Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 24 Mar 2012 13:34:55 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/24/t1332610537rj5d11jlj9rv0rv.htm/, Retrieved Sun, 28 Apr 2024 17:06:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164053, Retrieved Sun, 28 Apr 2024 17:06:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrum maten 2] [2012-03-24 17:34:55] [d77480184cff5133157c4adeb3391928] [Current]
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Dataseries X:
3,9
5,9
5,7
3,6
4,9
5,3
8,7
6,8
8,9
9,6
11,2
9,9
9,3
9,2
9,4
12,7
13,6
16,1
14,8
14,1
13,2
8,7
4,9
-1,3
-3,9
-6
-6,6
-8,7
-11,6
-14,6
-12,9
-13,8
-14,1
-13,2
-10,4
-3,3
1
3,1
4,5
1,9
3,9
7
5,6
8,1
6,1
8
6,5
5,6
4,8
5,1
7,8
10,3
8,6
6,8
4,9
5,4
5,5
4,7
4,2
5
5
6
2,9
3,6
5,1
2,9
4,7
3
5
2,6
3,2
2,4
3,2
2,6
2,4
2,1
2,7
4,4
4,3
4,2
5,5
8,8
10,1
7
5,7
5,2
5,5
7,3
5,9
7,1
6,9
6,7
4,7
6,7
8,5
2,1
-0,9
-4,7
4,8
2,6
1,7
-1,8
0,2
1,9
3,2
3,1
4,2
16,2
18,3
21,6
12,6
9,8
10,6
13
9,7
7,9
3,3
3,4
0,4
0,7
1,4
3,8
4
8
6
5,8
3,9
6,4
11




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164053&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164053&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.593023255813950.5477924182448768.38460537758075
Geometric MeanNaN
Harmonic Mean4.5728387580389
Quadratic Mean7.71399111450932
Winsorized Mean ( 1 / 43 )4.571317829457360.54109823386338.44822167838056
Winsorized Mean ( 2 / 43 )4.543410852713180.5338401233769198.51080811231061
Winsorized Mean ( 3 / 43 )4.555038759689920.5297438879058748.59856784322025
Winsorized Mean ( 4 / 43 )4.524031007751940.5207687268384638.68721713613046
Winsorized Mean ( 5 / 43 )4.547286821705430.5037673928934469.02656044407233
Winsorized Mean ( 6 / 43 )4.579844961240310.4866562214880099.41084231336218
Winsorized Mean ( 7 / 43 )4.650387596899220.46199312790490310.0659237465031
Winsorized Mean ( 8 / 43 )4.768217054263570.43204375117169211.0364217543531
Winsorized Mean ( 9 / 43 )4.78914728682170.42044734434626511.39059944419
Winsorized Mean ( 10 / 43 )4.882170542635660.39973866464857212.2134058433597
Winsorized Mean ( 11 / 43 )4.831007751937990.36999043836117913.0571151333971
Winsorized Mean ( 12 / 43 )4.868217054263570.35736130640306313.6226753345612
Winsorized Mean ( 13 / 43 )4.979069767441860.32611926086840715.267634773191
Winsorized Mean ( 14 / 43 )5.000775193798450.31309922417859715.9718543120565
Winsorized Mean ( 15 / 43 )5.024031007751940.30282658869713816.5904553803119
Winsorized Mean ( 16 / 43 )5.135658914728680.27968134563973418.3625364894521
Winsorized Mean ( 17 / 43 )5.148837209302330.27433216185482718.768624044989
Winsorized Mean ( 18 / 43 )5.176744186046510.26690996568480619.3950951691318
Winsorized Mean ( 19 / 43 )5.20620155038760.259263342077220.0807468910794
Winsorized Mean ( 20 / 43 )5.237209302325580.24748264994645121.1619251024618
Winsorized Mean ( 21 / 43 )5.269767441860460.23954041067605721.9994923903969
Winsorized Mean ( 22 / 43 )5.286821705426360.23338276360325922.6530084047412
Winsorized Mean ( 23 / 43 )5.233333333333330.22649517566492123.1057165697674
Winsorized Mean ( 24 / 43 )5.251937984496120.21992307492548923.8807955294163
Winsorized Mean ( 25 / 43 )5.232558139534880.21749477292206924.0583167550871
Winsorized Mean ( 26 / 43 )5.293023255813950.21084968505577525.1033016929279
Winsorized Mean ( 27 / 43 )5.272093023255810.20822180176639925.3196013987551
Winsorized Mean ( 28 / 43 )5.29379844961240.20089959967528726.3504678862912
Winsorized Mean ( 29 / 43 )5.203875968992250.18993063777768127.3988232224204
Winsorized Mean ( 30 / 43 )5.180620155038760.18717697471534827.6776572701705
Winsorized Mean ( 31 / 43 )5.20465116279070.18460904526695128.1928285543354
Winsorized Mean ( 32 / 43 )5.229457364341090.1764866363936729.6308971103982
Winsorized Mean ( 33 / 43 )5.203875968992250.17347900448208129.9971514393245
Winsorized Mean ( 34 / 43 )5.09844961240310.15572094344959632.7409370856616
Winsorized Mean ( 35 / 43 )5.071317829457360.14694562172533834.5115272569085
Winsorized Mean ( 36 / 43 )5.043410852713180.1439587924241935.0337118545162
Winsorized Mean ( 37 / 43 )5.072093023255810.14095800040484535.9830091849222
Winsorized Mean ( 38 / 43 )5.042635658914730.13783334853812636.5850188825666
Winsorized Mean ( 39 / 43 )5.012403100775190.13467413186117337.2187518976708
Winsorized Mean ( 40 / 43 )5.043410852713180.13143718177684838.3712643905876
Winsorized Mean ( 41 / 43 )5.043410852713180.12484896379703140.3960970065587
Winsorized Mean ( 42 / 43 )5.108527131782950.11825314768615743.1999251752769
Winsorized Mean ( 43 / 43 )5.041860465116280.11133493227375845.2855214634611
