Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 04:16:53 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t1228475934zyqsrzz2t43uhpz.htm/, Retrieved Thu, 16 May 2024 18:31:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29171, Retrieved Thu, 16 May 2024 18:31:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheidsgraa...] [2008-12-05 10:45:42] [e5d91604aae608e98a8ea24759233f66]
-   PD  [Univariate Data Series] [Inflatie op jaarb...] [2008-12-05 10:52:23] [e5d91604aae608e98a8ea24759233f66]
-   PD    [Univariate Data Series] [Investeringen vol...] [2008-12-05 10:58:14] [e5d91604aae608e98a8ea24759233f66]
- RMPD        [Central Tendency] [Central Tendency ...] [2008-12-05 11:16:53] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]
- RMP           [Univariate Explorative Data Analysis] [EDA Werkloosheids...] [2008-12-05 12:38:56] [e5d91604aae608e98a8ea24759233f66]
- RMP           [Tukey lambda PPCC Plot] [PPCC plot Werkloo...] [2008-12-05 12:48:59] [e5d91604aae608e98a8ea24759233f66]
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Dataseries X:
9.4
9.4
9.5
9.5
9.4
9.4
9.3
9.4
9.4
9.2
9.1
9.1
9.1
9.1
9
8.9
8.8
8.7
8.4
8.3
8.2
7.9
7.8
7.7
7.3
7.2
7.1
6.9
6.8
6.7
6.8
6.9
6.7
6.8
6.8
6.7
6.3
6.2
6.2
6.5
6.5
6.4
6.2
6.2
6.3
7.5
7.4
7.4
7.4
7.4
7.4
7.2
7.2
7.1
7.5
7.4
7.5
8
8.1
8.1
8.1
8.1
8.1
7.9
7.9
8
8.1
8.1
8.1
8.6
8.6
8.6
8.4
8.4
8.4
7.7
7.8
7.9
8.7
8.8
8.8
8.5
8.5
8.5
8.4
8.5
8.5
8.3
8.4
8.4
8.5
8.4
8.4
8.5
8.5
8.5
8.5
8.5
8.5
8.3
8.3
8.3
8.3
8.2
8.2
8.1
8
7.8
7.9
7.8
7.7
7.8
7.7
7.6
7.3
7.3
7.1
7.1
7.1
7




Summary of computational 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 computational 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=29171&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]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=29171&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29171&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.953333333333330.0776577037662611102.415252416834
Geometric Mean7.9069195954496
Harmonic Mean7.85922058628615
Quadratic Mean7.99832274084177
Winsorized Mean ( 1 / 40 )7.953333333333330.0776577037662611102.415252416834
Winsorized Mean ( 2 / 40 )7.951666666666670.077387157691292102.751760161382
Winsorized Mean ( 3 / 40 )7.951666666666670.077387157691292102.751760161382
Winsorized Mean ( 4 / 40 )7.9550.0767681401294546103.623716643199
Winsorized Mean ( 5 / 40 )7.9550.0767681401294546103.623716643199
Winsorized Mean ( 6 / 40 )7.960.0758832215006857104.898024129459
Winsorized Mean ( 7 / 40 )7.965833333333330.0748995203050289106.353596136429
Winsorized Mean ( 8 / 40 )7.959166666666670.073854424085829107.768312666239
Winsorized Mean ( 9 / 40 )7.966666666666670.07034661416953113.248757750694
Winsorized Mean ( 10 / 40 )7.958333333333330.0691543895823401115.080667784040
Winsorized Mean ( 11 / 40 )7.958333333333330.0691543895823401115.080667784040
Winsorized Mean ( 12 / 40 )7.968333333333330.0676639344841742117.763375631032
Winsorized Mean ( 13 / 40 )7.968333333333330.0676639344841742117.763375631032
Winsorized Mean ( 14 / 40 )7.956666666666670.0660694538781801120.428824511510
Winsorized Mean ( 15 / 40 )7.944166666666670.0644606565058217123.240548534426
Winsorized Mean ( 16 / 40 )7.944166666666670.0608851128392881130.477982156919
Winsorized Mean ( 17 / 40 )7.944166666666670.0608851128392881130.477982156919
Winsorized Mean ( 18 / 40 )7.959166666666670.0587747901489192135.418036312853
Winsorized Mean ( 19 / 40 )7.959166666666670.0547913771014065145.263125107004
Winsorized Mean ( 20 / 40 )7.959166666666670.0547913771014065145.263125107004
Winsorized Mean ( 21 / 40 )7.941666666666670.0528803857847781150.181708185509
Winsorized Mean ( 22 / 40 )7.941666666666670.0528803857847781150.181708185509
Winsorized Mean ( 23 / 40 )7.941666666666670.0528803857847781150.181708185509
Winsorized Mean ( 24 / 40 )7.941666666666670.0482259988538635164.676043117984
Winsorized Mean ( 25 / 40 )7.941666666666670.0482259988538635164.676043117984
Winsorized Mean ( 26 / 40 )7.941666666666670.0482259988538635164.676043117984
Winsorized Mean ( 27 / 40 )7.964166666666670.0453865414183923175.474191638654
Winsorized Mean ( 28 / 40 )7.964166666666670.0453865414183923175.474191638654
Winsorized Mean ( 29 / 40 )7.964166666666670.0453865414183923175.474191638654
