Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 07 Jun 2009 09:38:13 -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/Jun/07/t1244389116boxtvr80hpv0uox.htm/, Retrieved Sun, 12 May 2024 15:19:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42167, Retrieved Sun, 12 May 2024 15:19:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Quartiles] [] [2009-06-07 13:46:35] [20f4bab96040345df1f930341b3cf3a9]
- RM      [Central Tendency] [] [2009-06-07 15:38:13] [e921d89db97faa9283224ee60d8fb091] [Current]
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Dataseries X:
49.32
58.53
49.09
24.68
16.71
19.86
38.23
36.11
19.59
14.91
15.74
15.40
13.06
19.07
15.28
15.82
12.77
12.05
11.69
13.85
13.85
10.07
9.17
10.79
13.44
21.17
18.64
13.21
15.54
21.94
23.11
18.64
14.94
16.90
15.46
11.15
13.13
12.48
12.95
12.59
10.58
10.58
12.39
15.53
13.06
10.22
16.33
19.72
21.31
18.84
24.84
15.67
15.57
12.73
13.56
15.54
17.22
12.14
11.07
12.02
11.55
6.92
10.33
8.38
12.11
11.46
12.75
13.32
13.00
11.90
11.79
12.55
11.84
11.25
11.15
10.99
11.70
14.01
17.51
17.27
16.90
15.79
15.45
16.24
16.71
16.77
16.64
17.80
16.87
16.13
15.76
15.66
15.54
15.30
15.05
14.69
14.39
14.18
13.70
13.66
13.27
13.56
13.14
14.19
22.57
23.09
23.31
22.91
22.36
43.06
64.67
64.68
56.90
48.79
45.21
41.40
22.17
25.52
20.28
22.87
27.63
22.95
21.35
18.38
17.15
18.27
19.40
20.52




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42167&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42167&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42167&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.862968750.97789422769703319.2893752879826
Geometric Mean16.9185524260768
Harmonic Mean15.6868235534847
Quadratic Mean21.8462533257994
Winsorized Mean ( 1 / 42 )18.8742968750.9768344825728819.3218986550179
Winsorized Mean ( 2 / 42 )18.7907031250.94214449387422619.9446085469651
Winsorized Mean ( 3 / 42 )18.773593750.92799233843633820.2303327004115
Winsorized Mean ( 4 / 42 )18.541406250.85558326342285321.6710717035571
Winsorized Mean ( 5 / 42 )18.536718750.85271607588344821.7384417560033
Winsorized Mean ( 6 / 42 )18.5343750.84787982271935621.8596722122196
Winsorized Mean ( 7 / 42 )18.338593750.7942506150749523.0891779016998
Winsorized Mean ( 8 / 42 )18.217343750.75798910533969324.0337804615752
Winsorized Mean ( 9 / 42 )18.11468750.72712060839472324.9129061820873
Winsorized Mean ( 10 / 42 )17.873281250.66551847378121826.8561759802864
Winsorized Mean ( 11 / 42 )17.697968750.62175274892789728.4646409372810
Winsorized Mean ( 12 / 42 )16.902968750.45185234134409137.4081690043256
Winsorized Mean ( 13 / 42 )16.6988281250.41266152917505440.4661615983016
Winsorized Mean ( 14 / 42 )16.6474218750.39799766805316841.82793822997
Winsorized Mean ( 15 / 42 )16.639218750.39389344983138142.2429435095277
Winsorized Mean ( 16 / 42 )16.485468750.36571194217282945.0777424769172
Winsorized Mean ( 17 / 42 )16.4602343750.36170028650040545.5079384488725
Winsorized Mean ( 18 / 42 )16.4700781250.35998951647187945.7515493407058
Winsorized Mean ( 19 / 42 )16.456718750.35623504785197446.1962371451960
Winsorized Mean ( 20 / 42 )16.459843750.35438541928007546.4461652610815
Winsorized Mean ( 21 / 42 )16.472968750.35146551237631946.8693745756829
Winsorized Mean ( 22 / 42 )16.42656250.34362485978255547.803766323527
Winsorized Mean ( 23 / 42 )16.3996093750.33726259152042348.6256400422841
Winsorized Mean ( 24 / 42 )16.3696093750.33176752401262249.3406020487323
Winsorized Mean ( 25 / 42 )16.3735156250.32076677077483251.0449245894415
Winsorized Mean ( 26 / 42 )16.2719531250.30286521477269953.7267151568138
Winsorized Mean ( 27 / 42 )16.278281250.30030207702862254.2063558503078
Winsorized Mean ( 28 / 42 )16.256406250.29542110805148955.0279103521833