Trimmed Mean ( 1 / 43 )4.610236220472440.5182108407758858.89644881525408
Trimmed Mean ( 2 / 43 )4.65040.4924941447171189.44254880973485
Trimmed Mean ( 3 / 43 )4.706504065040650.46790463332269310.0586823251113
Trimmed Mean ( 4 / 43 )4.76033057851240.44183202269572810.774073254058
Trimmed Mean ( 5 / 43 )4.824369747899160.4152552551315111.6178415282699
Trimmed Mean ( 6 / 43 )4.885470085470090.39007783907607812.52434667153
Trimmed Mean ( 7 / 43 )4.942608695652170.36589557823472613.5082493193767
Trimmed Mean ( 8 / 43 )4.990265486725660.34433735213613114.4923734116211
Trimmed Mean ( 9 / 43 )5.022522522522520.32654768433860315.3806710731857
Trimmed Mean ( 10 / 43 )5.053211009174310.30864915860010416.3720226294912
Trimmed Mean ( 11 / 43 )5.073831775700930.29234136656515317.3558461305549
Trimmed Mean ( 12 / 43 )5.100952380952380.27919132056058818.2704547215515
Trimmed Mean ( 13 / 43 )5.12524271844660.26642759526583519.2369064222974
Trimmed Mean ( 14 / 43 )5.139603960396040.25713608989901819.9878747569602
Trimmed Mean ( 15 / 43 )5.152525252525250.24861746531916520.7247115399179
Trimmed Mean ( 16 / 43 )5.16391752577320.24049002079289521.4724815139845
Trimmed Mean ( 17 / 43 )5.166315789473680.23460247536527822.0215740751656
Trimmed Mean ( 18 / 43 )5.167741935483870.22864706297483622.6013921554401
Trimmed Mean ( 19 / 43 )5.167032967032970.22286871437303223.1842005351389
Trimmed Mean ( 20 / 43 )5.164044943820230.21728926596757523.7657618328502
Trimmed Mean ( 21 / 43 )5.158620689655170.21244086067417124.2826199879087
Trimmed Mean ( 22 / 43 )5.150588235294120.20788129241239324.7765836719757
Trimmed Mean ( 23 / 43 )5.140963855421690.2034021257419125.2748777165922
Trimmed Mean ( 24 / 43 )5.134567901234570.19912742131414225.7853381887285
Trimmed Mean ( 25 / 43 )5.126582278481010.19499339497930426.29105605872
Trimmed Mean ( 26 / 43 )5.119480519480520.19049562081140326.874531276228
Trimmed Mean ( 27 / 43 )5.1080.18606169663569927.4532592809859
Trimmed Mean ( 28 / 43 )5.09726027397260.1812141173502128.1283839719935
Trimmed Mean ( 29 / 43 )5.084507042253520.1764693746530528.812404714699
Trimmed Mean ( 30 / 43 )5.07681159420290.17242991493631729.4427541536392
Trimmed Mean ( 31 / 43 )5.070149253731340.16800926787036330.1777950585649
Trimmed Mean ( 32 / 43 )5.061538461538460.16306399622205231.0401963572997
Trimmed Mean ( 33 / 43 )5.050793650793650.15829792660745231.9068844364503
Trimmed Mean ( 34 / 43 )5.040983606557380.1530094652092132.9455671233466
Trimmed Mean ( 35 / 43 )5.037288135593220.14943686040896433.7084714026224
Trimmed Mean ( 36 / 43 )5.035087719298250.14639552349264434.3937273433859
Trimmed Mean ( 37 / 43 )5.034545454545450.14308336629117135.1860987412072
Trimmed Mean ( 38 / 43 )5.032075471698110.13942588026564336.0914018409687
Trimmed Mean ( 39 / 43 )5.031372549019610.13537139026609737.1671779327193
Trimmed Mean ( 40 / 43 )5.032653061224490.13081338148170238.4720049601994
Trimmed Mean ( 41 / 43 )5.031914893617020.1256290879638740.0537405402811
Trimmed Mean ( 42 / 43 )5.031111111111110.1203455555877341.8055414389068
Trimmed Mean ( 43 / 43 )5.025581395348840.1148976637088743.7396308429975
Median5
Midrange3.5
Midmean - Weighted Average at Xnp5.0171875
Midmean - Weighted Average at X(n+1)p5.06153846153846
Midmean - Empirical Distribution Function5.06153846153846
Midmean - Empirical Distribution Function - Averaging5.06153846153846
Midmean - Empirical Distribution Function - Interpolation5.06153846153846
Midmean - Closest Observation5.02575757575758
Midmean - True Basic - Statistics Graphics Toolkit5.06153846153846
Midmean - MS Excel (old versions)5.06153846153846
Number of observations129

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.59302325581395 & 0.547792418244876 & 8.38460537758075 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 4.5728387580389 &  &  \tabularnewline
Quadratic Mean & 7.71399111450932 &  &  \tabularnewline
Winsorized Mean ( 1 / 43 ) & 4.57131782945736 & 0.5410982338633 & 8.44822167838056 \tabularnewline
Winsorized Mean ( 2 / 43 ) & 4.54341085271318 & 0.533840123376919 & 8.51080811231061 \tabularnewline
Winsorized Mean ( 3 / 43 ) & 4.55503875968992 & 0.529743887905874 & 8.59856784322025 \tabularnewline
Winsorized Mean ( 4 / 43 ) & 4.52403100775194 & 0.520768726838463 & 8.68721713613046 \tabularnewline
Winsorized Mean ( 5 / 43 ) & 4.54728682170543 & 0.503767392893446 & 9.02656044407233 \tabularnewline
Winsorized Mean ( 6 / 43 ) & 4.57984496124031 & 0.486656221488009 & 9.41084231336218 \tabularnewline
Winsorized Mean ( 7 / 43 ) & 4.65038759689922 & 0.461993127904903 & 10.0659237465031 \tabularnewline