Winsorized Mean ( 30 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 31 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 32 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 33 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 34 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 35 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 36 / 40 )7.989166666666670.0359503983166017222.227486780788
Winsorized Mean ( 37 / 40 )7.989166666666670.0359503983166017222.227486780788
Winsorized Mean ( 38 / 40 )7.989166666666670.0359503983166017222.227486780788
Winsorized Mean ( 39 / 40 )8.021666666666670.0323059458354216248.303105178594
Winsorized Mean ( 40 / 40 )8.0550.0287423111140923280.24886266194
Trimmed Mean ( 1 / 40 )7.955084745762710.0764316964786694104.080965257429
Trimmed Mean ( 2 / 40 )7.956896551724140.075073418716598105.988200454297
Trimmed Mean ( 3 / 40 )7.959649122807020.0737228294268992107.967222428698
Trimmed Mean ( 4 / 40 )7.96250.0722203143826154110.252912467475
Trimmed Mean ( 5 / 40 )7.964545454545450.0707470722333106112.577739306015
Trimmed Mean ( 6 / 40 )7.966666666666670.0691014374200228115.289449309751
Trimmed Mean ( 7 / 40 )7.967924528301890.0674732940389454118.090047948494
Trimmed Mean ( 8 / 40 )7.968269230769230.0658611086252313120.985956615322
Trimmed Mean ( 9 / 40 )7.969607843137260.0642564088009765124.0282174471
Trimmed Mean ( 10 / 40 )7.970.0630936453282585126.320169940005
Trimmed Mean ( 11 / 40 )7.971428571428570.0619821275557313128.608501930836
Trimmed Mean ( 12 / 40 )7.972916666666670.0607244128243781131.296727227734
Trimmed Mean ( 13 / 40 )7.973404255319150.0595332937754424133.931851400572
Trimmed Mean ( 14 / 40 )7.973913043478260.0581788756340028137.058562177126
Trimmed Mean ( 15 / 40 )7.975555555555560.0568703348332654140.241051489122
Trimmed Mean ( 16 / 40 )7.978409090909090.055601791382128143.491943201556
Trimmed Mean ( 17 / 40 )7.981395348837210.054647524400819146.052276591647
Trimmed Mean ( 18 / 40 )7.984523809523810.0535459236794202149.115437009308
Trimmed Mean ( 19 / 40 )7.986585365853660.0525691123969695151.925436852422
Trimmed Mean ( 20 / 40 )7.988750.0519552433362272153.762151556119
Trimmed Mean ( 21 / 40 )7.991025641025640.0512314518935702155.978902523131
Trimmed Mean ( 22 / 40 )7.994736842105260.050606661264682157.977954725986
Trimmed Mean ( 23 / 40 )7.998648648648650.0498607183811025160.419843683604
Trimmed Mean ( 24 / 40 )8.002777777777780.0489711127451534163.418336426709
Trimmed Mean ( 25 / 40 )8.007142857142860.048510801280493165.058969256042
Trimmed Mean ( 26 / 40 )8.011764705882350.047939520161847167.122338288621
Trimmed Mean ( 27 / 40 )8.016666666666670.0472351323821341169.718306319362
Trimmed Mean ( 28 / 40 )8.02031250.0467802448373632171.446569548396
Trimmed Mean ( 29 / 40 )8.02419354838710.0462035985805492173.670315622669
Trimmed Mean ( 30 / 40 )8.028333333333330.0454787258060472176.529425375102
Trimmed Mean ( 31 / 40 )8.031034482758620.0450318766274915178.341101553289
Trimmed Mean ( 32 / 40 )8.033928571428570.0444502337885753180.739849640419
Trimmed Mean ( 33 / 40 )8.037037037037040.0437015716828267183.907276730629
Trimmed Mean ( 34 / 40 )8.040384615384620.042743368972694188.108350105044
Trimmed Mean ( 35 / 40 )8.0440.0415181297994119193.746684613764
Trimmed Mean ( 36 / 40 )8.047916666666670.0399456172128479201.471831660125
Trimmed Mean ( 37 / 40 )8.052173913043480.0391626276591214205.608622157100
Trimmed Mean ( 38 / 40 )8.056818181818180.0381104613595716211.406996777138
Trimmed Mean ( 39 / 40 )8.061904761904760.0366976504535119219.684493755737
Trimmed Mean ( 40 / 40 )8.0650.0357250899408532225.75170596778
Median8.1
Midrange7.85
Midmean - Weighted Average at Xnp8.03768115942029
Midmean - Weighted Average at X(n+1)p8.07121212121212
Midmean - Empirical Distribution Function8.03768115942029
Midmean - Empirical Distribution Function - Averaging8.07121212121212
Midmean - Empirical Distribution Function - Interpolation8.07121212121212
Midmean - Closest Observation8.03768115942029
Midmean - True Basic - Statistics Graphics Toolkit8.07121212121212
Midmean - MS Excel (old versions)8.03768115942029
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.95333333333333 & 0.0776577037662611 & 102.415252416834 \tabularnewline
Geometric Mean & 7.9069195954496 &  &  \tabularnewline
Harmonic Mean & 7.85922058628615 &  &  \tabularnewline
