized Mean ( 21 / 24 )11.91250.0158604906708226751.080168151078
Winsorized Mean ( 22 / 24 )11.91250.0132918221178012896.22776278702
Winsorized Mean ( 23 / 24 )11.90930555555560.0128298824530604928.247441013365
Winsorized Mean ( 24 / 24 )11.90597222222220.01144774431284171040.02779035400
Trimmed Mean ( 1 / 24 )11.9790.0558811034480108214.365845712848
Trimmed Mean ( 2 / 24 )11.96941176470590.0528415069982861226.515336988669
Trimmed Mean ( 3 / 24 )11.95909090909090.0494311356221129241.934375137865
Trimmed Mean ( 4 / 24 )11.947031250.0455105951423764262.510987004776
Trimmed Mean ( 5 / 24 )11.9350.0410438557672811290.786520342327
Trimmed Mean ( 6 / 24 )11.92266666666670.0358786928780374332.304933939356
Trimmed Mean ( 7 / 24 )11.91913793103450.034129290919304349.234853991439
Trimmed Mean ( 8 / 24 )11.91535714285710.0326153938295519365.329243152078
Trimmed Mean ( 9 / 24 )11.91166666666670.0308586076932045386.007910178325
Trimmed Mean ( 10 / 24 )11.90750.0286760064935181415.242617645926
Trimmed Mean ( 11 / 24 )11.90580.0274108424845769434.346372487419
Trimmed Mean ( 12 / 24 )11.90395833333330.026063784933261456.72408530897
Trimmed Mean ( 13 / 24 )11.90347826086960.0252623287762330471.194812097785
Trimmed Mean ( 14 / 24 )11.90318181818180.0242885506381240490.073779844989
Trimmed Mean ( 15 / 24 )11.90238095238100.0231563125546297514.001567576926
Trimmed Mean ( 16 / 24 )11.90150.0218196277201549545.449269466981
Trimmed Mean ( 17 / 24 )11.90184210526320.0206950879719694575.104687710615
Trimmed Mean ( 18 / 24 )11.90222222222220.0193551236443345614.939095246035
Trimmed Mean ( 19 / 24 )11.90264705882350.0179487725364923663.145462154798
Trimmed Mean ( 20 / 24 )11.90250.0167223532068364711.771833352617
Trimmed Mean ( 21 / 24 )11.9020.0153533103248464775.207414438754
Trimmed Mean ( 22 / 24 )11.90071428571430.0142346972640107836.035643399498
Trimmed Mean ( 23 / 24 )11.89923076923080.0135069563493218880.970550395555
Trimmed Mean ( 24 / 24 )11.89791666666670.0125394907592938948.83571391034
Median11.905
Midrange12.355
Midmean - Weighted Average at Xnp11.8951351351351
Midmean - Weighted Average at X(n+1)p11.9022222222222
Midmean - Empirical Distribution Function11.8951351351351
Midmean - Empirical Distribution Function - Averaging11.9022222222222
Midmean - Empirical Distribution Function - Interpolation11.9022222222222
Midmean - Closest Observation11.8951351351351
Midmean - True Basic - Statistics Graphics Toolkit11.9022222222222
Midmean - MS Excel (old versions)11.9018421052632
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11.9894444444444 & 0.0590813505394759 & 202.931116756269 \tabularnewline
Geometric Mean & 11.9794592783188 &  &  \tabularnewline
Harmonic Mean & 11.9698081265545 &  &  \tabularnewline
Quadratic Mean & 11.9997754608622 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 11.9880555555556 & 0.0583948833190362 & 205.292910511691 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 11.9883333333333 & 0.0579372873413637 & 206.919134178627 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 11.99125 & 0.0572819187183013 & 209.337436110862 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 11.9884722222222 & 0.0561400759426589 & 213.545707249616 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 11.9863888888889 & 0.0545400835912082 & 219.772103371347 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 11.9397222222222 & 0.0414156628486726 & 288.290018823274 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 11.9397222222222 & 0.0391517913127579 & 304.959794223555 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 11.9375 & 0.0386680376557983 & 308.717502198097 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 11.93875 & 0.0384703295523777 & 310.336566879296 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 11.9193055555556 & 0.0330056228842194 & 361.129544422396 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 11.9193055555556 & 0.0319454778018886 & 373.114017247565 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 11.9076388888889 & 0.0282146735480936 & 422.037096002249 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 11.9058333333333 & 0.0279172359972778 & 426.468914562111 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 11.9097222222222 & 0.0273067059571049 & 436.146426483325 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 11.9097222222222 & 0.0266431617523533 & 447.008592032824 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 11.8986111111111 & 0.024187343878462 & 491.9354175845 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 11.8986111111111 & 0.0234615070781932 & 507.154594607034 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 11.8986111111111 & 0.0219414728282553 & 542.288624115906 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 11.9038888888889 & 0.0195734597580415 & 608.164782110037 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 