Winsorized Mean ( 8 / 43 ) & 4.76821705426357 & 0.432043751171692 & 11.0364217543531 \tabularnewline
Winsorized Mean ( 9 / 43 ) & 4.7891472868217 & 0.420447344346265 & 11.39059944419 \tabularnewline
Winsorized Mean ( 10 / 43 ) & 4.88217054263566 & 0.399738664648572 & 12.2134058433597 \tabularnewline
Winsorized Mean ( 11 / 43 ) & 4.83100775193799 & 0.369990438361179 & 13.0571151333971 \tabularnewline
Winsorized Mean ( 12 / 43 ) & 4.86821705426357 & 0.357361306403063 & 13.6226753345612 \tabularnewline
Winsorized Mean ( 13 / 43 ) & 4.97906976744186 & 0.326119260868407 & 15.267634773191 \tabularnewline
Winsorized Mean ( 14 / 43 ) & 5.00077519379845 & 0.313099224178597 & 15.9718543120565 \tabularnewline
Winsorized Mean ( 15 / 43 ) & 5.02403100775194 & 0.302826588697138 & 16.5904553803119 \tabularnewline
Winsorized Mean ( 16 / 43 ) & 5.13565891472868 & 0.279681345639734 & 18.3625364894521 \tabularnewline
Winsorized Mean ( 17 / 43 ) & 5.14883720930233 & 0.274332161854827 & 18.768624044989 \tabularnewline
Winsorized Mean ( 18 / 43 ) & 5.17674418604651 & 0.266909965684806 & 19.3950951691318 \tabularnewline
Winsorized Mean ( 19 / 43 ) & 5.2062015503876 & 0.2592633420772 & 20.0807468910794 \tabularnewline
Winsorized Mean ( 20 / 43 ) & 5.23720930232558 & 0.247482649946451 & 21.1619251024618 \tabularnewline
Winsorized Mean ( 21 / 43 ) & 5.26976744186046 & 0.239540410676057 & 21.9994923903969 \tabularnewline
Winsorized Mean ( 22 / 43 ) & 5.28682170542636 & 0.233382763603259 & 22.6530084047412 \tabularnewline
Winsorized Mean ( 23 / 43 ) & 5.23333333333333 & 0.226495175664921 & 23.1057165697674 \tabularnewline
Winsorized Mean ( 24 / 43 ) & 5.25193798449612 & 0.219923074925489 & 23.8807955294163 \tabularnewline
Winsorized Mean ( 25 / 43 ) & 5.23255813953488 & 0.217494772922069 & 24.0583167550871 \tabularnewline
Winsorized Mean ( 26 / 43 ) & 5.29302325581395 & 0.210849685055775 & 25.1033016929279 \tabularnewline
Winsorized Mean ( 27 / 43 ) & 5.27209302325581 & 0.208221801766399 & 25.3196013987551 \tabularnewline
Winsorized Mean ( 28 / 43 ) & 5.2937984496124 & 0.200899599675287 & 26.3504678862912 \tabularnewline
Winsorized Mean ( 29 / 43 ) & 5.20387596899225 & 0.189930637777681 & 27.3988232224204 \tabularnewline
Winsorized Mean ( 30 / 43 ) & 5.18062015503876 & 0.187176974715348 & 27.6776572701705 \tabularnewline
Winsorized Mean ( 31 / 43 ) & 5.2046511627907 & 0.184609045266951 & 28.1928285543354 \tabularnewline
Winsorized Mean ( 32 / 43 ) & 5.22945736434109 & 0.17648663639367 & 29.6308971103982 \tabularnewline
Winsorized Mean ( 33 / 43 ) & 5.20387596899225 & 0.173479004482081 & 29.9971514393245 \tabularnewline
Winsorized Mean ( 34 / 43 ) & 5.0984496124031 & 0.155720943449596 & 32.7409370856616 \tabularnewline
Winsorized Mean ( 35 / 43 ) & 5.07131782945736 & 0.146945621725338 & 34.5115272569085 \tabularnewline
Winsorized Mean ( 36 / 43 ) & 5.04341085271318 & 0.14395879242419 & 35.0337118545162 \tabularnewline
Winsorized Mean ( 37 / 43 ) & 5.07209302325581 & 0.140958000404845 & 35.9830091849222 \tabularnewline
Winsorized Mean ( 38 / 43 ) & 5.04263565891473 & 0.137833348538126 & 36.5850188825666 \tabularnewline
Winsorized Mean ( 39 / 43 ) & 5.01240310077519 & 0.134674131861173 & 37.2187518976708 \tabularnewline
Winsorized Mean ( 40 / 43 ) & 5.04341085271318 & 0.131437181776848 & 38.3712643905876 \tabularnewline
Winsorized Mean ( 41 / 43 ) & 5.04341085271318 & 0.124848963797031 & 40.3960970065587 \tabularnewline
Winsorized Mean ( 42 / 43 ) & 5.10852713178295 & 0.118253147686157 & 43.1999251752769 \tabularnewline
Winsorized Mean ( 43 / 43 ) & 5.04186046511628 & 0.111334932273758 & 45.2855214634611 \tabularnewline
Trimmed Mean ( 1 / 43 ) & 4.61023622047244 & 0.518210840775885 & 8.89644881525408 \tabularnewline
Trimmed Mean ( 2 / 43 ) & 4.6504 & 0.492494144717118 & 9.44254880973485 \tabularnewline
Trimmed Mean ( 3 / 43 ) & 4.70650406504065 & 0.467904633322693 & 10.0586823251113 \tabularnewline
Trimmed Mean ( 4 / 43 ) & 4.7603305785124 & 0.441832022695728 & 10.774073254058 \tabularnewline
Trimmed Mean ( 5 / 43 ) & 4.82436974789916 & 0.41525525513151 & 11.6178415282699 \tabularnewline
Trimmed Mean ( 6 / 43 ) & 4.88547008547009 & 0.390077839076078 & 12.52434667153 \tabularnewline
Trimmed Mean ( 7 / 43 ) & 4.94260869565217 & 0.365895578234726 & 13.5082493193767 \tabularnewline
Trimmed Mean ( 8 / 43 ) & 4.99026548672566 & 0.344337352136131 & 14.4923734116211 \tabularnewline
Trimmed Mean ( 9 / 43 ) & 5.02252252252252 & 0.326547684338603 & 15.3806710731857 \tabularnewline
Trimmed Mean ( 10 / 43 ) & 5.05321100917431 & 0.308649158600104 & 16.3720226294912 \tabularnewline