Quadratic Mean & 7.99832274084177 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 7.95333333333333 & 0.0776577037662611 & 102.415252416834 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 7.95166666666667 & 0.077387157691292 & 102.751760161382 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 7.95166666666667 & 0.077387157691292 & 102.751760161382 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 7.955 & 0.0767681401294546 & 103.623716643199 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 7.955 & 0.0767681401294546 & 103.623716643199 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 7.96 & 0.0758832215006857 & 104.898024129459 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 7.96583333333333 & 0.0748995203050289 & 106.353596136429 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 7.95916666666667 & 0.073854424085829 & 107.768312666239 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 7.96666666666667 & 0.07034661416953 & 113.248757750694 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 7.95833333333333 & 0.0691543895823401 & 115.080667784040 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 7.95833333333333 & 0.0691543895823401 & 115.080667784040 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 7.96833333333333 & 0.0676639344841742 & 117.763375631032 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 7.96833333333333 & 0.0676639344841742 & 117.763375631032 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 7.95666666666667 & 0.0660694538781801 & 120.428824511510 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 7.94416666666667 & 0.0644606565058217 & 123.240548534426 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 7.94416666666667 & 0.0608851128392881 & 130.477982156919 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 7.94416666666667 & 0.0608851128392881 & 130.477982156919 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 7.95916666666667 & 0.0587747901489192 & 135.418036312853 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 7.95916666666667 & 0.0547913771014065 & 145.263125107004 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 7.95916666666667 & 0.0547913771014065 & 145.263125107004 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 7.94166666666667 & 0.0528803857847781 & 150.181708185509 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 7.94166666666667 & 0.0528803857847781 & 150.181708185509 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 7.94166666666667 & 0.0528803857847781 & 150.181708185509 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 7.94166666666667 & 0.0482259988538635 & 164.676043117984 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 7.94166666666667 & 0.0482259988538635 & 164.676043117984 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 7.94166666666667 & 0.0482259988538635 & 164.676043117984 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 7.96416666666667 & 0.0453865414183923 & 175.474191638654 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 7.96416666666667 & 0.0453865414183923 & 175.474191638654 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 7.96416666666667 & 0.0453865414183923 & 175.474191638654 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 7.98916666666667 & 0.042386705696416 & 188.482839970793 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 7.98916666666667 & 0.042386705696416 & 188.482839970793 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 7.98916666666667 & 0.042386705696416 & 188.482839970793 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 7.98916666666667 & 0.042386705696416 & 188.482839970793 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 7.98916666666667 & 0.042386705696416 & 188.482839970793 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 7.98916666666667 & 0.042386705696416 & 188.482839970793 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 7.98916666666667 & 0.0359503983166017 & 222.227486780788 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 7.98916666666667 & 0.0359503983166017 & 222.227486780788 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 7.98916666666667 & 0.0359503983166017 & 222.227486780788 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 8.02166666666667 & 0.0323059458354216 & 248.303105178594 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 8.055 & 0.0287423111140923 & 280.24886266194 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 7.95508474576271 & 0.0764316964786694 & 