11.9066666666667 & 0.0183557268272123 & 648.662228346909 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 11.9125 & 0.0158604906708226 & 751.080168151078 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 11.9125 & 0.0132918221178012 & 896.22776278702 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 11.9093055555556 & 0.0128298824530604 & 928.247441013365 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 11.9059722222222 & 0.0114477443128417 & 1040.02779035400 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 11.979 & 0.0558811034480108 & 214.365845712848 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 11.9694117647059 & 0.0528415069982861 & 226.515336988669 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 11.9590909090909 & 0.0494311356221129 & 241.934375137865 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 11.94703125 & 0.0455105951423764 & 262.510987004776 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 11.935 & 0.0410438557672811 & 290.786520342327 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 11.9226666666667 & 0.0358786928780374 & 332.304933939356 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 11.9191379310345 & 0.034129290919304 & 349.234853991439 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 11.9153571428571 & 0.0326153938295519 & 365.329243152078 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 11.9116666666667 & 0.0308586076932045 & 386.007910178325 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 11.9075 & 0.0286760064935181 & 415.242617645926 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 11.9058 & 0.0274108424845769 & 434.346372487419 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 11.9039583333333 & 0.026063784933261 & 456.72408530897 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 11.9034782608696 & 0.0252623287762330 & 471.194812097785 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 11.9031818181818 & 0.0242885506381240 & 490.073779844989 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 11.9023809523810 & 0.0231563125546297 & 514.001567576926 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 11.9015 & 0.0218196277201549 & 545.449269466981 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 11.9018421052632 & 0.0206950879719694 & 575.104687710615 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 11.9022222222222 & 0.0193551236443345 & 614.939095246035 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 11.9026470588235 & 0.0179487725364923 & 663.145462154798 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 11.9025 & 0.0167223532068364 & 711.771833352617 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 11.902 & 0.0153533103248464 & 775.207414438754 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 11.9007142857143 & 0.0142346972640107 & 836.035643399498 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 11.8992307692308 & 0.0135069563493218 & 880.970550395555 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 11.8979166666667 & 0.0125394907592938 & 948.83571391034 \tabularnewline
Median & 11.905 &  &  \tabularnewline
Midrange & 12.355 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.8951351351351 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.9022222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.8951351351351 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.9022222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.9022222222222 &  &  \tabularnewline
Midmean - Closest Observation & 11.8951351351351 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.9022222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.9018421052632 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10551&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]11.9894444444444[/C][C]0.0590813505394759[/C][C]202.931116756269[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]11.9794592783188[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11.9698081265545[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11.9997754608622[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]11.9880555555556[/C][C]0.0583948833190362[/C][C]205.292910511691[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]11.9883333333333[/C][C]0.0579372873413637[/C][C]206.919134178627[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]11.99125[/C][C]0.0572819187183013[/C][C]209.337436110862[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]11.9884722222222[/C][C]0.0561400759426589[/C][C]213.545707249616[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]11.9863888888889[/C][C]0.0545400835912082[/C][C]219.772103371347[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]11.9397222222222[/C][C]0.0414156628486726[/C][C]288.290018823274[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]11.9397222222222[/C][C]0.0391517913127579[/C][C]304