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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 15:26:54 -0500
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/07/t1331152115ytqaucp1c9sjw80.htm/, Retrieved Sun, 28 Apr 2024 22:37:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163699, Retrieved Sun, 28 Apr 2024 22:37:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave5 Oefening2...] [2012-03-07 20:26:54] [8c2ac70842cc3f093ee1ba38f92d16ef] [Current]
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Dataseries X:
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695
32.436
30.160
30.236
31.293
31.077
32.226
33.865
32.810
32.242
32.700
32.819
33.947
34.148
35.261
39.506
41.591
39.148
41.216
40.225
41.126
42.362




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163699&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163699&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163699&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23.60337333333330.95909883675096624.6099488695992
Geometric Mean22.30718729743
Harmonic Mean21.1905606559262
Quadratic Mean25.0037928229565
Winsorized Mean ( 1 / 25 )23.60285333333330.95513327058278824.7115811586499
Winsorized Mean ( 2 / 25 )23.60197333333330.95146089398523524.8060361519173
Winsorized Mean ( 3 / 25 )23.60017333333330.95033964689412924.8334092031861
Winsorized Mean ( 4 / 25 )23.55334666666670.93843081550697925.0986500842283
Winsorized Mean ( 5 / 25 )23.51761333333330.92557956401971825.4085269895094
Winsorized Mean ( 6 / 25 )23.49145333333330.91863500526514825.5721295168291
Winsorized Mean ( 7 / 25 )23.14145333333330.83959813859961627.5625353004373
Winsorized Mean ( 8 / 25 )23.051960.81340836932852728.3399592003578
Winsorized Mean ( 9 / 25 )23.029640.80876161826930528.4751890789302
Winsorized Mean ( 10 / 25 )23.02590666666670.80587813604325628.5724424535458
Winsorized Mean ( 11 / 25 )22.87762666666670.7780408682782129.4041452055011
Winsorized Mean ( 12 / 25 )22.88098666666670.77719321713094929.4405382887065
Winsorized Mean ( 13 / 25 )22.883760.77119848296176229.6729836813419
Winsorized Mean ( 14 / 25 )22.85109333333330.76071751600811830.0388683742225
Winsorized Mean ( 15 / 25 )22.81409333333330.75391417179997430.260862823237
Winsorized Mean ( 16 / 25 )22.82518666666670.75155367210309830.3706674771399
Winsorized Mean ( 17 / 25 )22.62390666666670.71508450283067131.6380883337698
Winsorized Mean ( 18 / 25 )22.60110666666670.70301628101899432.1487670725168
Winsorized Mean ( 19 / 25 )22.54917333333330.68179249158081533.073367060776
Winsorized Mean ( 20 / 25 )22.45077333333330.65918805983165734.0582220786384
Winsorized Mean ( 21 / 25 )22.59581333333330.63568525547918335.5455992388883
Winsorized Mean ( 22 / 25 )21.83226666666670.51411674326528842.4655818987811
Winsorized Mean ( 23 / 25 )21.69150666666670.44066137655027549.2248874554857
Winsorized Mean ( 24 / 25 )21.48478666666670.40682262965277352.8111887114149
Winsorized Mean ( 25 / 25 )21.41778666666670.36807363750780758.1888635428622
Trimmed Mean ( 1 / 25 )23.48053424657530.9412360226913324.946489170098
Trimmed Mean ( 2 / 25 )23.3513239436620.92444851530768725.2597343789231
Trimmed Mean ( 3 / 25 )23.21510144927540.90646282047531425.6106493558139
Trimmed Mean ( 4 / 25 )23.07141791044780.88513638842783226.0653818011334
Trimmed Mean ( 5 / 25 )22.93240.86367596749413126.5520876614595
Trimmed Mean ( 6 / 25 )22.79306349206350.84157504995521727.0838156303189
Trimmed Mean ( 7 / 25 )22.64995081967210.81642028125393227.7430036217183
Trimmed Mean ( 8 / 25 )22.56069491525420.80654958879791527.9718633901714
Trimmed Mean ( 9 / 25 )22.47989473684210.79996578587716328.1010702378888
Trimmed Mean ( 10 / 25 )22.39660.79209342568716928.2751999621385
Trimmed Mean ( 11 / 25 )22.30754716981130.78213115344839228.5214916596252
Trimmed Mean ( 12 / 25 )22.23133333333330.77491403984592228.688773451251
Trimmed Mean ( 13 / 25 )22.14846938775510.76501986830166328.9514956479817
Trimmed Mean ( 14 / 25 )22.05821276595740.75272972923178229.3042933065358
Trimmed Mean ( 15 / 25 )21.96382222222220.738314595349429.7485954640082
Trimmed Mean ( 16 / 25 )21.86495348837210.72026929253515330.3566370453103
Trimmed Mean ( 17 / 25 )21.75517073170730.69613321449277831.2514476809712
Trimmed Mean ( 18 / 25 )21.65689743589740.67280435802439332.1889969611526
Trimmed Mean ( 19 / 25 )21.55056756756760.64351631569010833.4887663950784
Trimmed Mean ( 20 / 25 )21.43794285714290.608391971923235.2370574341652
Trimmed Mean ( 21 / 25 )21.32284848484850.56543858868850937.710281737766
Trimmed Mean ( 22 / 25 )21.17619354838710.50847843531600141.646197906558