104.080965257429 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 7.95689655172414 & 0.075073418716598 & 105.988200454297 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 7.95964912280702 & 0.0737228294268992 & 107.967222428698 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 7.9625 & 0.0722203143826154 & 110.252912467475 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 7.96454545454545 & 0.0707470722333106 & 112.577739306015 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 7.96666666666667 & 0.0691014374200228 & 115.289449309751 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 7.96792452830189 & 0.0674732940389454 & 118.090047948494 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 7.96826923076923 & 0.0658611086252313 & 120.985956615322 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 7.96960784313726 & 0.0642564088009765 & 124.0282174471 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 7.97 & 0.0630936453282585 & 126.320169940005 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 7.97142857142857 & 0.0619821275557313 & 128.608501930836 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 7.97291666666667 & 0.0607244128243781 & 131.296727227734 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 7.97340425531915 & 0.0595332937754424 & 133.931851400572 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 7.97391304347826 & 0.0581788756340028 & 137.058562177126 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 7.97555555555556 & 0.0568703348332654 & 140.241051489122 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 7.97840909090909 & 0.055601791382128 & 143.491943201556 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 7.98139534883721 & 0.054647524400819 & 146.052276591647 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 7.98452380952381 & 0.0535459236794202 & 149.115437009308 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 7.98658536585366 & 0.0525691123969695 & 151.925436852422 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 7.98875 & 0.0519552433362272 & 153.762151556119 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 7.99102564102564 & 0.0512314518935702 & 155.978902523131 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 7.99473684210526 & 0.050606661264682 & 157.977954725986 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 7.99864864864865 & 0.0498607183811025 & 160.419843683604 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 8.00277777777778 & 0.0489711127451534 & 163.418336426709 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 8.00714285714286 & 0.048510801280493 & 165.058969256042 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 8.01176470588235 & 0.047939520161847 & 167.122338288621 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 8.01666666666667 & 0.0472351323821341 & 169.718306319362 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 8.0203125 & 0.0467802448373632 & 171.446569548396 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 8.0241935483871 & 0.0462035985805492 & 173.670315622669 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 8.02833333333333 & 0.0454787258060472 & 176.529425375102 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 8.03103448275862 & 0.0450318766274915 & 178.341101553289 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 8.03392857142857 & 0.0444502337885753 & 180.739849640419 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 8.03703703703704 & 0.0437015716828267 & 183.907276730629 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 8.04038461538462 & 0.042743368972694 & 188.108350105044 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 8.044 & 0.0415181297994119 & 193.746684613764 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 8.04791666666667 & 0.0399456172128479 & 201.471831660125 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 8.05217391304348 & 0.0391626276591214 & 205.608622157100 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 8.05681818181818 & 0.0381104613595716 & 211.406996777138 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 8.06190476190476 & 0.0366976504535119 & 219.684493755737 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 8.065 & 0.0357250899408532 & 225.75170596778 \tabularnewline
Median & 8.1 &  &  \tabularnewline
