Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 23 Apr 2009 04:38:07 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Apr/23/t12404831394kd0vu70xzhra5x.htm/, Retrieved Mon, 13 May 2024 11:41:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39326, Retrieved Mon, 13 May 2024 11:41:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 OEFENING...] [2009-04-23 10:38:07] [be8f2ceb4bab9280e3447d0ad1b6c819] [Current]
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Dataseries X:
3,27
3,27
3,27
3,27
3,27
3,28
3,32
3,34
3,34
3,35
3,35
3,35
3,35
3,35
3,4
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,43
3,47
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,58
3,6
3,61
3,61
3,61
3,63
3,68
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,78
3,79
3,79
3,8
3,8
3,8
3,8
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68
4,69
4,69
4,69
4,69
4,69
4,69
4,69
4,73
4,78
4,79
4,79
4,8
4,8
4,81
5,16
5,26
5,29
5,29
5,29
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,35
5,44
5,47
5,47
5,48
5,48
5,48
5,48




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39326&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39326&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39326&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.16816793893130.061271687020828568.0276346481921
Geometric Mean4.11137339186683
Harmonic Mean4.05688417191626
Quadratic Mean4.22630719648773
Winsorized Mean ( 1 / 43 )4.16816793893130.061271687020828568.0276346481921
Winsorized Mean ( 2 / 43 )4.16816793893130.061271687020828568.0276346481921
Winsorized Mean ( 3 / 43 )4.16816793893130.061271687020828568.0276346481921
Winsorized Mean ( 4 / 43 )4.167862595419850.061221564409290868.078341931219
Winsorized Mean ( 5 / 43 )4.168244274809160.061178721360783268.1322554982506
Winsorized Mean ( 6 / 43 )4.168702290076340.06075492937928768.6150462631854
Winsorized Mean ( 7 / 43 )4.164961832061070.059887678585326969.546222703004
Winsorized Mean ( 8 / 43 )4.161908396946560.059430366493765570.0299971628673
Winsorized Mean ( 9 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 10 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 11 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 12 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 13 / 43 )4.162595419847330.059357648619475470.1273638134239
Winsorized Mean ( 14 / 43 )4.167938931297710.058807858910264270.8738425192054
Winsorized Mean ( 15 / 43 )4.170229007633590.05858003299749671.1885738919239
Winsorized Mean ( 16 / 43 )4.169007633587790.058399263076801571.3880178266133
Winsorized Mean ( 17 / 43 )4.169007633587790.058399263076801571.3880178266133
Winsorized Mean ( 18 / 43 )4.169007633587790.058399263076801571.3880178266133
Winsorized Mean ( 19 / 43 )4.164656488549620.05776064748803972.1019702802332
Winsorized Mean ( 20 / 43 )4.14938931297710.055578498836199174.65817537113
Winsorized Mean ( 21 / 43 )4.093282442748090.048409396547386484.5555353853938
Winsorized Mean ( 22 / 43 )4.091603053435110.048218870832198884.8548085597826
Winsorized Mean ( 23 / 43 )4.091603053435110.048218870832198884.8548085597826
Winsorized Mean ( 24 / 43 )4.089770992366410.048012582228487585.18123380458
Winsorized Mean ( 25 / 43 )4.089770992366410.048012582228487585.18123380458
Winsorized Mean ( 26 / 43 )4.089770992366410.047578160270128385.9589981862782
Winsorized Mean ( 27 / 43 )4.087709923664120.045574503911272889.6929110105581
Winsorized Mean ( 28 / 43 )4.087709923664120.043778598053275293.3723350092137
Winsorized Mean ( 29 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 30 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 31 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 32 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 33 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 34 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 35 / 43 )4.087251908396950.043272485109238194.4538289880738
Winsorized Mean ( 36 / 43 )4.087251908396950.043272485109238194.4538289880738
Winsorized Mean ( 37 / 43 )4.084427480916030.042975659896902295.0404831645285
Winsorized Mean ( 38 / 43 )4.075725190839690.0385500613335939105.725517673508
Winsorized Mean ( 39 / 43 )4.051908396946570.0350597367080331115.571558072145
Winsorized Mean ( 40 / 43 )4.048854961832060.0341882875318640118.428130044784
Winsorized Mean ( 41 / 43 )4.048854961832060.0341882875318640118.428130044784
Winsorized Mean ( 42 / 43 )4.048854961832060.0341882875318640118.428130044784
Winsorized Mean ( 43 / 43 )4.052137404580150.0332405258947081121.903528765327
Trimmed Mean ( 1 / 43 )4.164961240310080.060982262086079368.2979131608965