Trimmed Mean ( 23 / 25 )21.09906896551720.47481111082528344.4367633454161
Trimmed Mean ( 24 / 25 )21.02751851851850.45114799237799646.6089151980544
Trimmed Mean ( 25 / 25 )20.970360.42783673630642549.0148652989458
Median20.83
Midrange28.087
Midmean - Weighted Average at Xnp21.409
Midmean - Weighted Average at X(n+1)p21.6568974358974
Midmean - Empirical Distribution Function21.6568974358974
Midmean - Empirical Distribution Function - Averaging21.6568974358974
Midmean - Empirical Distribution Function - Interpolation21.5505675675676
Midmean - Closest Observation21.409
Midmean - True Basic - Statistics Graphics Toolkit21.6568974358974
Midmean - MS Excel (old versions)21.6568974358974
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23.6033733333333 & 0.959098836750966 & 24.6099488695992 \tabularnewline
Geometric Mean & 22.30718729743 &  &  \tabularnewline
Harmonic Mean & 21.1905606559262 &  &  \tabularnewline
Quadratic Mean & 25.0037928229565 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 23.6028533333333 & 0.955133270582788 & 24.7115811586499 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 23.6019733333333 & 0.951460893985235 & 24.8060361519173 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 23.6001733333333 & 0.950339646894129 & 24.8334092031861 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 23.5533466666667 & 0.938430815506979 & 25.0986500842283 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 23.5176133333333 & 0.925579564019718 & 25.4085269895094 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 23.4914533333333 & 0.918635005265148 & 25.5721295168291 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 23.1414533333333 & 0.839598138599616 & 27.5625353004373 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 23.05196 & 0.813408369328527 & 28.3399592003578 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 23.02964 & 0.808761618269305 & 28.4751890789302 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 23.0259066666667 & 0.805878136043256 & 28.5724424535458 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 22.8776266666667 & 0.77804086827821 & 29.4041452055011 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 22.8809866666667 & 0.777193217130949 & 29.4405382887065 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 22.88376 & 0.771198482961762 & 29.6729836813419 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 22.8510933333333 & 0.760717516008118 & 30.0388683742225 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 22.8140933333333 & 0.753914171799974 & 30.260862823237 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 22.8251866666667 & 0.751553672103098 & 30.3706674771399 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 22.6239066666667 & 0.715084502830671 & 31.6380883337698 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 22.6011066666667 & 0.703016281018994 & 32.1487670725168 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 22.5491733333333 & 0.681792491580815 & 33.073367060776 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 22.4507733333333 & 0.659188059831657 & 34.0582220786384 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 22.5958133333333 & 0.635685255479183 & 35.5455992388883 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 21.8322666666667 & 0.514116743265288 & 42.4655818987811 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 21.6915066666667 & 0.440661376550275 & 49.2248874554857 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 21.4847866666667 & 0.406822629652773 & 52.8111887114149 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 21.4177866666667 & 0.368073637507807 & 58.1888635428622 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 23.4805342465753 & 0.94123602269133 & 24.946489170098 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 23.351323943662 & 0.924448515307687 & 25.2597343789231 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 23.2151014492754 & 0.906462820475314 & 25.6106493558139 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 23.0714179104478 & 0.885136388427832 & 26.0653818011334 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 22.9324 & 0.863675967494131 & 26.5520876614595 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 22.7930634920635 & 0.841575049955217 & 27.0838156303189 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 22.6499508196721 & 0.816420281253932 & 27.7430036217183 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 22.5606949152542 & 0.806549588797915 & 27.9718633901714 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 