Midrange & 7.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.03768115942029 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.07121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.03768115942029 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.07121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.07121212121212 &  &  \tabularnewline
Midmean - Closest Observation & 8.03768115942029 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.07121212121212 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.03768115942029 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29171&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]7.95333333333333[/C][C]0.0776577037662611[/C][C]102.415252416834[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.9069195954496[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.85922058628615[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.99832274084177[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]7.95333333333333[/C][C]0.0776577037662611[/C][C]102.415252416834[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]7.95166666666667[/C][C]0.077387157691292[/C][C]102.751760161382[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]7.95166666666667[/C][C]0.077387157691292[/C][C]102.751760161382[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]7.955[/C][C]0.0767681401294546[/C][C]103.623716643199[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]7.955[/C][C]0.0767681401294546[/C][C]103.623716643199[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]7.96[/C][C]0.0758832215006857[/C][C]104.898024129459[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]7.96583333333333[/C][C]0.0748995203050289[/C][C]106.353596136429[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]7.95916666666667[/C][C]0.073854424085829[/C][C]107.768312666239[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]7.96666666666667[/C][C]0.07034661416953[/C][C]113.248757750694[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]7.95833333333333[/C][C]0.0691543895823401[/C][C]115.080667784040[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]7.95833333333333[/C][C]0.0691543895823401[/C][C]115.080667784040[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]7.96833333333333[/C][C]0.0676639344841742[/C][C]117.763375631032[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]7.96833333333333[/C][C]0.0676639344841742[/C][C]117.763375631032[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]7.95666666666667[/C][C]0.0660694538781801[/C][C]120.428824511510[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]7.94416666666667[/C][C]0.0644606565058217[/C][C]123.240548534426[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]7.94416666666667[/C][C]0.0608851128392881[/C][C]130.477982156919[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]7.94416666666667[/C][C]0.0608851128392881[/C][C]130.477982156919[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]7.95916666666667[/C][C]0.0587747901489192[/C][C]135.418036312853[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]7.95916666666667[/C][C]0.0547913771014065[/C][C]145.263125107004[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]7.95916666666667[/C][C]0.0547913771014065[/C][C]145.263125107004[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]7.94166666666667[/C][C]0.0528803857847781[/C][C]150.181708185509[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]7.94166666666667[/C][C]0.0528803857847781[/C][C]150.181708185509[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]7.94166666666667[/C][C]0.0528803857847781[/C][C]150.181708185509[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]7.94166666666667[/C][C]0.0482259988538635[/C][C]164.676043117984[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]7.94166666666667[/C][C]0.0482259988538635[/C][C]164.676043117984[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]7.94166666666667[/C][C]0.0482259988538635[/C][C]164.676043117984[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]7.96416666666667[/C][C]0.0453865414183923[/C][C]175.474191638654[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]7.96416666666667[/C][C]0.0453865414183923[/C][C]175.474191638654[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]7.96416666666667[/C][C]0.0453865414183923[/C][C]175.474191638654[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]7.98916666666667[/C][C]0.042386705696416[/C][C]188.482839970793[