Winsorized Mean ( 29 / 42 )16.1408593750.27336873071885859.0442781533775
Winsorized Mean ( 30 / 42 )16.0892968750.26586767362146860.5161833172215
Winsorized Mean ( 31 / 42 )15.9924218750.25294504870337963.2248860255565
Winsorized Mean ( 32 / 42 )16.0024218750.24426917619533165.5114252409956
Winsorized Mean ( 33 / 42 )15.9817968750.23900137840162366.8690573329826
Winsorized Mean ( 34 / 42 )15.9472656250.23147176839205768.895078375127
Winsorized Mean ( 35 / 42 )15.857031250.22100486774529171.7496922659426
Winsorized Mean ( 36 / 42 )15.812031250.21169545354439274.6923516082233
Winsorized Mean ( 37 / 42 )15.7571093750.20494787460093876.8834973560047
Winsorized Mean ( 38 / 42 )15.7778906250.20286744429557177.7743845484254
Winsorized Mean ( 39 / 42 )15.7169531250.19231979622007781.7230125754432
Winsorized Mean ( 40 / 42 )15.6982031250.18701964169005383.9387937178094
Winsorized Mean ( 41 / 42 )15.586093750.16713473933390493.2546627476522
Winsorized Mean ( 42 / 42 )15.53031250.153348209783002101.274821023189
Trimmed Mean ( 1 / 42 )18.5941269841270.9187396216096520.2387341818890
Trimmed Mean ( 2 / 42 )18.30491935483870.85142747798914221.4990939663708
Trimmed Mean ( 3 / 42 )18.05008196721310.79573388747168422.6835657641330
Trimmed Mean ( 4 / 42 )17.79283333333330.73746516020193924.1270154761767
Trimmed Mean ( 5 / 42 )17.58983050847460.69715563109579525.2308519416629
Trimmed Mean ( 6 / 42 )17.38086206896550.65137631441662926.6832884221953
Trimmed Mean ( 7 / 42 )17.1650.59899165191884628.6564928659901
Trimmed Mean ( 8 / 42 )16.97339285714290.55199048312590830.7494302456502
Trimmed Mean ( 9 / 42 )16.79245454545450.50564806906337233.2097669759913
Trimmed Mean ( 10 / 42 )16.61833333333330.45791458261402636.2913389620982
Trimmed Mean ( 11 / 42 )16.46679245283020.41564705177260239.6172482942067
Trimmed Mean ( 12 / 42 )16.32903846153850.37504653729735643.5386994350303
Trimmed Mean ( 13 / 42 )16.26901960784310.36224553952093544.9115802208598
Trimmed Mean ( 14 / 42 )16.22670.35403832055900745.8331741444794
Trimmed Mean ( 15 / 42 )16.18744897959180.34688291604247546.6654546273755
Trimmed Mean ( 16 / 42 )16.14729166666670.33931876667865247.587381696335
Trimmed Mean ( 17 / 42 )16.11851063829790.33461235822649448.1706973517921
Trimmed Mean ( 18 / 42 )16.09054347826090.32974922655848748.7963039252403
Trimmed Mean ( 19 / 42 )16.06055555555560.32436583133416949.5137095343733
Trimmed Mean ( 20 / 42 )16.03022727272730.3186552521616750.3058624139492
Trimmed Mean ( 21 / 42 )15.99825581395350.31229288367579051.2283713469508
Trimmed Mean ( 22 / 42 )15.96380952380950.30528294038145852.2918493377401
Trimmed Mean ( 23 / 42 )15.93097560975610.29822472877250353.4193649042056
Trimmed Mean ( 24 / 42 )15.8983750.29087082498513354.6578537081284
Trimmed Mean ( 25 / 42 )15.86615384615380.28304550800070156.0551338836811
Trimmed Mean ( 26 / 42 )15.83197368421050.27533240004961757.501309985158
Trimmed Mean ( 27 / 42 )15.80270270270270.26881528015079658.7864748381787
Trimmed Mean ( 28 / 42 )15.77138888888890.26142757725922160.3279464784644
Trimmed Mean ( 29 / 42 )15.73971428571430.25335839241555562.1243059511454
Trimmed Mean ( 30 / 42 )15.71367647058820.24705658876346263.6035515152073
Trimmed Mean ( 31 / 42 )15.68939393939390.24063376681941565.2003006343168
Trimmed Mean ( 32 / 42 )15.669843750.23489565103334766.7098078702846
Trimmed Mean ( 33 / 42 )15.64838709677420.22917761529457768.280608804923
Trimmed Mean ( 34 / 42 )15.62683333333330.22301319811804870.0713386705549
Trimmed Mean ( 35 / 42 )15.60603448275860.21667549979507272.0249151266228
Trimmed Mean ( 36 / 42 )15.58964285714290.21068425385810873.9952918723684
Trimmed Mean ( 37 / 42 )15.5750.20484040420524676.0348040730976
Trimmed Mean ( 38 / 42 )15.56288461538460.19874916859316778.3041495244758