22.4798947368421 & 0.799965785877163 & 28.1010702378888 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 22.3966 & 0.792093425687169 & 28.2751999621385 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 22.3075471698113 & 0.782131153448392 & 28.5214916596252 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 22.2313333333333 & 0.774914039845922 & 28.688773451251 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 22.1484693877551 & 0.765019868301663 & 28.9514956479817 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 22.0582127659574 & 0.752729729231782 & 29.3042933065358 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 21.9638222222222 & 0.7383145953494 & 29.7485954640082 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 21.8649534883721 & 0.720269292535153 & 30.3566370453103 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 21.7551707317073 & 0.696133214492778 & 31.2514476809712 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 21.6568974358974 & 0.672804358024393 & 32.1889969611526 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 21.5505675675676 & 0.643516315690108 & 33.4887663950784 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 21.4379428571429 & 0.6083919719232 & 35.2370574341652 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 21.3228484848485 & 0.565438588688509 & 37.710281737766 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 21.1761935483871 & 0.508478435316001 & 41.646197906558 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 21.0990689655172 & 0.474811110825283 & 44.4367633454161 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 21.0275185185185 & 0.451147992377996 & 46.6089151980544 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 20.97036 & 0.427836736306425 & 49.0148652989458 \tabularnewline
Median & 20.83 &  &  \tabularnewline
Midrange & 28.087 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.409 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.6568974358974 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.6568974358974 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.6568974358974 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.5505675675676 &  &  \tabularnewline
Midmean - Closest Observation & 21.409 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.6568974358974 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.6568974358974 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163699&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]23.6033733333333[/C][C]0.959098836750966[/C][C]24.6099488695992[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22.30718729743[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.1905606559262[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]25.0037928229565[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]23.6028533333333[/C][C]0.955133270582788[/C][C]24.7115811586499[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]23.6019733333333[/C][C]0.951460893985235[/C][C]24.8060361519173[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]23.6001733333333[/C][C]0.950339646894129[/C][C]24.8334092031861[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]23.5533466666667[/C][C]0.938430815506979[/C][C]25.0986500842283[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]23.5176133333333[/C][C]0.925579564019718[/C][C]25.4085269895094[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]23.4914533333333[/C][C]0.918635005265148[/C][C]25.5721295168291[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]23.1414533333333[/C][C]0.839598138599616[/C][C]27.5625353004373[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]23.05196[/C][C]0.813408369328527[/C][C]28.3399592003578[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]23.02964[/C][C]0.808761618269305[/C][C]28.4751890789302[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]23.0259066666667[/C][C]0.805878136043256[/C][C]28.5724424535458[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]22.8776266666667[/C][C]0.77804086827821[/C][C]29.4041452055011[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]22.8809866666667[/C][C]0.777193217130949[/C][C]29.4405382887065[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]22.88376[/C][C]0.771198482961762[/C][C]29.6729836813419[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]22.8510933333333[/C][C]0.760717516008118[/C][C]30.0388683742225[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]22.8140933333333[/C][C]0.753914171799974[/C][C]30.260862823237[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