Trimmed Mean ( 2 / 43 )4.161653543307090.060655994374318968.6107545715067
Trimmed Mean ( 3 / 43 )4.158240.060289202371408568.9715543818838
Trimmed Mean ( 4 / 43 )4.154715447154470.05987773820013569.3866463904794
Trimmed Mean ( 5 / 43 )4.151157024793390.059432253035392169.8468729146337
Trimmed Mean ( 6 / 43 )4.147394957983190.058944021709326370.3615877863824
Trimmed Mean ( 7 / 43 )4.14341880341880.058489580109038270.8402897694684
Trimmed Mean ( 8 / 43 )4.139913043478260.058148065254028871.1960582934688
Trimmed Mean ( 9 / 43 )4.136725663716810.05784032503118971.5197513410615
Trimmed Mean ( 10 / 43 )4.133333333333330.057498542990952871.8858795080025
Trimmed Mean ( 11 / 43 )4.129816513761470.05710717753175672.3169431979889
Trimmed Mean ( 12 / 43 )4.126168224299070.056660370158172972.8228250676878
Trimmed Mean ( 13 / 43 )4.122380952380950.056151372436905473.4154976712827
Trimmed Mean ( 14 / 43 )4.118446601941750.055572365288623474.1096151036937
Trimmed Mean ( 15 / 43 )4.113861386138610.054980819391232174.8235735969162
Trimmed Mean ( 16 / 43 )4.108888888888890.054332380809132275.6250476731965
Trimmed Mean ( 17 / 43 )4.103814432989690.053615309804426176.5418394104086
Trimmed Mean ( 18 / 43 )4.098526315789470.052795315297673977.6304922639613
Trimmed Mean ( 19 / 43 )4.093010752688170.051856777838706178.9291375838847
Trimmed Mean ( 20 / 43 )4.087582417582420.050866326447702880.3593006030224
Trimmed Mean ( 21 / 43 )4.083033707865170.050016699074121781.6334101099787
Trimmed Mean ( 22 / 43 )4.082298850574710.049892882089777281.8212674751686
Trimmed Mean ( 23 / 43 )4.081647058823530.049748906511869382.044960281684
Trimmed Mean ( 24 / 43 )4.080963855421690.049560695581406382.3427477670985
Trimmed Mean ( 25 / 43 )4.080370370370370.04934398172255682.6923614173025
Trimmed Mean ( 26 / 43 )4.079746835443040.049071209470998283.1393169115635
Trimmed Mean ( 27 / 43 )4.079090909090910.048781173960373483.6201874191156
Trimmed Mean ( 28 / 43 )4.078533333333330.048640506358989183.8505525257467
Trimmed Mean ( 29 / 43 )4.077945205479450.048637430584740583.8437630535291
Trimmed Mean ( 30 / 43 )4.077183098591550.048617996476945283.8616025760124
Trimmed Mean ( 31 / 43 )4.07637681159420.048554541718611583.9545934800098
Trimmed Mean ( 32 / 43 )4.07552238805970.048438896674934884.137390977541
Trimmed Mean ( 33 / 43 )4.074615384615380.048261147039927184.4284820094391
Trimmed Mean ( 34 / 43 )4.073650793650790.048009163225097784.851526666918
Trimmed Mean ( 35 / 43 )4.072622950819670.047667966835803485.4373119132224
Trimmed Mean ( 36 / 43 )4.071694915254240.047256807723697786.1610233822971
Trimmed Mean ( 37 / 43 )4.070701754385960.046720694411426487.1284514425025
Trimmed Mean ( 38 / 43 )4.069818181818180.046075250197333388.3298118705328
Trimmed Mean ( 39 / 43 )4.069433962264150.045894128729488688.6700341616769
Trimmed Mean ( 40 / 43 )4.070588235294120.046085523025413988.3268316831164
Trimmed Mean ( 41 / 43 )4.072040816326530.046346061842247687.8616360153084
Trimmed Mean ( 42 / 43 )4.07361702127660.046565110167522487.4821729535563
Trimmed Mean ( 43 / 43 )4.075333333333330.046728962748984387.2121505291045
Median4.16
Midrange4.375
Midmean - Weighted Average at Xnp4.08621621621621
Midmean - Weighted Average at X(n+1)p4.08621621621621
Midmean - Empirical Distribution Function4.08621621621621
Midmean - Empirical Distribution Function - Averaging4.08621621621621
Midmean - Empirical Distribution Function - Interpolation4.08621621621621
Midmean - Closest Observation4.08621621621621
Midmean - True Basic - Statistics Graphics Toolkit4.08621621621621
Midmean - MS Excel (old versions)4.08621621621621
Number of observations131

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.1681679389313 & 0.0612716870208285 & 68.0276346481921 \tabularnewline
Geometric Mean & 4.11137339186683 &  &  \tabularnewline
Harmonic Mean & 4.05688417191626 &  &  \tabularnewline
Quadratic Mean & 4.22630719648773 &  &  \tabularnewline
Winsorized Mean ( 1 / 43 ) & 4.1681679389313 & 0.0612716870208285 & 68.0276346481921 \tabularnewline
Winsorized Mean ( 2 / 43 ) & 4.1681679389313 & 0.0612716870208285 & 68.0276346481921 \tabularnewline
Winsorized Mean ( 3 / 43 ) & 4.1681679389313 & 0.0612716870208285 & 68.0276346481921 \tabularnewline
Winsorized Mean ( 4 / 43 ) & 4.16786259541985 & 0.0612215644092908 & 68.078341931219 \tabularnewline
Winsorized Mean ( 5 / 43 ) & 4.16824427480916 & 0.0611787213607832 & 68.1322554982506 \tabularnewline
Winsorized Mean ( 6 / 43 ) & 4.16870229007634 & 0.060754929379287 & 68.6150462631854 \tabularnewline
Winsorized Mean ( 7 / 43 ) & 4.16496183206107 & 0.0598876785853269 & 69.546222703004 \tabularnewline