Trimmed Mean ( 11 / 43 ) & 5.07383177570093 & 0.292341366565153 & 17.3558461305549 \tabularnewline
Trimmed Mean ( 12 / 43 ) & 5.10095238095238 & 0.279191320560588 & 18.2704547215515 \tabularnewline
Trimmed Mean ( 13 / 43 ) & 5.1252427184466 & 0.266427595265835 & 19.2369064222974 \tabularnewline
Trimmed Mean ( 14 / 43 ) & 5.13960396039604 & 0.257136089899018 & 19.9878747569602 \tabularnewline
Trimmed Mean ( 15 / 43 ) & 5.15252525252525 & 0.248617465319165 & 20.7247115399179 \tabularnewline
Trimmed Mean ( 16 / 43 ) & 5.1639175257732 & 0.240490020792895 & 21.4724815139845 \tabularnewline
Trimmed Mean ( 17 / 43 ) & 5.16631578947368 & 0.234602475365278 & 22.0215740751656 \tabularnewline
Trimmed Mean ( 18 / 43 ) & 5.16774193548387 & 0.228647062974836 & 22.6013921554401 \tabularnewline
Trimmed Mean ( 19 / 43 ) & 5.16703296703297 & 0.222868714373032 & 23.1842005351389 \tabularnewline
Trimmed Mean ( 20 / 43 ) & 5.16404494382023 & 0.217289265967575 & 23.7657618328502 \tabularnewline
Trimmed Mean ( 21 / 43 ) & 5.15862068965517 & 0.212440860674171 & 24.2826199879087 \tabularnewline
Trimmed Mean ( 22 / 43 ) & 5.15058823529412 & 0.207881292412393 & 24.7765836719757 \tabularnewline
Trimmed Mean ( 23 / 43 ) & 5.14096385542169 & 0.20340212574191 & 25.2748777165922 \tabularnewline
Trimmed Mean ( 24 / 43 ) & 5.13456790123457 & 0.199127421314142 & 25.7853381887285 \tabularnewline
Trimmed Mean ( 25 / 43 ) & 5.12658227848101 & 0.194993394979304 & 26.29105605872 \tabularnewline
Trimmed Mean ( 26 / 43 ) & 5.11948051948052 & 0.190495620811403 & 26.874531276228 \tabularnewline
Trimmed Mean ( 27 / 43 ) & 5.108 & 0.186061696635699 & 27.4532592809859 \tabularnewline
Trimmed Mean ( 28 / 43 ) & 5.0972602739726 & 0.18121411735021 & 28.1283839719935 \tabularnewline
Trimmed Mean ( 29 / 43 ) & 5.08450704225352 & 0.17646937465305 & 28.812404714699 \tabularnewline
Trimmed Mean ( 30 / 43 ) & 5.0768115942029 & 0.172429914936317 & 29.4427541536392 \tabularnewline
Trimmed Mean ( 31 / 43 ) & 5.07014925373134 & 0.168009267870363 & 30.1777950585649 \tabularnewline
Trimmed Mean ( 32 / 43 ) & 5.06153846153846 & 0.163063996222052 & 31.0401963572997 \tabularnewline
Trimmed Mean ( 33 / 43 ) & 5.05079365079365 & 0.158297926607452 & 31.9068844364503 \tabularnewline
Trimmed Mean ( 34 / 43 ) & 5.04098360655738 & 0.15300946520921 & 32.9455671233466 \tabularnewline
Trimmed Mean ( 35 / 43 ) & 5.03728813559322 & 0.149436860408964 & 33.7084714026224 \tabularnewline
Trimmed Mean ( 36 / 43 ) & 5.03508771929825 & 0.146395523492644 & 34.3937273433859 \tabularnewline
Trimmed Mean ( 37 / 43 ) & 5.03454545454545 & 0.143083366291171 & 35.1860987412072 \tabularnewline
Trimmed Mean ( 38 / 43 ) & 5.03207547169811 & 0.139425880265643 & 36.0914018409687 \tabularnewline
Trimmed Mean ( 39 / 43 ) & 5.03137254901961 & 0.135371390266097 & 37.1671779327193 \tabularnewline
Trimmed Mean ( 40 / 43 ) & 5.03265306122449 & 0.130813381481702 & 38.4720049601994 \tabularnewline
Trimmed Mean ( 41 / 43 ) & 5.03191489361702 & 0.12562908796387 & 40.0537405402811 \tabularnewline
Trimmed Mean ( 42 / 43 ) & 5.03111111111111 & 0.12034555558773 & 41.8055414389068 \tabularnewline
Trimmed Mean ( 43 / 43 ) & 5.02558139534884 & 0.11489766370887 & 43.7396308429975 \tabularnewline
Median & 5 &  &  \tabularnewline
Midrange & 3.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.0171875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.06153846153846 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.06153846153846 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.06153846153846 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.06153846153846 &  &  \tabularnewline
Midmean - Closest Observation & 5.02575757575758 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.06153846153846 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.06153846153846 &  &  \tabularnewline
Number of observations & 129 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164053&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]4.59302325581395[/C][C]0.547792418244876[/C][C]8.38460537758075[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.5728387580389[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.71399111450932[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 43 )[/C][C]4.57131782945736[/C][C]0.5410982338633[/C][C]8.44822167838056[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 43 )[/C][C]4.54341085271318[/C][C]0.533840123376919[/C][C]8.51080811231061[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 43 )[/C][C]4.55503875968992[/C][C]0.529743887905874[/C][C]8.59856784322025[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 