]22.8251866666667[/C][C]0.751553672103098[/C][C]30.3706674771399[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]22.6239066666667[/C][C]0.715084502830671[/C][C]31.6380883337698[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]22.6011066666667[/C][C]0.703016281018994[/C][C]32.1487670725168[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]22.5491733333333[/C][C]0.681792491580815[/C][C]33.073367060776[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]22.4507733333333[/C][C]0.659188059831657[/C][C]34.0582220786384[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]22.5958133333333[/C][C]0.635685255479183[/C][C]35.5455992388883[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]21.8322666666667[/C][C]0.514116743265288[/C][C]42.4655818987811[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]21.6915066666667[/C][C]0.440661376550275[/C][C]49.2248874554857[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]21.4847866666667[/C][C]0.406822629652773[/C][C]52.8111887114149[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]21.4177866666667[/C][C]0.368073637507807[/C][C]58.1888635428622[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]23.4805342465753[/C][C]0.94123602269133[/C][C]24.946489170098[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]23.351323943662[/C][C]0.924448515307687[/C][C]25.2597343789231[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]23.2151014492754[/C][C]0.906462820475314[/C][C]25.6106493558139[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]23.0714179104478[/C][C]0.885136388427832[/C][C]26.0653818011334[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]22.9324[/C][C]0.863675967494131[/C][C]26.5520876614595[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]22.7930634920635[/C][C]0.841575049955217[/C][C]27.0838156303189[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]22.6499508196721[/C][C]0.816420281253932[/C][C]27.7430036217183[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]22.5606949152542[/C][C]0.806549588797915[/C][C]27.9718633901714[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]22.4798947368421[/C][C]0.799965785877163[/C][C]28.1010702378888[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]22.3966[/C][C]0.792093425687169[/C][C]28.2751999621385[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]22.3075471698113[/C][C]0.782131153448392[/C][C]28.5214916596252[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]22.2313333333333[/C][C]0.774914039845922[/C][C]28.688773451251[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]22.1484693877551[/C][C]0.765019868301663[/C][C]28.9514956479817[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]22.0582127659574[/C][C]0.752729729231782[/C][C]29.3042933065358[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]21.9638222222222[/C][C]0.7383145953494[/C][C]29.7485954640082[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]21.8649534883721[/C][C]0.720269292535153[/C][C]30.3566370453103[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]21.7551707317073[/C][C]0.696133214492778[/C][C]31.2514476809712[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]21.6568974358974[/C][C]0.672804358024393[/C][C]32.1889969611526[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]21.5505675675676[/C][C]0.643516315690108[/C][C]33.4887663950784[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]21.4379428571429[/C][C]0.6083919719232[/C][C]35.2370574341652[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]21.3228484848485[/C][C]0.565438588688509[/C][C]37.710281737766[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]21.1761935483871[/C][C]0.508478435316001[/C][C]41.646197906558[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]21.0990689655172[/C][C]0.474811110825283[/C][C]44.4367633454161[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]21.0275185185185[/C][C]0.451147992377996[/C][C]46.6089151980544[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]20.97036[/C][C]0.427836736306425[/C][C]49.0148652989458[/C][/ROW]
[ROW][C]Median[/C][C]20.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]28.087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.409[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.6568974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.6568974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.6568974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.5505675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.409[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.6568974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.6568974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163699&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163699&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 Mean23.60337333333330.95909883675096624.6099488695992