Winsorized Mean ( 8 / 43 ) & 4.16190839694656 & 0.0594303664937655 & 70.0299971628673 \tabularnewline
Winsorized Mean ( 9 / 43 ) & 4.16259541984733 & 0.0593576486194754 & 70.1273638134238 \tabularnewline
Winsorized Mean ( 10 / 43 ) & 4.16259541984733 & 0.0593576486194754 & 70.1273638134238 \tabularnewline
Winsorized Mean ( 11 / 43 ) & 4.16259541984733 & 0.0593576486194754 & 70.1273638134238 \tabularnewline
Winsorized Mean ( 12 / 43 ) & 4.16259541984733 & 0.0593576486194754 & 70.1273638134238 \tabularnewline
Winsorized Mean ( 13 / 43 ) & 4.16259541984733 & 0.0593576486194754 & 70.1273638134239 \tabularnewline
Winsorized Mean ( 14 / 43 ) & 4.16793893129771 & 0.0588078589102642 & 70.8738425192054 \tabularnewline
Winsorized Mean ( 15 / 43 ) & 4.17022900763359 & 0.058580032997496 & 71.1885738919239 \tabularnewline
Winsorized Mean ( 16 / 43 ) & 4.16900763358779 & 0.0583992630768015 & 71.3880178266133 \tabularnewline
Winsorized Mean ( 17 / 43 ) & 4.16900763358779 & 0.0583992630768015 & 71.3880178266133 \tabularnewline
Winsorized Mean ( 18 / 43 ) & 4.16900763358779 & 0.0583992630768015 & 71.3880178266133 \tabularnewline
Winsorized Mean ( 19 / 43 ) & 4.16465648854962 & 0.057760647488039 & 72.1019702802332 \tabularnewline
Winsorized Mean ( 20 / 43 ) & 4.1493893129771 & 0.0555784988361991 & 74.65817537113 \tabularnewline
Winsorized Mean ( 21 / 43 ) & 4.09328244274809 & 0.0484093965473864 & 84.5555353853938 \tabularnewline
Winsorized Mean ( 22 / 43 ) & 4.09160305343511 & 0.0482188708321988 & 84.8548085597826 \tabularnewline
Winsorized Mean ( 23 / 43 ) & 4.09160305343511 & 0.0482188708321988 & 84.8548085597826 \tabularnewline
Winsorized Mean ( 24 / 43 ) & 4.08977099236641 & 0.0480125822284875 & 85.18123380458 \tabularnewline
Winsorized Mean ( 25 / 43 ) & 4.08977099236641 & 0.0480125822284875 & 85.18123380458 \tabularnewline
Winsorized Mean ( 26 / 43 ) & 4.08977099236641 & 0.0475781602701283 & 85.9589981862782 \tabularnewline
Winsorized Mean ( 27 / 43 ) & 4.08770992366412 & 0.0455745039112728 & 89.6929110105581 \tabularnewline
Winsorized Mean ( 28 / 43 ) & 4.08770992366412 & 0.0437785980532752 & 93.3723350092137 \tabularnewline
Winsorized Mean ( 29 / 43 ) & 4.08992366412214 & 0.043554825862802 & 93.9028817841088 \tabularnewline
Winsorized Mean ( 30 / 43 ) & 4.08992366412214 & 0.043554825862802 & 93.9028817841088 \tabularnewline
Winsorized Mean ( 31 / 43 ) & 4.08992366412214 & 0.043554825862802 & 93.9028817841088 \tabularnewline
Winsorized Mean ( 32 / 43 ) & 4.08992366412214 & 0.043554825862802 & 93.9028817841088 \tabularnewline
Winsorized Mean ( 33 / 43 ) & 4.08992366412214 & 0.043554825862802 & 93.9028817841088 \tabularnewline
Winsorized Mean ( 34 / 43 ) & 4.08992366412214 & 0.043554825862802 & 93.9028817841088 \tabularnewline
Winsorized Mean ( 35 / 43 ) & 4.08725190839695 & 0.0432724851092381 & 94.4538289880738 \tabularnewline
Winsorized Mean ( 36 / 43 ) & 4.08725190839695 & 0.0432724851092381 & 94.4538289880738 \tabularnewline
Winsorized Mean ( 37 / 43 ) & 4.08442748091603 & 0.0429756598969022 & 95.0404831645285 \tabularnewline
Winsorized Mean ( 38 / 43 ) & 4.07572519083969 & 0.0385500613335939 & 105.725517673508 \tabularnewline
Winsorized Mean ( 39 / 43 ) & 4.05190839694657 & 0.0350597367080331 & 115.571558072145 \tabularnewline
Winsorized Mean ( 40 / 43 ) & 4.04885496183206 & 0.0341882875318640 & 118.428130044784 \tabularnewline
Winsorized Mean ( 41 / 43 ) & 4.04885496183206 & 0.0341882875318640 & 118.428130044784 \tabularnewline
Winsorized Mean ( 42 / 43 ) & 4.04885496183206 & 0.0341882875318640 & 118.428130044784 \tabularnewline
Winsorized Mean ( 43 / 43 ) & 4.05213740458015 & 0.0332405258947081 & 121.903528765327 \tabularnewline
Trimmed Mean ( 1 / 43 ) & 4.16496124031008 & 0.0609822620860793 & 68.2979131608965 \tabularnewline
Trimmed Mean ( 2 / 43 ) & 4.16165354330709 & 0.0606559943743189 & 68.6107545715067 \tabularnewline
Trimmed Mean ( 3 / 43 ) & 4.15824 & 0.0602892023714085 & 68.9715543818838 \tabularnewline
Trimmed Mean ( 4 / 43 ) & 4.15471544715447 & 0.059877738200135 & 69.3866463904794 \tabularnewline
Trimmed Mean ( 5 / 43 ) & 4.15115702479339 & 0.0594322530353921 & 69.8468729146337 \tabularnewline
Trimmed Mean ( 6 / 43 ) & 4.14739495798319 & 0.0589440217093263 & 70.3615877863824 \tabularnewline
Trimmed Mean ( 7 / 43 ) & 4.1434188034188 & 0.0584895801090382 & 70.8402897694684 \tabularnewline
Trimmed Mean ( 8 / 43 ) & 4.13991304347826 & 0.0581480652540288 & 71.1960582934688 \tabularnewline
Trimmed Mean ( 9 / 43 ) & 4.13672566371681 & 0.057840325031189 & 71.5197513410615 \tabularnewline