43 )[/C][C]4.52403100775194[/C][C]0.520768726838463[/C][C]8.68721713613046[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 43 )[/C][C]4.54728682170543[/C][C]0.503767392893446[/C][C]9.02656044407233[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 43 )[/C][C]4.57984496124031[/C][C]0.486656221488009[/C][C]9.41084231336218[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 43 )[/C][C]4.65038759689922[/C][C]0.461993127904903[/C][C]10.0659237465031[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 43 )[/C][C]4.76821705426357[/C][C]0.432043751171692[/C][C]11.0364217543531[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 43 )[/C][C]4.7891472868217[/C][C]0.420447344346265[/C][C]11.39059944419[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 43 )[/C][C]4.88217054263566[/C][C]0.399738664648572[/C][C]12.2134058433597[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 43 )[/C][C]4.83100775193799[/C][C]0.369990438361179[/C][C]13.0571151333971[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 43 )[/C][C]4.86821705426357[/C][C]0.357361306403063[/C][C]13.6226753345612[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 43 )[/C][C]4.97906976744186[/C][C]0.326119260868407[/C][C]15.267634773191[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 43 )[/C][C]5.00077519379845[/C][C]0.313099224178597[/C][C]15.9718543120565[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 43 )[/C][C]5.02403100775194[/C][C]0.302826588697138[/C][C]16.5904553803119[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 43 )[/C][C]5.13565891472868[/C][C]0.279681345639734[/C][C]18.3625364894521[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 43 )[/C][C]5.14883720930233[/C][C]0.274332161854827[/C][C]18.768624044989[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 43 )[/C][C]5.17674418604651[/C][C]0.266909965684806[/C][C]19.3950951691318[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 43 )[/C][C]5.2062015503876[/C][C]0.2592633420772[/C][C]20.0807468910794[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 43 )[/C][C]5.23720930232558[/C][C]0.247482649946451[/C][C]21.1619251024618[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 43 )[/C][C]5.26976744186046[/C][C]0.239540410676057[/C][C]21.9994923903969[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 43 )[/C][C]5.28682170542636[/C][C]0.233382763603259[/C][C]22.6530084047412[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 43 )[/C][C]5.23333333333333[/C][C]0.226495175664921[/C][C]23.1057165697674[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 43 )[/C][C]5.25193798449612[/C][C]0.219923074925489[/C][C]23.8807955294163[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 43 )[/C][C]5.23255813953488[/C][C]0.217494772922069[/C][C]24.0583167550871[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 43 )[/C][C]5.29302325581395[/C][C]0.210849685055775[/C][C]25.1033016929279[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 43 )[/C][C]5.27209302325581[/C][C]0.208221801766399[/C][C]25.3196013987551[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 43 )[/C][C]5.2937984496124[/C][C]0.200899599675287[/C][C]26.3504678862912[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 43 )[/C][C]5.20387596899225[/C][C]0.189930637777681[/C][C]27.3988232224204[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 43 )[/C][C]5.18062015503876[/C][C]0.187176974715348[/C][C]27.6776572701705[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 43 )[/C][C]5.2046511627907[/C][C]0.184609045266951[/C][C]28.1928285543354[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 43 )[/C][C]5.22945736434109[/C][C]0.17648663639367[/C][C]29.6308971103982[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 43 )[/C][C]5.20387596899225[/C][C]0.173479004482081[/C][C]29.9971514393245[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 43 )[/C][C]5.0984496124031[/C][C]0.155720943449596[/C][C]32.7409370856616[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 43 )[/C][C]5.07131782945736[/C][C]0.146945621725338[/C][C]34.5115272569085[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 43 )[/C][C]5.04341085271318[/C][C]0.14395879242419[/C][C]35.0337118545162[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 43 )[/C][C]5.07209302325581[/C][C]0.140958000404845[/C][C]35.9830091849222[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 43 )[/C][C]5.04263565891473[/C][C]0.137833348538126[/C][C]36.5850188825666[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 43 )[/C][C]5.01240310077519[/C][C]0.134674131861173[/C][C]37.2187518976708[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 