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]7.98916666666667[/C][C]0.042386705696416[/C][C]188.482839970793[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]7.98916666666667[/C][C]0.042386705696416[/C][C]188.482839970793[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]7.98916666666667[/C][C]0.042386705696416[/C][C]188.482839970793[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]7.98916666666667[/C][C]0.042386705696416[/C][C]188.482839970793[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]7.98916666666667[/C][C]0.042386705696416[/C][C]188.482839970793[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]7.98916666666667[/C][C]0.0359503983166017[/C][C]222.227486780788[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]7.98916666666667[/C][C]0.0359503983166017[/C][C]222.227486780788[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]7.98916666666667[/C][C]0.0359503983166017[/C][C]222.227486780788[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]8.02166666666667[/C][C]0.0323059458354216[/C][C]248.303105178594[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]8.055[/C][C]0.0287423111140923[/C][C]280.24886266194[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]7.95508474576271[/C][C]0.0764316964786694[/C][C]104.080965257429[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]7.95689655172414[/C][C]0.075073418716598[/C][C]105.988200454297[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]7.95964912280702[/C][C]0.0737228294268992[/C][C]107.967222428698[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]7.9625[/C][C]0.0722203143826154[/C][C]110.252912467475[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]7.96454545454545[/C][C]0.0707470722333106[/C][C]112.577739306015[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]7.96666666666667[/C][C]0.0691014374200228[/C][C]115.289449309751[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]7.96792452830189[/C][C]0.0674732940389454[/C][C]118.090047948494[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]7.96826923076923[/C][C]0.0658611086252313[/C][C]120.985956615322[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]7.96960784313726[/C][C]0.0642564088009765[/C][C]124.0282174471[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]7.97[/C][C]0.0630936453282585[/C][C]126.320169940005[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]7.97142857142857[/C][C]0.0619821275557313[/C][C]128.608501930836[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]7.97291666666667[/C][C]0.0607244128243781[/C][C]131.296727227734[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]7.97340425531915[/C][C]0.0595332937754424[/C][C]133.931851400572[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]7.97391304347826[/C][C]0.0581788756340028[/C][C]137.058562177126[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]7.97555555555556[/C][C]0.0568703348332654[/C][C]140.241051489122[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]7.97840909090909[/C][C]0.055601791382128[/C][C]143.491943201556[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]7.98139534883721[/C][C]0.054647524400819[/C][C]146.052276591647[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]7.98452380952381[/C][C]0.0535459236794202[/C][C]149.115437009308[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]7.98658536585366[/C][C]0.0525691123969695[/C][C]151.925436852422[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]7.98875[/C][C]0.0519552433362272[/C][C]153.762151556119[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]7.99102564102564[/C][C]0.0512314518935702[/C][C]155.978902523131[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]7.99473684210526[/C][C]0.050606661264682[/C][C]157.977954725986[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]7.99864864864865[/C][C]0.0498607183811025[/C][C]160.419843683604[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]8.00277777777778[/C][C]0.0489711127451534[/C][C]163.418336426709[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]8.00714285714286[/C][C]0.048510801280493[/C][C]165.058969256042[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]8.01176470588235[/C][C]0.047939520161847[/C][C]167.122338288621[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]8.01666666666667[/C][C]0.0472351323821341[/C][C]169.718306319362[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