Trimmed Mean ( 10 / 43 ) & 4.13333333333333 & 0.0574985429909528 & 71.8858795080025 \tabularnewline
Trimmed Mean ( 11 / 43 ) & 4.12981651376147 & 0.057107177531756 & 72.3169431979889 \tabularnewline
Trimmed Mean ( 12 / 43 ) & 4.12616822429907 & 0.0566603701581729 & 72.8228250676878 \tabularnewline
Trimmed Mean ( 13 / 43 ) & 4.12238095238095 & 0.0561513724369054 & 73.4154976712827 \tabularnewline
Trimmed Mean ( 14 / 43 ) & 4.11844660194175 & 0.0555723652886234 & 74.1096151036937 \tabularnewline
Trimmed Mean ( 15 / 43 ) & 4.11386138613861 & 0.0549808193912321 & 74.8235735969162 \tabularnewline
Trimmed Mean ( 16 / 43 ) & 4.10888888888889 & 0.0543323808091322 & 75.6250476731965 \tabularnewline
Trimmed Mean ( 17 / 43 ) & 4.10381443298969 & 0.0536153098044261 & 76.5418394104086 \tabularnewline
Trimmed Mean ( 18 / 43 ) & 4.09852631578947 & 0.0527953152976739 & 77.6304922639613 \tabularnewline
Trimmed Mean ( 19 / 43 ) & 4.09301075268817 & 0.0518567778387061 & 78.9291375838847 \tabularnewline
Trimmed Mean ( 20 / 43 ) & 4.08758241758242 & 0.0508663264477028 & 80.3593006030224 \tabularnewline
Trimmed Mean ( 21 / 43 ) & 4.08303370786517 & 0.0500166990741217 & 81.6334101099787 \tabularnewline
Trimmed Mean ( 22 / 43 ) & 4.08229885057471 & 0.0498928820897772 & 81.8212674751686 \tabularnewline
Trimmed Mean ( 23 / 43 ) & 4.08164705882353 & 0.0497489065118693 & 82.044960281684 \tabularnewline
Trimmed Mean ( 24 / 43 ) & 4.08096385542169 & 0.0495606955814063 & 82.3427477670985 \tabularnewline
Trimmed Mean ( 25 / 43 ) & 4.08037037037037 & 0.049343981722556 & 82.6923614173025 \tabularnewline
Trimmed Mean ( 26 / 43 ) & 4.07974683544304 & 0.0490712094709982 & 83.1393169115635 \tabularnewline
Trimmed Mean ( 27 / 43 ) & 4.07909090909091 & 0.0487811739603734 & 83.6201874191156 \tabularnewline
Trimmed Mean ( 28 / 43 ) & 4.07853333333333 & 0.0486405063589891 & 83.8505525257467 \tabularnewline
Trimmed Mean ( 29 / 43 ) & 4.07794520547945 & 0.0486374305847405 & 83.8437630535291 \tabularnewline
Trimmed Mean ( 30 / 43 ) & 4.07718309859155 & 0.0486179964769452 & 83.8616025760124 \tabularnewline
Trimmed Mean ( 31 / 43 ) & 4.0763768115942 & 0.0485545417186115 & 83.9545934800098 \tabularnewline
Trimmed Mean ( 32 / 43 ) & 4.0755223880597 & 0.0484388966749348 & 84.137390977541 \tabularnewline
Trimmed Mean ( 33 / 43 ) & 4.07461538461538 & 0.0482611470399271 & 84.4284820094391 \tabularnewline
Trimmed Mean ( 34 / 43 ) & 4.07365079365079 & 0.0480091632250977 & 84.851526666918 \tabularnewline
Trimmed Mean ( 35 / 43 ) & 4.07262295081967 & 0.0476679668358034 & 85.4373119132224 \tabularnewline
Trimmed Mean ( 36 / 43 ) & 4.07169491525424 & 0.0472568077236977 & 86.1610233822971 \tabularnewline
Trimmed Mean ( 37 / 43 ) & 4.07070175438596 & 0.0467206944114264 & 87.1284514425025 \tabularnewline
Trimmed Mean ( 38 / 43 ) & 4.06981818181818 & 0.0460752501973333 & 88.3298118705328 \tabularnewline
Trimmed Mean ( 39 / 43 ) & 4.06943396226415 & 0.0458941287294886 & 88.6700341616769 \tabularnewline
Trimmed Mean ( 40 / 43 ) & 4.07058823529412 & 0.0460855230254139 & 88.3268316831164 \tabularnewline
Trimmed Mean ( 41 / 43 ) & 4.07204081632653 & 0.0463460618422476 & 87.8616360153084 \tabularnewline
Trimmed Mean ( 42 / 43 ) & 4.0736170212766 & 0.0465651101675224 & 87.4821729535563 \tabularnewline
Trimmed Mean ( 43 / 43 ) & 4.07533333333333 & 0.0467289627489843 & 87.2121505291045 \tabularnewline
Median & 4.16 &  &  \tabularnewline
Midrange & 4.375 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.08621621621621 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.08621621621621 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.08621621621621 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.08621621621621 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.08621621621621 &  &  \tabularnewline
Midmean - Closest Observation & 4.08621621621621 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.08621621621621 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.08621621621621 &  &  \tabularnewline