43 )[/C][C]5.04341085271318[/C][C]0.131437181776848[/C][C]38.3712643905876[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 43 )[/C][C]5.04341085271318[/C][C]0.124848963797031[/C][C]40.3960970065587[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 43 )[/C][C]5.10852713178295[/C][C]0.118253147686157[/C][C]43.1999251752769[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 43 )[/C][C]5.04186046511628[/C][C]0.111334932273758[/C][C]45.2855214634611[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 43 )[/C][C]4.61023622047244[/C][C]0.518210840775885[/C][C]8.89644881525408[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 43 )[/C][C]4.6504[/C][C]0.492494144717118[/C][C]9.44254880973485[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 43 )[/C][C]4.70650406504065[/C][C]0.467904633322693[/C][C]10.0586823251113[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 43 )[/C][C]4.7603305785124[/C][C]0.441832022695728[/C][C]10.774073254058[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 43 )[/C][C]4.82436974789916[/C][C]0.41525525513151[/C][C]11.6178415282699[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 43 )[/C][C]4.88547008547009[/C][C]0.390077839076078[/C][C]12.52434667153[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 43 )[/C][C]4.94260869565217[/C][C]0.365895578234726[/C][C]13.5082493193767[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 43 )[/C][C]4.99026548672566[/C][C]0.344337352136131[/C][C]14.4923734116211[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 43 )[/C][C]5.02252252252252[/C][C]0.326547684338603[/C][C]15.3806710731857[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 43 )[/C][C]5.05321100917431[/C][C]0.308649158600104[/C][C]16.3720226294912[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 43 )[/C][C]5.07383177570093[/C][C]0.292341366565153[/C][C]17.3558461305549[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 43 )[/C][C]5.10095238095238[/C][C]0.279191320560588[/C][C]18.2704547215515[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 43 )[/C][C]5.1252427184466[/C][C]0.266427595265835[/C][C]19.2369064222974[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 43 )[/C][C]5.13960396039604[/C][C]0.257136089899018[/C][C]19.9878747569602[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 43 )[/C][C]5.15252525252525[/C][C]0.248617465319165[/C][C]20.7247115399179[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 43 )[/C][C]5.1639175257732[/C][C]0.240490020792895[/C][C]21.4724815139845[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 43 )[/C][C]5.16631578947368[/C][C]0.234602475365278[/C][C]22.0215740751656[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 43 )[/C][C]5.16774193548387[/C][C]0.228647062974836[/C][C]22.6013921554401[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 43 )[/C][C]5.16703296703297[/C][C]0.222868714373032[/C][C]23.1842005351389[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 43 )[/C][C]5.16404494382023[/C][C]0.217289265967575[/C][C]23.7657618328502[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 43 )[/C][C]5.15862068965517[/C][C]0.212440860674171[/C][C]24.2826199879087[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 43 )[/C][C]5.15058823529412[/C][C]0.207881292412393[/C][C]24.7765836719757[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 43 )[/C][C]5.14096385542169[/C][C]0.20340212574191[/C][C]25.2748777165922[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 43 )[/C][C]5.13456790123457[/C][C]0.199127421314142[/C][C]25.7853381887285[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 43 )[/C][C]5.12658227848101[/C][C]0.194993394979304[/C][C]26.29105605872[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 43 )[/C][C]5.11948051948052[/C][C]0.190495620811403[/C][C]26.874531276228[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 43 )[/C][C]5.108[/C][C]0.186061696635699[/C][C]27.4532592809859[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 43 )[/C][C]5.0972602739726[/C][C]0.18121411735021[/C][C]28.1283839719935[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 43 )[/C][C]5.08450704225352[/C][C]0.17646937465305[/C][C]28.812404714699[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 43 )[/C][C]5.0768115942029[/C][C]0.172429914936317[/C][C]29.4427541536392[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 43 )[/C][C]5.07014925373134[/C][C]0.168009267870363[/C][C]30.1777950585649[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 43 )[/C][C]5.06153846153846[/C][C]0.163063996222052[/C][C]31.0401963572997[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 