Geometric Mean22.30718729743
Harmonic Mean21.1905606559262
Quadratic Mean25.0037928229565
Winsorized Mean ( 1 / 25 )23.60285333333330.95513327058278824.7115811586499
Winsorized Mean ( 2 / 25 )23.60197333333330.95146089398523524.8060361519173
Winsorized Mean ( 3 / 25 )23.60017333333330.95033964689412924.8334092031861
Winsorized Mean ( 4 / 25 )23.55334666666670.93843081550697925.0986500842283
Winsorized Mean ( 5 / 25 )23.51761333333330.92557956401971825.4085269895094
Winsorized Mean ( 6 / 25 )23.49145333333330.91863500526514825.5721295168291
Winsorized Mean ( 7 / 25 )23.14145333333330.83959813859961627.5625353004373
Winsorized Mean ( 8 / 25 )23.051960.81340836932852728.3399592003578
Winsorized Mean ( 9 / 25 )23.029640.80876161826930528.4751890789302
Winsorized Mean ( 10 / 25 )23.02590666666670.80587813604325628.5724424535458
Winsorized Mean ( 11 / 25 )22.87762666666670.7780408682782129.4041452055011
Winsorized Mean ( 12 / 25 )22.88098666666670.77719321713094929.4405382887065
Winsorized Mean ( 13 / 25 )22.883760.77119848296176229.6729836813419
Winsorized Mean ( 14 / 25 )22.85109333333330.76071751600811830.0388683742225
Winsorized Mean ( 15 / 25 )22.81409333333330.75391417179997430.260862823237
Winsorized Mean ( 16 / 25 )22.82518666666670.75155367210309830.3706674771399
Winsorized Mean ( 17 / 25 )22.62390666666670.71508450283067131.6380883337698
Winsorized Mean ( 18 / 25 )22.60110666666670.70301628101899432.1487670725168
Winsorized Mean ( 19 / 25 )22.54917333333330.68179249158081533.073367060776
Winsorized Mean ( 20 / 25 )22.45077333333330.65918805983165734.0582220786384
Winsorized Mean ( 21 / 25 )22.59581333333330.63568525547918335.5455992388883
Winsorized Mean ( 22 / 25 )21.83226666666670.51411674326528842.4655818987811
Winsorized Mean ( 23 / 25 )21.69150666666670.44066137655027549.2248874554857
Winsorized Mean ( 24 / 25 )21.48478666666670.40682262965277352.8111887114149
Winsorized Mean ( 25 / 25 )21.41778666666670.36807363750780758.1888635428622
Trimmed Mean ( 1 / 25 )23.48053424657530.9412360226913324.946489170098
Trimmed Mean ( 2 / 25 )23.3513239436620.92444851530768725.2597343789231
Trimmed Mean ( 3 / 25 )23.21510144927540.90646282047531425.6106493558139
Trimmed Mean ( 4 / 25 )23.07141791044780.88513638842783226.0653818011334
Trimmed Mean ( 5 / 25 )22.93240.86367596749413126.5520876614595
Trimmed Mean ( 6 / 25 )22.79306349206350.84157504995521727.0838156303189
Trimmed Mean ( 7 / 25 )22.64995081967210.81642028125393227.7430036217183
Trimmed Mean ( 8 / 25 )22.56069491525420.80654958879791527.9718633901714
Trimmed Mean ( 9 / 25 )22.47989473684210.79996578587716328.1010702378888
Trimmed Mean ( 10 / 25 )22.39660.79209342568716928.2751999621385
Trimmed Mean ( 11 / 25 )22.30754716981130.78213115344839228.5214916596252
Trimmed Mean ( 12 / 25 )22.23133333333330.77491403984592228.688773451251
Trimmed Mean ( 13 / 25 )22.14846938775510.76501986830166328.9514956479817
Trimmed Mean ( 14 / 25 )22.05821276595740.75272972923178229.3042933065358
Trimmed Mean ( 15 / 25 )21.96382222222220.738314595349429.7485954640082
Trimmed Mean ( 16 / 25 )21.86495348837210.72026929253515330.3566370453103
Trimmed Mean ( 17 / 25 )21.75517073170730.69613321449277831.2514476809712
Trimmed Mean ( 18 / 25 )21.65689743589740.67280435802439332.1889969611526
Trimmed Mean ( 19 / 25 )21.55056756756760.64351631569010833.4887663950784
Trimmed Mean ( 20 / 25 )21.43794285714290.608391971923235.2370574341652
Trimmed Mean ( 21 / 25 )21.32284848484850.56543858868850937.710281737766
Trimmed Mean ( 22 / 25 )21.17619354838710.50847843531600141.646197906558
Trimmed Mean ( 23 / 25 )21.09906896551720.47481111082528344.4367633454161
Trimmed Mean ( 24 / 25 )21.02751851851850.45114799237799646.6089151980544
Trimmed Mean ( 25 / 25 )20.970360.42783673630642549.0148652989458
Median20.83
Midrange28.087
Midmean - Weighted Average at Xnp21.409
Midmean - Weighted Average at X(n+1)p21.6568974358974
Midmean - Empirical Distribution Function21.6568974358974
Midmean - Empirical Distribution Function - Averaging21.6568974358974
Midmean - Empirical Distribution Function - Interpolation21.5505675675676
Midmean - Closest Observation21.409
Midmean - True Basic - Statistics Graphics Toolkit21.6568974358974
Midmean - MS Excel (old versions)21.6568974358974
Number of observations75



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')