Trimmed Mean ( 39 / 42 )15.54840.19138813218916581.2401470360359
Trimmed Mean ( 40 / 42 )15.5368750.18417757491121884.3581256159415
Trimmed Mean ( 41 / 42 )15.52565217391300.17602197166705388.2029216402594
Trimmed Mean ( 42 / 42 )15.52136363636360.16989755366994891.3571932090103
Median15.54
Midrange35.8
Midmean - Weighted Average at Xnp15.6252307692308
Midmean - Weighted Average at X(n+1)p15.66984375
Midmean - Empirical Distribution Function15.6252307692308
Midmean - Empirical Distribution Function - Averaging15.66984375
Midmean - Empirical Distribution Function - Interpolation15.66984375
Midmean - Closest Observation15.6252307692308
Midmean - True Basic - Statistics Graphics Toolkit15.66984375
Midmean - MS Excel (old versions)15.6893939393939
Number of observations128

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.86296875 & 0.977894227697033 & 19.2893752879826 \tabularnewline
Geometric Mean & 16.9185524260768 &  &  \tabularnewline
Harmonic Mean & 15.6868235534847 &  &  \tabularnewline
Quadratic Mean & 21.8462533257994 &  &  \tabularnewline
Winsorized Mean ( 1 / 42 ) & 18.874296875 & 0.97683448257288 & 19.3218986550179 \tabularnewline
Winsorized Mean ( 2 / 42 ) & 18.790703125 & 0.942144493874226 & 19.9446085469651 \tabularnewline
Winsorized Mean ( 3 / 42 ) & 18.77359375 & 0.927992338436338 & 20.2303327004115 \tabularnewline
Winsorized Mean ( 4 / 42 ) & 18.54140625 & 0.855583263422853 & 21.6710717035571 \tabularnewline
Winsorized Mean ( 5 / 42 ) & 18.53671875 & 0.852716075883448 & 21.7384417560033 \tabularnewline
Winsorized Mean ( 6 / 42 ) & 18.534375 & 0.847879822719356 & 21.8596722122196 \tabularnewline
Winsorized Mean ( 7 / 42 ) & 18.33859375 & 0.79425061507495 & 23.0891779016998 \tabularnewline
Winsorized Mean ( 8 / 42 ) & 18.21734375 & 0.757989105339693 & 24.0337804615752 \tabularnewline
Winsorized Mean ( 9 / 42 ) & 18.1146875 & 0.727120608394723 & 24.9129061820873 \tabularnewline
Winsorized Mean ( 10 / 42 ) & 17.87328125 & 0.665518473781218 & 26.8561759802864 \tabularnewline
Winsorized Mean ( 11 / 42 ) & 17.69796875 & 0.621752748927897 & 28.4646409372810 \tabularnewline
Winsorized Mean ( 12 / 42 ) & 16.90296875 & 0.451852341344091 & 37.4081690043256 \tabularnewline
Winsorized Mean ( 13 / 42 ) & 16.698828125 & 0.412661529175054 & 40.4661615983016 \tabularnewline
Winsorized Mean ( 14 / 42 ) & 16.647421875 & 0.397997668053168 & 41.82793822997 \tabularnewline
Winsorized Mean ( 15 / 42 ) & 16.63921875 & 0.393893449831381 & 42.2429435095277 \tabularnewline
Winsorized Mean ( 16 / 42 ) & 16.48546875 & 0.365711942172829 & 45.0777424769172 \tabularnewline
Winsorized Mean ( 17 / 42 ) & 16.460234375 & 0.361700286500405 & 45.5079384488725 \tabularnewline
Winsorized Mean ( 18 / 42 ) & 16.470078125 & 0.359989516471879 & 45.7515493407058 \tabularnewline
Winsorized Mean ( 19 / 42 ) & 16.45671875 & 0.356235047851974 & 46.1962371451960 \tabularnewline
Winsorized Mean ( 20 / 42 ) & 16.45984375 & 0.354385419280075 & 46.4461652610815 \tabularnewline
Winsorized Mean ( 21 / 42 ) & 16.47296875 & 0.351465512376319 & 46.8693745756829 \tabularnewline
Winsorized Mean ( 22 / 42 ) & 16.4265625 & 0.343624859782555 & 47.803766323527 \tabularnewline
Winsorized Mean ( 23 / 42 ) & 16.399609375 & 0.337262591520423 & 48.6256400422841 \tabularnewline
Winsorized Mean ( 24 / 42 ) & 16.369609375 & 0.331767524012622 & 49.3406020487323 \tabularnewline
Winsorized Mean ( 25 / 42 ) & 16.373515625 & 0.320766770774832 & 51.0449245894415 \tabularnewline
Winsorized Mean ( 26 / 42 ) & 16.271953125 & 0.302865214772699 & 53.7267151568138 \tabularnewline
Winsorized Mean ( 27 / 42 ) & 16.27828125 & 0.300302077028622 & 54.2063558503078 \tabularnewline
Winsorized Mean ( 28 / 42 ) & 16.25640625 & 0.295421108051489 & 55.0279103521833 \tabularnewline