43 )[/C][C]5.05079365079365[/C][C]0.158297926607452[/C][C]31.9068844364503[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 43 )[/C][C]5.04098360655738[/C][C]0.15300946520921[/C][C]32.9455671233466[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 43 )[/C][C]5.03728813559322[/C][C]0.149436860408964[/C][C]33.7084714026224[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 43 )[/C][C]5.03508771929825[/C][C]0.146395523492644[/C][C]34.3937273433859[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 43 )[/C][C]5.03454545454545[/C][C]0.143083366291171[/C][C]35.1860987412072[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 43 )[/C][C]5.03207547169811[/C][C]0.139425880265643[/C][C]36.0914018409687[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 43 )[/C][C]5.03137254901961[/C][C]0.135371390266097[/C][C]37.1671779327193[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 43 )[/C][C]5.03265306122449[/C][C]0.130813381481702[/C][C]38.4720049601994[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 43 )[/C][C]5.03191489361702[/C][C]0.12562908796387[/C][C]40.0537405402811[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 43 )[/C][C]5.03111111111111[/C][C]0.12034555558773[/C][C]41.8055414389068[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 43 )[/C][C]5.02558139534884[/C][C]0.11489766370887[/C][C]43.7396308429975[/C][/ROW]
[ROW][C]Median[/C][C]5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.0171875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.06153846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.06153846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.06153846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.06153846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.02575757575758[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.06153846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.06153846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]129[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164053&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 Mean4.593023255813950.5477924182448768.38460537758075
Geometric MeanNaN
Harmonic Mean4.5728387580389
Quadratic Mean7.71399111450932
Winsorized Mean ( 1 / 43 )4.571317829457360.54109823386338.44822167838056
Winsorized Mean ( 2 / 43 )4.543410852713180.5338401233769198.51080811231061
Winsorized Mean ( 3 / 43 )4.555038759689920.5297438879058748.59856784322025
Winsorized Mean ( 4 / 43 )4.524031007751940.5207687268384638.68721713613046
Winsorized Mean ( 5 / 43 )4.547286821705430.5037673928934469.02656044407233
Winsorized Mean ( 6 / 43 )4.579844961240310.4866562214880099.41084231336218
Winsorized Mean ( 7 / 43 )4.650387596899220.46199312790490310.0659237465031
Winsorized Mean ( 8 / 43 )4.768217054263570.43204375117169211.0364217543531
Winsorized Mean ( 9 / 43 )4.78914728682170.42044734434626511.39059944419
Winsorized Mean ( 10 / 43 )4.882170542635660.39973866464857212.2134058433597
Winsorized Mean ( 11 / 43 )4.831007751937990.36999043836117913.0571151333971
Winsorized Mean ( 12 / 43 )4.868217054263570.35736130640306313.6226753345612
Winsorized Mean ( 13 / 43 )4.979069767441860.32611926086840715.267634773191
Winsorized Mean ( 14 / 43 )5.000775193798450.31309922417859715.9718543120565
Winsorized Mean ( 15 / 43 )5.024031007751940.30282658869713816.5904553803119
Winsorized Mean ( 16 / 43 )5.135658914728680.27968134563973418.3625364894521
Winsorized Mean ( 17 / 43 )5.148837209302330.27433216185482718.768624044989
Winsorized Mean ( 18 / 43 )5.176744186046510.26690996568480619.3950951691318
Winsorized Mean ( 19 / 43 )5.20620155038760.259263342077220.0807468910794
Winsorized Mean ( 20 / 43 )5.237209302325580.24748264994645121.1619251024618
Winsorized Mean ( 21 / 43 )5.269767441860460.23954041067605721.9994923903969
Winsorized Mean ( 22 / 43 )5.286821705426360.23338276360325922.6530084047412
Winsorized Mean ( 23 / 43 )5.233333333333330.22649517566492123.1057165697674
Winsorized Mean ( 24 / 43 )5.251937984496120.21992307492548923.8807955294163
Winsorized Mean ( 25 / 43 )5.232558139534880.21749477292206924.0583167550871
Winsorized Mean ( 26 / 43 )5.293023255813950.21084968505577525.1033016929279
Winsorized Mean ( 27 / 43 )5.272093023255810.20822180176639925.3196013987551
Winsorized Mean ( 28 / 43 )5.29379844961240.20089959967528726.3504678862912
Winsorized Mean ( 29 / 43 )5.203875968992250.18993063777768127.3988232224204
Winsorized Mean ( 30 / 43 )5.180620155038760.18717697471534827.6776572701705
Winsorized Mean ( 31 / 43 )5.20465116279070.18460904526695128.1928285543354