Number of observations & 131 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39326&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]4.1681679389313[/C][C]0.0612716870208285[/C][C]68.0276346481921[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.11137339186683[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.05688417191626[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.22630719648773[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 43 )[/C][C]4.1681679389313[/C][C]0.0612716870208285[/C][C]68.0276346481921[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 43 )[/C][C]4.1681679389313[/C][C]0.0612716870208285[/C][C]68.0276346481921[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 43 )[/C][C]4.1681679389313[/C][C]0.0612716870208285[/C][C]68.0276346481921[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 43 )[/C][C]4.16786259541985[/C][C]0.0612215644092908[/C][C]68.078341931219[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 43 )[/C][C]4.16824427480916[/C][C]0.0611787213607832[/C][C]68.1322554982506[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 43 )[/C][C]4.16870229007634[/C][C]0.060754929379287[/C][C]68.6150462631854[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 43 )[/C][C]4.16496183206107[/C][C]0.0598876785853269[/C][C]69.546222703004[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 43 )[/C][C]4.16190839694656[/C][C]0.0594303664937655[/C][C]70.0299971628673[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 43 )[/C][C]4.16259541984733[/C][C]0.0593576486194754[/C][C]70.1273638134238[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 43 )[/C][C]4.16259541984733[/C][C]0.0593576486194754[/C][C]70.1273638134238[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 43 )[/C][C]4.16259541984733[/C][C]0.0593576486194754[/C][C]70.1273638134238[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 43 )[/C][C]4.16259541984733[/C][C]0.0593576486194754[/C][C]70.1273638134238[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 43 )[/C][C]4.16259541984733[/C][C]0.0593576486194754[/C][C]70.1273638134239[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 43 )[/C][C]4.16793893129771[/C][C]0.0588078589102642[/C][C]70.8738425192054[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 43 )[/C][C]4.17022900763359[/C][C]0.058580032997496[/C][C]71.1885738919239[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 43 )[/C][C]4.16900763358779[/C][C]0.0583992630768015[/C][C]71.3880178266133[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 43 )[/C][C]4.16900763358779[/C][C]0.0583992630768015[/C][C]71.3880178266133[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 43 )[/C][C]4.16900763358779[/C][C]0.0583992630768015[/C][C]71.3880178266133[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 43 )[/C][C]4.16465648854962[/C][C]0.057760647488039[/C][C]72.1019702802332[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 43 )[/C][C]4.1493893129771[/C][C]0.0555784988361991[/C][C]74.65817537113[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 43 )[/C][C]4.09328244274809[/C][C]0.0484093965473864[/C][C]84.5555353853938[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 43 )[/C][C]4.09160305343511[/C][C]0.0482188708321988[/C][C]84.8548085597826[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 43 )[/C][C]4.09160305343511[/C][C]0.0482188708321988[/C][C]84.8548085597826[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 43 )[/C][C]4.08977099236641[/C][C]0.0480125822284875[/C][C]85.18123380458[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 43 )[/C][C]4.08977099236641[/C][C]0.0480125822284875[/C][C]85.18123380458[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 43 )[/C][C]4.08977099236641[/C][C]0.0475781602701283[/C][C]85.9589981862782[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 43 )[/C][C]4.08770992366412[/C][C]0.0455745039112728[/C][C]89.6929110105581[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 43 )[/C][C]4.08770992366412[/C][C]0.0437785980532752[/C][C]93.3723350092137[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 43 )[/C][C]4.08992366412214[/C][C]0.043554825862802[/C][C]93.9028817841088[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 43 )[/C][C]4.08992366412214[/C][C]0.043554825862802[/C][C]93.9028817841088[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 43 )[/C][C]4.08992366412214[/C][C]0.043554825862802[/C][C]93.9028817841088[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 43 )[/C][C]4.08992366412214[/C][C]0.043554825862802[/C][C]93.9028817841088[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 43 )[/C][C]4.08992366412214[/C][C]0.043554825862802[/C][C]93.9028817841088[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 43 )[/C][C]4.08992366412214[/C][C]0.043554825862802[/C][C]93.9028817841088[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 43 )[/C][C]4.08725190839695[/C][C]0.0432724851092381[/C][C]94.4538289880738[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 43 )[/C][C]4.08725190839695[/C][C]0.0432724851092381[/C][C]94.4538289880738[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 43 )[/C][C]4.08442748091603[/C][C]0.0429756598969022[/C][C]95.0404831645285[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 43 )[/C][C]4.07572519083969[/C][C]0.0385500613335939[/C][C]105.725517673508[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 43 )[/C][C]4.05190839694657[/C][C]0.0350597367080331[/C][C]115.571558072145[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 43 )[/C][C]4.04885496183206[/C][C]0.0341882875318640[/C][C]118.428130044784[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 43 )[/C][C]4.04885496183206[/C][C]0.0341882875318640[/C][C]118.428130044784[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 43 )[/C][C]4.04885496183206[/C][C]0.0341882875318640[/C][C]118.428130044784[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 43 )[/C][C]4.05213740458015[/C][C]0.0332405258947081[/C][C]121.903528765327[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 43 )[/C][C]4.16496124031008[/C][C]0.0609822620860793[/C][C]68.2979131608965[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 43 )[/C][C]4.16165354330709[/C][C]0.0606559943743189[/C][C]68.6107545715067[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 43 )[/C][C]4.15824[/C][C]0.0602892023714085[/C][C]68.9715543818838[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 43 )[/C][C]4.15471544715447[/C][C]0.059877738200135[/C][C]69.3866463904794[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 43 )[/C][C]4.15115702479339[/C][C]0.0594322530353921[/C][C]69.8468729146337[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 43 )[/C][C]4.14739495798319[/C][C]0.0589440217093263[/C][C]70.3615877863824[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 43 )[/C][C]4.1434188034188[/C][C]0.0584895801090382[/C][C]70.8402897694684[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 43 )[/C][C]4.13991304347826[/C][C]0.0581480652540288[/C][C]71.1960582934688[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 43 )[/C][C]4.13672566371681[/C][C]0.057840325031189[/C][C]71.5197513410615[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 43 )[/C][C]4.13333333333333[/C][C]0.0574985429909528[/C][C]71.8858795080025[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 43 )[/C][C]4.12981651376147[/C][C]0.057107177531756[/C][C]72.3169431979889[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 43 )[/C][C]4.12616822429907[/C][C]0.0566603701581729[/C][C]72.8228250676878[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 43 )[/C][C]4.12238095238095[/C][C]0.0561513724369054[/C][C]73.4154976712827[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 43 )[/C][C]4.11844660194175[/C][C]0.0555723652886234[/C][C]74.1096151036937[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 43 )[/C][C]4.11386138613861[/C][C]0.0549808193912321[/C][C]74.8235735969162[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 43 )[/C][C]4.10888888888889[/C][C]0.0543323808091322[/C][C]75.6250476731965[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 43 )[/C][C]4.10381443298969[/C][C]0.0536153098044261[/C][C]76.5418394104086[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 43 )[/C][C]4.09852631578947[/C][C]0.0527953152976739[/C][C]77.6304922639613[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 43 )[/C][C]4.09301075268817[/C][C]0.0518567778387061[/C][C]78.9291375838847[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 43 )[/C][C]4.08758241758242[/C][C]0.0508663264477028[/C][C]80.3593006030224[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 43 )[/C][C]4.08303370786517[/C][C]0.0500166990741217[/C][C]81.6334101099787[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 43 )[/C][C]4.08229885057471[/C][C]0.0498928820897772[/C][C]81.8212674751686[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 43 )[/C][C]4.08164705882353[/C][C]0.0497489065118693[/C][C]82.044960281684[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 43 )[/C][C]4.08096385542169[/C][C]0.0495606955814063[/C][C]82.3427477670985[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 43 )[/C][C]4.08037037037037[/C][C]0.049343981722556[/C][C]82.6923614173025[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 43 )[/C][C]4.07974683544304[/C][C]0.0490712094709982[/C][C]83.1393169115635[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 43 )[/C][C]4.07909090909091[/C][C]0.0487811739603734[/C][C]83.6201874191156[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 43 )[/C][C]4.07853333333333[/C][C]0.0486405063589891[/C][C]83.8505525257467[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 43 )[/C][C]4.07794520547945[/C][C]0.0486374305847405[/C][C]83.8437630535291[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 