]8.0203125[/C][C]0.0467802448373632[/C][C]171.446569548396[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]8.0241935483871[/C][C]0.0462035985805492[/C][C]173.670315622669[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]8.02833333333333[/C][C]0.0454787258060472[/C][C]176.529425375102[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]8.03103448275862[/C][C]0.0450318766274915[/C][C]178.341101553289[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]8.03392857142857[/C][C]0.0444502337885753[/C][C]180.739849640419[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]8.03703703703704[/C][C]0.0437015716828267[/C][C]183.907276730629[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]8.04038461538462[/C][C]0.042743368972694[/C][C]188.108350105044[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]8.044[/C][C]0.0415181297994119[/C][C]193.746684613764[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]8.04791666666667[/C][C]0.0399456172128479[/C][C]201.471831660125[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]8.05217391304348[/C][C]0.0391626276591214[/C][C]205.608622157100[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]8.05681818181818[/C][C]0.0381104613595716[/C][C]211.406996777138[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]8.06190476190476[/C][C]0.0366976504535119[/C][C]219.684493755737[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]8.065[/C][C]0.0357250899408532[/C][C]225.75170596778[/C][/ROW]
[ROW][C]Median[/C][C]8.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.03768115942029[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.07121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.03768115942029[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.07121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.07121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.03768115942029[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.07121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.03768115942029[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29171&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29171&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 Mean7.953333333333330.0776577037662611102.415252416834
Geometric Mean7.9069195954496
Harmonic Mean7.85922058628615
Quadratic Mean7.99832274084177
Winsorized Mean ( 1 / 40 )7.953333333333330.0776577037662611102.415252416834
Winsorized Mean ( 2 / 40 )7.951666666666670.077387157691292102.751760161382
Winsorized Mean ( 3 / 40 )7.951666666666670.077387157691292102.751760161382
Winsorized Mean ( 4 / 40 )7.9550.0767681401294546103.623716643199
Winsorized Mean ( 5 / 40 )7.9550.0767681401294546103.623716643199
Winsorized Mean ( 6 / 40 )7.960.0758832215006857104.898024129459
Winsorized Mean ( 7 / 40 )7.965833333333330.0748995203050289106.353596136429
Winsorized Mean ( 8 / 40 )7.959166666666670.073854424085829107.768312666239
Winsorized Mean ( 9 / 40 )7.966666666666670.07034661416953113.248757750694
Winsorized Mean ( 10 / 40 )7.958333333333330.0691543895823401115.080667784040
Winsorized Mean ( 11 / 40 )7.958333333333330.0691543895823401115.080667784040
Winsorized Mean ( 12 / 40 )7.968333333333330.0676639344841742117.763375631032
Winsorized Mean ( 13 / 40 )7.968333333333330.0676639344841742117.763375631032
Winsorized Mean ( 14 / 40 )7.956666666666670.0660694538781801120.428824511510
Winsorized Mean ( 15 / 40 )7.944166666666670.0644606565058217123.240548534426
Winsorized Mean ( 16 / 40 )7.944166666666670.0608851128392881130.477982156919
Winsorized Mean ( 17 / 40 )7.944166666666670.0608851128392881130.477982156919
Winsorized Mean ( 18 / 40 )7.959166666666670.0587747901489192135.418036312853
Winsorized Mean ( 19 / 40 )7.959166666666670.0547913771014065145.263125107004
Winsorized Mean ( 20 / 40 )7.959166666666670.0547913771014065145.263125107004
Winsorized Mean ( 21 / 40 )7.941666666666670.0528803857847781150.181708185509
Winsorized Mean ( 22 / 40 )7.941666666666670.0528803857847781150.181708185509
Winsorized Mean ( 23 / 40 )7.941666666666670.0528803857847781150.181708185509
Winsorized Mean ( 24 / 40 )7.941666666666670.0482259988538635164.676043117984
Winsorized Mean ( 25 / 40 )7.941666666666670.0482259988538635164.676043117984
Winsorized Mean ( 26 / 40 )7.941666666666670.0482259988538635164.676043117984
Winsorized Mean ( 27 / 40 )7.964166666666670.0453865414183923175.474191638654