Winsorized Mean ( 32 / 43 )5.229457364341090.1764866363936729.6308971103982
Winsorized Mean ( 33 / 43 )5.203875968992250.17347900448208129.9971514393245
Winsorized Mean ( 34 / 43 )5.09844961240310.15572094344959632.7409370856616
Winsorized Mean ( 35 / 43 )5.071317829457360.14694562172533834.5115272569085
Winsorized Mean ( 36 / 43 )5.043410852713180.1439587924241935.0337118545162
Winsorized Mean ( 37 / 43 )5.072093023255810.14095800040484535.9830091849222
Winsorized Mean ( 38 / 43 )5.042635658914730.13783334853812636.5850188825666
Winsorized Mean ( 39 / 43 )5.012403100775190.13467413186117337.2187518976708
Winsorized Mean ( 40 / 43 )5.043410852713180.13143718177684838.3712643905876
Winsorized Mean ( 41 / 43 )5.043410852713180.12484896379703140.3960970065587
Winsorized Mean ( 42 / 43 )5.108527131782950.11825314768615743.1999251752769
Winsorized Mean ( 43 / 43 )5.041860465116280.11133493227375845.2855214634611
Trimmed Mean ( 1 / 43 )4.610236220472440.5182108407758858.89644881525408
Trimmed Mean ( 2 / 43 )4.65040.4924941447171189.44254880973485
Trimmed Mean ( 3 / 43 )4.706504065040650.46790463332269310.0586823251113
Trimmed Mean ( 4 / 43 )4.76033057851240.44183202269572810.774073254058
Trimmed Mean ( 5 / 43 )4.824369747899160.4152552551315111.6178415282699
Trimmed Mean ( 6 / 43 )4.885470085470090.39007783907607812.52434667153
Trimmed Mean ( 7 / 43 )4.942608695652170.36589557823472613.5082493193767
Trimmed Mean ( 8 / 43 )4.990265486725660.34433735213613114.4923734116211
Trimmed Mean ( 9 / 43 )5.022522522522520.32654768433860315.3806710731857
Trimmed Mean ( 10 / 43 )5.053211009174310.30864915860010416.3720226294912
Trimmed Mean ( 11 / 43 )5.073831775700930.29234136656515317.3558461305549
Trimmed Mean ( 12 / 43 )5.100952380952380.27919132056058818.2704547215515
Trimmed Mean ( 13 / 43 )5.12524271844660.26642759526583519.2369064222974
Trimmed Mean ( 14 / 43 )5.139603960396040.25713608989901819.9878747569602
Trimmed Mean ( 15 / 43 )5.152525252525250.24861746531916520.7247115399179
Trimmed Mean ( 16 / 43 )5.16391752577320.24049002079289521.4724815139845
Trimmed Mean ( 17 / 43 )5.166315789473680.23460247536527822.0215740751656
Trimmed Mean ( 18 / 43 )5.167741935483870.22864706297483622.6013921554401
Trimmed Mean ( 19 / 43 )5.167032967032970.22286871437303223.1842005351389
Trimmed Mean ( 20 / 43 )5.164044943820230.21728926596757523.7657618328502
Trimmed Mean ( 21 / 43 )5.158620689655170.21244086067417124.2826199879087
Trimmed Mean ( 22 / 43 )5.150588235294120.20788129241239324.7765836719757
Trimmed Mean ( 23 / 43 )5.140963855421690.2034021257419125.2748777165922
Trimmed Mean ( 24 / 43 )5.134567901234570.19912742131414225.7853381887285
Trimmed Mean ( 25 / 43 )5.126582278481010.19499339497930426.29105605872
Trimmed Mean ( 26 / 43 )5.119480519480520.19049562081140326.874531276228
Trimmed Mean ( 27 / 43 )5.1080.18606169663569927.4532592809859
Trimmed Mean ( 28 / 43 )5.09726027397260.1812141173502128.1283839719935
Trimmed Mean ( 29 / 43 )5.084507042253520.1764693746530528.812404714699
Trimmed Mean ( 30 / 43 )5.07681159420290.17242991493631729.4427541536392
Trimmed Mean ( 31 / 43 )5.070149253731340.16800926787036330.1777950585649
Trimmed Mean ( 32 / 43 )5.061538461538460.16306399622205231.0401963572997
Trimmed Mean ( 33 / 43 )5.050793650793650.15829792660745231.9068844364503
Trimmed Mean ( 34 / 43 )5.040983606557380.1530094652092132.9455671233466
Trimmed Mean ( 35 / 43 )5.037288135593220.14943686040896433.7084714026224
Trimmed Mean ( 36 / 43 )5.035087719298250.14639552349264434.3937273433859
Trimmed Mean ( 37 / 43 )5.034545454545450.14308336629117135.1860987412072
Trimmed Mean ( 38 / 43 )5.032075471698110.13942588026564336.0914018409687
Trimmed Mean ( 39 / 43 )5.031372549019610.13537139026609737.1671779327193
Trimmed Mean ( 40 / 43 )5.032653061224490.13081338148170238.4720049601994
Trimmed Mean ( 41 / 43 )5.031914893617020.1256290879638740.0537405402811
Trimmed Mean ( 42 / 43 )5.031111111111110.1203455555877341.8055414389068
Trimmed Mean ( 43 / 43 )5.025581395348840.1148976637088743.7396308429975
Median5
Midrange3.5
Midmean - Weighted Average at Xnp5.0171875
Midmean - Weighted Average at X(n+1)p5.06153846153846
Midmean - Empirical Distribution Function5.06153846153846
Midmean - Empirical Distribution Function - Averaging5.06153846153846
Midmean - Empirical Distribution Function - Interpolation5.06153846153846
Midmean - Closest Observation5.02575757575758
Midmean - True Basic - Statistics Graphics Toolkit5.06153846153846
Midmean - MS Excel (old versions)5.06153846153846
Number of observations129



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')