43 )[/C][C]4.07718309859155[/C][C]0.0486179964769452[/C][C]83.8616025760124[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 43 )[/C][C]4.0763768115942[/C][C]0.0485545417186115[/C][C]83.9545934800098[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 43 )[/C][C]4.0755223880597[/C][C]0.0484388966749348[/C][C]84.137390977541[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 43 )[/C][C]4.07461538461538[/C][C]0.0482611470399271[/C][C]84.4284820094391[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 43 )[/C][C]4.07365079365079[/C][C]0.0480091632250977[/C][C]84.851526666918[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 43 )[/C][C]4.07262295081967[/C][C]0.0476679668358034[/C][C]85.4373119132224[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 43 )[/C][C]4.07169491525424[/C][C]0.0472568077236977[/C][C]86.1610233822971[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 43 )[/C][C]4.07070175438596[/C][C]0.0467206944114264[/C][C]87.1284514425025[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 43 )[/C][C]4.06981818181818[/C][C]0.0460752501973333[/C][C]88.3298118705328[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 43 )[/C][C]4.06943396226415[/C][C]0.0458941287294886[/C][C]88.6700341616769[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 43 )[/C][C]4.07058823529412[/C][C]0.0460855230254139[/C][C]88.3268316831164[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 43 )[/C][C]4.07204081632653[/C][C]0.0463460618422476[/C][C]87.8616360153084[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 43 )[/C][C]4.0736170212766[/C][C]0.0465651101675224[/C][C]87.4821729535563[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 43 )[/C][C]4.07533333333333[/C][C]0.0467289627489843[/C][C]87.2121505291045[/C][/ROW]
[ROW][C]Median[/C][C]4.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.08621621621621[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]131[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39326&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39326&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 Mean4.16816793893130.061271687020828568.0276346481921
Geometric Mean4.11137339186683
Harmonic Mean4.05688417191626
Quadratic Mean4.22630719648773
Winsorized Mean ( 1 / 43 )4.16816793893130.061271687020828568.0276346481921
Winsorized Mean ( 2 / 43 )4.16816793893130.061271687020828568.0276346481921
Winsorized Mean ( 3 / 43 )4.16816793893130.061271687020828568.0276346481921
Winsorized Mean ( 4 / 43 )4.167862595419850.061221564409290868.078341931219
Winsorized Mean ( 5 / 43 )4.168244274809160.061178721360783268.1322554982506
Winsorized Mean ( 6 / 43 )4.168702290076340.06075492937928768.6150462631854
Winsorized Mean ( 7 / 43 )4.164961832061070.059887678585326969.546222703004
Winsorized Mean ( 8 / 43 )4.161908396946560.059430366493765570.0299971628673
Winsorized Mean ( 9 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 10 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 11 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 12 / 43 )4.162595419847330.059357648619475470.1273638134238
Winsorized Mean ( 13 / 43 )4.162595419847330.059357648619475470.1273638134239
Winsorized Mean ( 14 / 43 )4.167938931297710.058807858910264270.8738425192054
Winsorized Mean ( 15 / 43 )4.170229007633590.05858003299749671.1885738919239
Winsorized Mean ( 16 / 43 )4.169007633587790.058399263076801571.3880178266133
Winsorized Mean ( 17 / 43 )4.169007633587790.058399263076801571.3880178266133
Winsorized Mean ( 18 / 43 )4.169007633587790.058399263076801571.3880178266133
Winsorized Mean ( 19 / 43 )4.164656488549620.05776064748803972.1019702802332
Winsorized Mean ( 20 / 43 )4.14938931297710.055578498836199174.65817537113
Winsorized Mean ( 21 / 43 )4.093282442748090.048409396547386484.5555353853938
Winsorized Mean ( 22 / 43 )4.091603053435110.048218870832198884.8548085597826
Winsorized Mean ( 23 / 43 )4.091603053435110.048218870832198884.8548085597826
Winsorized Mean ( 24 / 43 )4.089770992366410.048012582228487585.18123380458
Winsorized Mean ( 25 / 43 )4.089770992366410.048012582228487585.18123380458
Winsorized Mean ( 26 / 43 )4.089770992366410.047578160270128385.9589981862782
Winsorized Mean ( 27 / 43 )4.087709923664120.045574503911272889.6929110105581
Winsorized Mean ( 28 / 43 )4.087709923664120.043778598053275293.3723350092137
Winsorized Mean ( 29 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 30 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 31 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 32 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 33 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 34 / 43 )4.089923664122140.04355482586280293.9028817841088