Winsorized Mean ( 28 / 40 )7.964166666666670.0453865414183923175.474191638654
Winsorized Mean ( 29 / 40 )7.964166666666670.0453865414183923175.474191638654
Winsorized Mean ( 30 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 31 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 32 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 33 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 34 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 35 / 40 )7.989166666666670.042386705696416188.482839970793
Winsorized Mean ( 36 / 40 )7.989166666666670.0359503983166017222.227486780788
Winsorized Mean ( 37 / 40 )7.989166666666670.0359503983166017222.227486780788
Winsorized Mean ( 38 / 40 )7.989166666666670.0359503983166017222.227486780788
Winsorized Mean ( 39 / 40 )8.021666666666670.0323059458354216248.303105178594
Winsorized Mean ( 40 / 40 )8.0550.0287423111140923280.24886266194
Trimmed Mean ( 1 / 40 )7.955084745762710.0764316964786694104.080965257429
Trimmed Mean ( 2 / 40 )7.956896551724140.075073418716598105.988200454297
Trimmed Mean ( 3 / 40 )7.959649122807020.0737228294268992107.967222428698
Trimmed Mean ( 4 / 40 )7.96250.0722203143826154110.252912467475
Trimmed Mean ( 5 / 40 )7.964545454545450.0707470722333106112.577739306015
Trimmed Mean ( 6 / 40 )7.966666666666670.0691014374200228115.289449309751
Trimmed Mean ( 7 / 40 )7.967924528301890.0674732940389454118.090047948494
Trimmed Mean ( 8 / 40 )7.968269230769230.0658611086252313120.985956615322
Trimmed Mean ( 9 / 40 )7.969607843137260.0642564088009765124.0282174471
Trimmed Mean ( 10 / 40 )7.970.0630936453282585126.320169940005
Trimmed Mean ( 11 / 40 )7.971428571428570.0619821275557313128.608501930836
Trimmed Mean ( 12 / 40 )7.972916666666670.0607244128243781131.296727227734
Trimmed Mean ( 13 / 40 )7.973404255319150.0595332937754424133.931851400572
Trimmed Mean ( 14 / 40 )7.973913043478260.0581788756340028137.058562177126
Trimmed Mean ( 15 / 40 )7.975555555555560.0568703348332654140.241051489122
Trimmed Mean ( 16 / 40 )7.978409090909090.055601791382128143.491943201556
Trimmed Mean ( 17 / 40 )7.981395348837210.054647524400819146.052276591647
Trimmed Mean ( 18 / 40 )7.984523809523810.0535459236794202149.115437009308
Trimmed Mean ( 19 / 40 )7.986585365853660.0525691123969695151.925436852422
Trimmed Mean ( 20 / 40 )7.988750.0519552433362272153.762151556119
Trimmed Mean ( 21 / 40 )7.991025641025640.0512314518935702155.978902523131
Trimmed Mean ( 22 / 40 )7.994736842105260.050606661264682157.977954725986
Trimmed Mean ( 23 / 40 )7.998648648648650.0498607183811025160.419843683604
Trimmed Mean ( 24 / 40 )8.002777777777780.0489711127451534163.418336426709
Trimmed Mean ( 25 / 40 )8.007142857142860.048510801280493165.058969256042
Trimmed Mean ( 26 / 40 )8.011764705882350.047939520161847167.122338288621
Trimmed Mean ( 27 / 40 )8.016666666666670.0472351323821341169.718306319362
Trimmed Mean ( 28 / 40 )8.02031250.0467802448373632171.446569548396
Trimmed Mean ( 29 / 40 )8.02419354838710.0462035985805492173.670315622669
Trimmed Mean ( 30 / 40 )8.028333333333330.0454787258060472176.529425375102
Trimmed Mean ( 31 / 40 )8.031034482758620.0450318766274915178.341101553289
Trimmed Mean ( 32 / 40 )8.033928571428570.0444502337885753180.739849640419
Trimmed Mean ( 33 / 40 )8.037037037037040.0437015716828267183.907276730629
Trimmed Mean ( 34 / 40 )8.040384615384620.042743368972694188.108350105044
Trimmed Mean ( 35 / 40 )8.0440.0415181297994119193.746684613764
Trimmed Mean ( 36 / 40 )8.047916666666670.0399456172128479201.471831660125
Trimmed Mean ( 37 / 40 )8.052173913043480.0391626276591214205.608622157100
Trimmed Mean ( 38 / 40 )8.056818181818180.0381104613595716211.406996777138
Trimmed Mean ( 39 / 40 )8.061904761904760.0366976504535119219.684493755737
Trimmed Mean ( 40 / 40 )8.0650.0357250899408532225.75170596778
Median8.1
Midrange7.85
Midmean - Weighted Average at Xnp8.03768115942029
Midmean - Weighted Average at X(n+1)p8.07121212121212
Midmean - Empirical Distribution Function8.03768115942029
Midmean - Empirical Distribution Function - Averaging8.07121212121212
Midmean - Empirical Distribution Function - Interpolation8.07121212121212
Midmean - Closest Observation8.03768115942029
Midmean - True Basic - Statistics Graphics Toolkit8.07121212121212
Midmean - MS Excel (old versions)8.03768115942029
Number of observations120



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')