Winsorized Mean ( 29 / 42 ) & 16.140859375 & 0.273368730718858 & 59.0442781533775 \tabularnewline
Winsorized Mean ( 30 / 42 ) & 16.089296875 & 0.265867673621468 & 60.5161833172215 \tabularnewline
Winsorized Mean ( 31 / 42 ) & 15.992421875 & 0.252945048703379 & 63.2248860255565 \tabularnewline
Winsorized Mean ( 32 / 42 ) & 16.002421875 & 0.244269176195331 & 65.5114252409956 \tabularnewline
Winsorized Mean ( 33 / 42 ) & 15.981796875 & 0.239001378401623 & 66.8690573329826 \tabularnewline
Winsorized Mean ( 34 / 42 ) & 15.947265625 & 0.231471768392057 & 68.895078375127 \tabularnewline
Winsorized Mean ( 35 / 42 ) & 15.85703125 & 0.221004867745291 & 71.7496922659426 \tabularnewline
Winsorized Mean ( 36 / 42 ) & 15.81203125 & 0.211695453544392 & 74.6923516082233 \tabularnewline
Winsorized Mean ( 37 / 42 ) & 15.757109375 & 0.204947874600938 & 76.8834973560047 \tabularnewline
Winsorized Mean ( 38 / 42 ) & 15.777890625 & 0.202867444295571 & 77.7743845484254 \tabularnewline
Winsorized Mean ( 39 / 42 ) & 15.716953125 & 0.192319796220077 & 81.7230125754432 \tabularnewline
Winsorized Mean ( 40 / 42 ) & 15.698203125 & 0.187019641690053 & 83.9387937178094 \tabularnewline
Winsorized Mean ( 41 / 42 ) & 15.58609375 & 0.167134739333904 & 93.2546627476522 \tabularnewline
Winsorized Mean ( 42 / 42 ) & 15.5303125 & 0.153348209783002 & 101.274821023189 \tabularnewline
Trimmed Mean ( 1 / 42 ) & 18.594126984127 & 0.91873962160965 & 20.2387341818890 \tabularnewline
Trimmed Mean ( 2 / 42 ) & 18.3049193548387 & 0.851427477989142 & 21.4990939663708 \tabularnewline
Trimmed Mean ( 3 / 42 ) & 18.0500819672131 & 0.795733887471684 & 22.6835657641330 \tabularnewline
Trimmed Mean ( 4 / 42 ) & 17.7928333333333 & 0.737465160201939 & 24.1270154761767 \tabularnewline
Trimmed Mean ( 5 / 42 ) & 17.5898305084746 & 0.697155631095795 & 25.2308519416629 \tabularnewline
Trimmed Mean ( 6 / 42 ) & 17.3808620689655 & 0.651376314416629 & 26.6832884221953 \tabularnewline
Trimmed Mean ( 7 / 42 ) & 17.165 & 0.598991651918846 & 28.6564928659901 \tabularnewline
Trimmed Mean ( 8 / 42 ) & 16.9733928571429 & 0.551990483125908 & 30.7494302456502 \tabularnewline
Trimmed Mean ( 9 / 42 ) & 16.7924545454545 & 0.505648069063372 & 33.2097669759913 \tabularnewline
Trimmed Mean ( 10 / 42 ) & 16.6183333333333 & 0.457914582614026 & 36.2913389620982 \tabularnewline
Trimmed Mean ( 11 / 42 ) & 16.4667924528302 & 0.415647051772602 & 39.6172482942067 \tabularnewline
Trimmed Mean ( 12 / 42 ) & 16.3290384615385 & 0.375046537297356 & 43.5386994350303 \tabularnewline
Trimmed Mean ( 13 / 42 ) & 16.2690196078431 & 0.362245539520935 & 44.9115802208598 \tabularnewline
Trimmed Mean ( 14 / 42 ) & 16.2267 & 0.354038320559007 & 45.8331741444794 \tabularnewline
Trimmed Mean ( 15 / 42 ) & 16.1874489795918 & 0.346882916042475 & 46.6654546273755 \tabularnewline
Trimmed Mean ( 16 / 42 ) & 16.1472916666667 & 0.339318766678652 & 47.587381696335 \tabularnewline
Trimmed Mean ( 17 / 42 ) & 16.1185106382979 & 0.334612358226494 & 48.1706973517921 \tabularnewline
Trimmed Mean ( 18 / 42 ) & 16.0905434782609 & 0.329749226558487 & 48.7963039252403 \tabularnewline
Trimmed Mean ( 19 / 42 ) & 16.0605555555556 & 0.324365831334169 & 49.5137095343733 \tabularnewline
Trimmed Mean ( 20 / 42 ) & 16.0302272727273 & 0.31865525216167 & 50.3058624139492 \tabularnewline
Trimmed Mean ( 21 / 42 ) & 15.9982558139535 & 0.312292883675790 & 51.2283713469508 \tabularnewline
Trimmed Mean ( 22 / 42 ) & 15.9638095238095 & 0.305282940381458 & 52.2918493377401 \tabularnewline
Trimmed Mean ( 23 / 42 ) & 15.9309756097561 & 0.298224728772503 & 53.4193649042056 \tabularnewline
Trimmed Mean ( 24 / 42 ) & 15.898375 & 0.290870824985133 & 54.6578537081284 \tabularnewline
Trimmed Mean ( 25 / 42 ) & 15.8661538461538 & 0.283045508000701 & 56.0551338836811 \tabularnewline