.959794223555[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]11.9375[/C][C]0.0386680376557983[/C][C]308.717502198097[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]11.93875[/C][C]0.0384703295523777[/C][C]310.336566879296[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]11.9193055555556[/C][C]0.0330056228842194[/C][C]361.129544422396[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]11.9193055555556[/C][C]0.0319454778018886[/C][C]373.114017247565[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]11.9076388888889[/C][C]0.0282146735480936[/C][C]422.037096002249[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]11.9058333333333[/C][C]0.0279172359972778[/C][C]426.468914562111[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]11.9097222222222[/C][C]0.0273067059571049[/C][C]436.146426483325[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]11.9097222222222[/C][C]0.0266431617523533[/C][C]447.008592032824[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]11.8986111111111[/C][C]0.024187343878462[/C][C]491.9354175845[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]11.8986111111111[/C][C]0.0234615070781932[/C][C]507.154594607034[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]11.8986111111111[/C][C]0.0219414728282553[/C][C]542.288624115906[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]11.9038888888889[/C][C]0.0195734597580415[/C][C]608.164782110037[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]11.9066666666667[/C][C]0.0183557268272123[/C][C]648.662228346909[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]11.9125[/C][C]0.0158604906708226[/C][C]751.080168151078[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]11.9125[/C][C]0.0132918221178012[/C][C]896.22776278702[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]11.9093055555556[/C][C]0.0128298824530604[/C][C]928.247441013365[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]11.9059722222222[/C][C]0.0114477443128417[/C][C]1040.02779035400[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]11.979[/C][C]0.0558811034480108[/C][C]214.365845712848[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]11.9694117647059[/C][C]0.0528415069982861[/C][C]226.515336988669[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]11.9590909090909[/C][C]0.0494311356221129[/C][C]241.934375137865[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]11.94703125[/C][C]0.0455105951423764[/C][C]262.510987004776[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]11.935[/C][C]0.0410438557672811[/C][C]290.786520342327[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]11.9226666666667[/C][C]0.0358786928780374[/C][C]332.304933939356[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]11.9191379310345[/C][C]0.034129290919304[/C][C]349.234853991439[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]11.9153571428571[/C][C]0.0326153938295519[/C][C]365.329243152078[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]11.9116666666667[/C][C]0.0308586076932045[/C][C]386.007910178325[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]11.9075[/C][C]0.0286760064935181[/C][C]415.242617645926[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]11.9058[/C][C]0.0274108424845769[/C][C]434.346372487419[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]11.9039583333333[/C][C]0.026063784933261[/C][C]456.72408530897[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]11.9034782608696[/C][C]0.0252623287762330[/C][C]471.194812097785[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]11.9031818181818[/C][C]0.0242885506381240[/C][C]490.073779844989[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]11.9023809523810[/C][C]0.0231563125546297[/C][C]514.001567576926[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]11.9015[/C][C]0.0218196277201549[/C][C]545.449269466981[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]11.9018421052632[/C][C]0.0206950879719694[/C][C]575.104687710615[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]11.9022222222222[/C][C]0.0193551236443345[/C][C]614.939095246035[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]11.9026470588235[/C][C]0.0179487725364923[/C][C]663.145462154798[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]11.9025[/C][C]0.0167223532068364[/C][C]711.771833352617[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]11.902[/C][C]0.0153533103248464[/C][C]775.207414438754[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]11.9007142857143[/C][C]0.0142346972640107[/C][C]836.035643399498[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]11.8992307692308[/C][C]0.0135069563493218[/C][C]880.970550395555[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]11.8979166666667[/C][C]0.0125394907592938[/C][C]948.83571391034[/C][/ROW]