Winsorized Mean ( 35 / 43 )4.087251908396950.043272485109238194.4538289880738
Winsorized Mean ( 36 / 43 )4.087251908396950.043272485109238194.4538289880738
Winsorized Mean ( 37 / 43 )4.084427480916030.042975659896902295.0404831645285
Winsorized Mean ( 38 / 43 )4.075725190839690.0385500613335939105.725517673508
Winsorized Mean ( 39 / 43 )4.051908396946570.0350597367080331115.571558072145
Winsorized Mean ( 40 / 43 )4.048854961832060.0341882875318640118.428130044784
Winsorized Mean ( 41 / 43 )4.048854961832060.0341882875318640118.428130044784
Winsorized Mean ( 42 / 43 )4.048854961832060.0341882875318640118.428130044784
Winsorized Mean ( 43 / 43 )4.052137404580150.0332405258947081121.903528765327
Trimmed Mean ( 1 / 43 )4.164961240310080.060982262086079368.2979131608965
Trimmed Mean ( 2 / 43 )4.161653543307090.060655994374318968.6107545715067
Trimmed Mean ( 3 / 43 )4.158240.060289202371408568.9715543818838
Trimmed Mean ( 4 / 43 )4.154715447154470.05987773820013569.3866463904794
Trimmed Mean ( 5 / 43 )4.151157024793390.059432253035392169.8468729146337
Trimmed Mean ( 6 / 43 )4.147394957983190.058944021709326370.3615877863824
Trimmed Mean ( 7 / 43 )4.14341880341880.058489580109038270.8402897694684
Trimmed Mean ( 8 / 43 )4.139913043478260.058148065254028871.1960582934688
Trimmed Mean ( 9 / 43 )4.136725663716810.05784032503118971.5197513410615
Trimmed Mean ( 10 / 43 )4.133333333333330.057498542990952871.8858795080025
Trimmed Mean ( 11 / 43 )4.129816513761470.05710717753175672.3169431979889
Trimmed Mean ( 12 / 43 )4.126168224299070.056660370158172972.8228250676878
Trimmed Mean ( 13 / 43 )4.122380952380950.056151372436905473.4154976712827
Trimmed Mean ( 14 / 43 )4.118446601941750.055572365288623474.1096151036937
Trimmed Mean ( 15 / 43 )4.113861386138610.054980819391232174.8235735969162
Trimmed Mean ( 16 / 43 )4.108888888888890.054332380809132275.6250476731965
Trimmed Mean ( 17 / 43 )4.103814432989690.053615309804426176.5418394104086
Trimmed Mean ( 18 / 43 )4.098526315789470.052795315297673977.6304922639613
Trimmed Mean ( 19 / 43 )4.093010752688170.051856777838706178.9291375838847
Trimmed Mean ( 20 / 43 )4.087582417582420.050866326447702880.3593006030224
Trimmed Mean ( 21 / 43 )4.083033707865170.050016699074121781.6334101099787
Trimmed Mean ( 22 / 43 )4.082298850574710.049892882089777281.8212674751686
Trimmed Mean ( 23 / 43 )4.081647058823530.049748906511869382.044960281684
Trimmed Mean ( 24 / 43 )4.080963855421690.049560695581406382.3427477670985
Trimmed Mean ( 25 / 43 )4.080370370370370.04934398172255682.6923614173025
Trimmed Mean ( 26 / 43 )4.079746835443040.049071209470998283.1393169115635
Trimmed Mean ( 27 / 43 )4.079090909090910.048781173960373483.6201874191156
Trimmed Mean ( 28 / 43 )4.078533333333330.048640506358989183.8505525257467
Trimmed Mean ( 29 / 43 )4.077945205479450.048637430584740583.8437630535291
Trimmed Mean ( 30 / 43 )4.077183098591550.048617996476945283.8616025760124
Trimmed Mean ( 31 / 43 )4.07637681159420.048554541718611583.9545934800098
Trimmed Mean ( 32 / 43 )4.07552238805970.048438896674934884.137390977541
Trimmed Mean ( 33 / 43 )4.074615384615380.048261147039927184.4284820094391
Trimmed Mean ( 34 / 43 )4.073650793650790.048009163225097784.851526666918
Trimmed Mean ( 35 / 43 )4.072622950819670.047667966835803485.4373119132224
Trimmed Mean ( 36 / 43 )4.071694915254240.047256807723697786.1610233822971
Trimmed Mean ( 37 / 43 )4.070701754385960.046720694411426487.1284514425025
Trimmed Mean ( 38 / 43 )4.069818181818180.046075250197333388.3298118705328
Trimmed Mean ( 39 / 43 )4.069433962264150.045894128729488688.6700341616769
Trimmed Mean ( 40 / 43 )4.070588235294120.046085523025413988.3268316831164
Trimmed Mean ( 41 / 43 )4.072040816326530.046346061842247687.8616360153084
Trimmed Mean ( 42 / 43 )4.07361702127660.046565110167522487.4821729535563
Trimmed Mean ( 43 / 43 )4.075333333333330.046728962748984387.2121505291045
Median4.16
Midrange4.375
Midmean - Weighted Average at Xnp4.08621621621621
Midmean - Weighted Average at X(n+1)p4.08621621621621
Midmean - Empirical Distribution Function4.08621621621621
Midmean - Empirical Distribution Function - Averaging4.08621621621621
Midmean - Empirical Distribution Function - Interpolation4.08621621621621
Midmean - Closest Observation4.08621621621621
Midmean - True Basic - Statistics Graphics Toolkit4.08621621621621
Midmean - MS Excel (old versions)4.08621621621621
Number of observations131



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')