[ROW][C]Median[/C][C]11.905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]12.355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.8951351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.9022222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.8951351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.9022222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.9022222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.8951351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.9022222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.9018421052632[/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=10551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10551&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 Mean11.98944444444440.0590813505394759202.931116756269
Geometric Mean11.9794592783188
Harmonic Mean11.9698081265545
Quadratic Mean11.9997754608622
Winsorized Mean ( 1 / 24 )11.98805555555560.0583948833190362205.292910511691
Winsorized Mean ( 2 / 24 )11.98833333333330.0579372873413637206.919134178627
Winsorized Mean ( 3 / 24 )11.991250.0572819187183013209.337436110862
Winsorized Mean ( 4 / 24 )11.98847222222220.0561400759426589213.545707249616
Winsorized Mean ( 5 / 24 )11.98638888888890.0545400835912082219.772103371347
Winsorized Mean ( 6 / 24 )11.93972222222220.0414156628486726288.290018823274
Winsorized Mean ( 7 / 24 )11.93972222222220.0391517913127579304.959794223555
Winsorized Mean ( 8 / 24 )11.93750.0386680376557983308.717502198097
Winsorized Mean ( 9 / 24 )11.938750.0384703295523777310.336566879296
Winsorized Mean ( 10 / 24 )11.91930555555560.0330056228842194361.129544422396
Winsorized Mean ( 11 / 24 )11.91930555555560.0319454778018886373.114017247565
Winsorized Mean ( 12 / 24 )11.90763888888890.0282146735480936422.037096002249
Winsorized Mean ( 13 / 24 )11.90583333333330.0279172359972778426.468914562111
Winsorized Mean ( 14 / 24 )11.90972222222220.0273067059571049436.146426483325
Winsorized Mean ( 15 / 24 )11.90972222222220.0266431617523533447.008592032824
Winsorized Mean ( 16 / 24 )11.89861111111110.024187343878462491.9354175845
Winsorized Mean ( 17 / 24 )11.89861111111110.0234615070781932507.154594607034
Winsorized Mean ( 18 / 24 )11.89861111111110.0219414728282553542.288624115906
Winsorized Mean ( 19 / 24 )11.90388888888890.0195734597580415608.164782110037
Winsorized Mean ( 20 / 24 )11.90666666666670.0183557268272123648.662228346909
Winsorized Mean ( 21 / 24 )11.91250.0158604906708226751.080168151078
Winsorized Mean ( 22 / 24 )11.91250.0132918221178012896.22776278702
Winsorized Mean ( 23 / 24 )11.90930555555560.0128298824530604928.247441013365
Winsorized Mean ( 24 / 24 )11.90597222222220.01144774431284171040.02779035400
Trimmed Mean ( 1 / 24 )11.9790.0558811034480108214.365845712848
Trimmed Mean ( 2 / 24 )11.96941176470590.0528415069982861226.515336988669
Trimmed Mean ( 3 / 24 )11.95909090909090.0494311356221129241.934375137865
Trimmed Mean ( 4 / 24 )11.947031250.0455105951423764262.510987004776
Trimmed Mean ( 5 / 24 )11.9350.0410438557672811290.786520342327
Trimmed Mean ( 6 / 24 )11.92266666666670.0358786928780374332.304933939356
Trimmed Mean ( 7 / 24 )11.91913793103450.034129290919304349.234853991439
Trimmed Mean ( 8 / 24 )11.91535714285710.0326153938295519365.329243152078
Trimmed Mean ( 9 / 24 )11.91166666666670.0308586076932045386.007910178325
Trimmed Mean ( 10 / 24 )11.90750.0286760064935181415.242617645926
Trimmed Mean ( 11 / 24 )11.90580.0274108424845769434.346372487419
Trimmed Mean ( 12 / 24 )11.90395833333330.026063784933261456.72408530897
Trimmed Mean ( 13 / 24 )11.90347826086960.0252623287762330471.194812097785
Trimmed Mean ( 14 / 24 )11.90318181818180.0242885506381240490.073779844989
Trimmed Mean ( 15 / 24 )11.90238095238100.0231563125546297514.001567576926
Trimmed Mean ( 16 / 24 )11.90150.0218196277201549545.449269466981
Trimmed Mean ( 17 / 24 )11.90184210526320.0206950879719694575.104687710615
Trimmed Mean ( 18 / 24 )11.90222222222220.0193551236443345614.939095246035
Trimmed Mean ( 19 / 24 )11.90264705882350.0179487725364923663.145462154798
Trimmed Mean ( 20 / 24 )11.90250.0167223532068364711.771833352617
Trimmed Mean ( 21 / 24 )11.9020.0153533103248464775.207414438754
Trimmed Mean ( 22 / 24 )11.90071428571430.0142346972640107836.035643399498
Trimmed Mean ( 23 / 24 )11.89923076923080.0135069563493218880.970550395555
Trimmed Mean ( 24 / 24 )11.89791666666670.0125394907592938948.83571391034
Median11.905
Midrange12.355
Midmean - Weighted Average at Xnp11.8951351351351
Midmean - Weighted Average at X(n+1)p11.9022222222222
Midmean - Empirical Distribution Function11.8951351351351
Midmean - Empirical Distribution Function - Averaging11.9022222222222
Midmean - Empirical Distribution Function - Interpolation11.9022222222222
Midmean - Closest Observation11.8951351351351
Midmean - True Basic - Statistics Graphics Toolkit11.9022222222222
Midmean - MS Excel (old versions)11.9018421052632
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')