Trimmed Mean ( 26 / 42 ) & 15.8319736842105 & 0.275332400049617 & 57.501309985158 \tabularnewline
Trimmed Mean ( 27 / 42 ) & 15.8027027027027 & 0.268815280150796 & 58.7864748381787 \tabularnewline
Trimmed Mean ( 28 / 42 ) & 15.7713888888889 & 0.261427577259221 & 60.3279464784644 \tabularnewline
Trimmed Mean ( 29 / 42 ) & 15.7397142857143 & 0.253358392415555 & 62.1243059511454 \tabularnewline
Trimmed Mean ( 30 / 42 ) & 15.7136764705882 & 0.247056588763462 & 63.6035515152073 \tabularnewline
Trimmed Mean ( 31 / 42 ) & 15.6893939393939 & 0.240633766819415 & 65.2003006343168 \tabularnewline
Trimmed Mean ( 32 / 42 ) & 15.66984375 & 0.234895651033347 & 66.7098078702846 \tabularnewline
Trimmed Mean ( 33 / 42 ) & 15.6483870967742 & 0.229177615294577 & 68.280608804923 \tabularnewline
Trimmed Mean ( 34 / 42 ) & 15.6268333333333 & 0.223013198118048 & 70.0713386705549 \tabularnewline
Trimmed Mean ( 35 / 42 ) & 15.6060344827586 & 0.216675499795072 & 72.0249151266228 \tabularnewline
Trimmed Mean ( 36 / 42 ) & 15.5896428571429 & 0.210684253858108 & 73.9952918723684 \tabularnewline
Trimmed Mean ( 37 / 42 ) & 15.575 & 0.204840404205246 & 76.0348040730976 \tabularnewline
Trimmed Mean ( 38 / 42 ) & 15.5628846153846 & 0.198749168593167 & 78.3041495244758 \tabularnewline
Trimmed Mean ( 39 / 42 ) & 15.5484 & 0.191388132189165 & 81.2401470360359 \tabularnewline
Trimmed Mean ( 40 / 42 ) & 15.536875 & 0.184177574911218 & 84.3581256159415 \tabularnewline
Trimmed Mean ( 41 / 42 ) & 15.5256521739130 & 0.176021971667053 & 88.2029216402594 \tabularnewline
Trimmed Mean ( 42 / 42 ) & 15.5213636363636 & 0.169897553669948 & 91.3571932090103 \tabularnewline
Median & 15.54 &  &  \tabularnewline
Midrange & 35.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.6252307692308 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.66984375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.6252307692308 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.66984375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.66984375 &  &  \tabularnewline
Midmean - Closest Observation & 15.6252307692308 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.66984375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.6893939393939 &  &  \tabularnewline
Number of observations & 128 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42167&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]18.86296875[/C][C]0.977894227697033[/C][C]19.2893752879826[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.9185524260768[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.6868235534847[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.8462533257994[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 42 )[/C][C]18.874296875[/C][C]0.97683448257288[/C][C]19.3218986550179[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 42 )[/C][C]18.790703125[/C][C]0.942144493874226[/C][C]19.9446085469651[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 42 )[/C][C]18.77359375[/C][C]0.927992338436338[/C][C]20.2303327004115[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 42 )[/C][C]18.54140625[/C][C]0.855583263422853[/C][C]21.6710717035571[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 42 )[/C][C]18.53671875[/C][C]0.852716075883448[/C][C]21.7384417560033[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 42 )[/C][C]18.534375[/C][C]0.847879822719356[/C][C]21.8596722122196[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 42 )[/C][C]18.33859375[/C][C]0.79425061507495[/C][C]23.0891779016998[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 42 )[/C][C]18.21734375[/C][C]0.757989105339693[/C][C]24.0337804615752[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 42 )[/C][C]18.1146875[/C][C]0.727120608394723[/C][C]24.9129061820873[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 42 )[/C][C]17.87328125[/C][C]0.665518473781218[/C][C]26.8561759802864[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 42 )[/C][C]17.69796875[/C][C]0.621752748927897[/C][C]28.4646409372810[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 42 )[/C][C]16.90296875[/C][C]0.451852341344091[/C][C]37.4081690043256[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 42 )[/C][C]16.698828125[/C][C]0.412661529175054[/C][C]40.4661615983016[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 42 )[/C][C]16.647421875[/C][C]0.397997668053168[/C][C]41.82793822997[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 42 )[/C][C]16.63921875[/C][C]0.393893449831381[/C][C]42.2429435095277[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 42 )[/C][C]16.48546875[/C][C]0.365711942172829[/C][C]45.0777424769172[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 42 )[/C][C]16.460234375[/C][C]0.361700286500405[/C][C]45.5079384488725[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 42 )[/C][C]16.470078125[/C][C]0.359989516471879[/C][C]45.7515493407058[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 42 )[/C][C]16.45671875[/C][C]0.356235047851974[/C][C]46.1962371451960[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 42 )[/C][C]16.45984375[/C][C]0.354385419280075[/C][C]46.4461652610815[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 42 )[/C][C]16.47296875[/C][C]0.351465512376319[/C][C]46.8693745756829[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 42 )[/C][C]16.4265625[/C][C]0.343624859782555[/C][C]47.803766323527[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 42 )[/C][C]16.399609375[/C][C]0.337262591520423[/C][C]48.6256400422841[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 42 )[/C][C]16.369609375[/C][C]0.331767524012622[/C][C]49.3406020487323[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 42 )[/C][C]16.373515625[/C][C]0.320766770774832[/C][C]51.0449245894415[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 42 )[/C][C]16.271953125[/C][C]0.302865214772699[/C][C]53.7267151568138[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 42 )[/C][C]16.27828125[/C][C]0.300302077028622[/C][C]54.2063558503078[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 42 )[/C][C]16.25640625[/C][C]0.295421108051489[/C][C]55.0279103521833[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 42 )[/C][C]16.140859375[/C][C]0.273368730718858[/C][C]59.0442781533775[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 42 )[/C][C]16.089296875[/C][C]0.265867673621468[/C][C]60.5161833172215[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 42 )[/C][C]15.992421875[/C][C]0.252945048703379[/C][C]63.2248860255565[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 42 )[/C][C]16.002421875[/C][C]0.244269176195331[/C][C]65.5114252409956[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 42 )[/C][C]15.981796875[/C][C]0.239001378401623[/C][C]66.8690573329826[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 42 )[/C][C]15.947265625[/C][C]0.231471768392057[/C][C]68.895078375127[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 42 )[/C][C]15.85703125[/C][C]0.221004867745291[/C][C]71.7496922659426[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 42 )[/C][C]15.81203125[/C][C]0.211695453544392[/C][C]74.6923516082233[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 42 )[/C][C]15.757109375[/C][C]0.204947874600938[/C][C]76.8834973560047[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 42 )[/C][C]15.777890625[/C][C]0.202867444295571[/C][C]77.7743845484254[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 42 )[/C][C]15.716953125[/C][C]0.192319796220077[/C][C]81.7230125754432[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 42 )[/C][C]15.698203125[/C][C]0.187019641690053[/C][C]83.9387937178094[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 42 )[/C][C]15.58609375[/C][C]0.167134739333904[/C][C]93.2546627476522[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 42 )[/C][C]15.5303125[/C][C]0.153348209783002[/C][C]101.274821023189[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 42 )[/C][C]18.594126984127[/C][C]0.91873962160965[/C][C]20.2387341818890[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 42 )[/C][C]18.3049193548387[/C][C]0.851427477989142[/C][C]21.4990939663708[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 42 )[/C][C]18.0500819672131[/C][C]0.795733887471684[/C][C]22.6835657641330[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 42 )[/C][C]17.7928333333333[/C][C]0.737465160201939[/C][C]24.1270154761767[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 42 )[/C][C]17.5898305084746[/C][C]0.697155631095795[/C][C]25.2308519416629[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 42 )[/C][C]17.3808620689655[/C][C]0.651376314416629[/C][C]26.6832884221953[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 42 )[/C][C]17.165[/C][C]0.598991651918846[/C][C]28.6564928659901[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 42 )[/C][C]16.9733928571429[/C][C]0.551990483125908[/C][C]30.7494302456502[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 42 )[/C][C]16.7924545454545[/C][C]0.505648069063372[/C][C]33.2097669759913[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 42 )[/C][C]16.6183333333333[/C][C]0.457914582614026[/C][C]36.2913389620982[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 42 )[/C][C]16.4667924528302[/C][C]0.415647051772602[/C][C]39.6172482942067[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 42 )[/C][C]16.3290384615385[/C][C]0.375046537297356[/C][C]43.5386994350303[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 42 )[/C][C]16.2690196078431[/C][C]0.362245539520935[/C][C]44.9115802208598[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 42 )[/C][C]16.2267[/C][C]0.354038320559007[/C][C]45.8331741444794[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 42 )[/C][C]16.1874489795918[/C][C]0.346882916042475[/C][C]46.6654546273755[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 42 )[/C][C]16.1472916666667[/C][C]0.339318766678652[/C][C]47.587381696335[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 42 )[/C][C]16.1185106382979[/C][C]0.334612358226494[/C][C]48.1706973517921[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 42 )[/C][C]16.0905434782609[/C][C]0.329749226558487[/C][C]48.7963039252403[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 42 )[/C][C]16.0605555555556[/C][C]0.324365831334169[/C][C]49.5137095343733[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 42 )[/C][C]16.0302272727273[/C][C]0.31865525216167[/C][C]50.3058624139492[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 42 )[/C][C]15.9982558139535[/C][C]0.312292883675790[/C][C]51.2283713469508[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 42 )[/C][C]15.9638095238095[/C][C]0.305282940381458[/C][C]52.2918493377401[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 42 )[/C][C]15.9309756097561[/C][C]0.298224728772503[/C][C]53.4193649042056[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 42 )[/C][C]15.898375[/C][C]0.290870824985133[/C][C]54.6578537081284[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 42 )[/C][C]15.8661538461538[/C][C]0.283045508000701[/C][C]56.0551338836811[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 42 )[/C][C]15.8319736842105[/C][C]0.275332400049617[/C][C]57.501309985158[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 42 )[/C][C]15.8027027027027[/C][C]0.268815280150796[/C][C]58.7864748381787[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 42 )[/C][C]15.7713888888889[/C][C]0.261427577259221[/C][C]60.3279464784644[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 42 )[/C][C]15.7397142857143[/C][C]0.253358392415555[/C][C]62.1243059511454[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 42 )[/C][C]15.7136764705882[/C][C]0.247056588763462[/C][C]63.6035515152073[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 42 )[/C][C]15.6893939393939[/C][C]0.240633766819415[/C][C]65.2003006343168[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 42 )[/C][C]15.66984375[/C][C]0.234895651033347[/C][C]66.7098078702846[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 42 )[/C][C]15.6483870967742[/C][C]0.229177615294577[/C][C]68.280608804923[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 42 )[/C][C]15.6268333333333[/C][C]0.223013198118048[/C][C]70.0713386705549[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 42 )[/C][C]15.6060344827586[/C][C]0.216675499795072[/C][C]72.0249151266228[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 42 )[/C][C]15.5896428571429[/C][C]0.210684253858108[/C][C]73.9952918723684[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 42 )[/C][C]15.575[/C][C]0.204840404205246[/C][C]76.0348040730976[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 42 )[/C][C]15.5628846153846[/C][C]0.198749168593167[/C][C]78.3041495244758[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 42 )[/C][C]15.5484[/C][C]0.191388132189165[/C][C]81.2401470360359[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 42 )[/C][C]15.536875[/C][C]0.184177574911218[/C][C]84.3581256159415[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 42 )[/C][C]15.5256521739130[/C][C]0.176021971667053[/C][C]88.2029216402594[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 42 )[/C][C]15.5213636363636[/C][C]0.169897553669948[/C][C]91.3571932090103[/C][/ROW]
[ROW][C]Median[/C][C]15.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]35.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.6252307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.66984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.6252307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.66984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.66984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.6252307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.66984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.6893939393939[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]128[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42167&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42167&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 Mean18.862968750.97789422769703319.2893752879826
Geometric Mean16.9185524260768
Harmonic Mean15.6868235534847
Quadratic Mean21.8462533257994
Winsorized Mean ( 1 / 42 )18.8742968750.9768344825728819.3218986550179
Winsorized Mean ( 2 / 42 )18.7907031250.94214449387422619.9446085469651
Winsorized Mean ( 3 / 42 )18.773593750.92799233843633820.2303327004115
Winsorized Mean ( 4 / 42 )18.541406250.85558326342285321.6710717035571
Winsorized Mean ( 5 / 42 )18.536718750.85271607588344821.7384417560033
Winsorized Mean ( 6 / 42 )18.5343750.84787982271935621.8596722122196
Winsorized Mean ( 7 / 42 )18.338593750.7942506150749523.0891779016998
Winsorized Mean ( 8 / 42 )18.217343750.75798910533969324.0337804615752
Winsorized Mean ( 9 / 42 )18.11468750.72712060839472324.9129061820873
Winsorized Mean ( 10 / 42 )17.873281250.66551847378121826.8561759802864
Winsorized Mean ( 11 / 42 )17.697968750.62175274892789728.4646409372810
Winsorized Mean ( 12 / 42 )16.902968750.45185234134409137.4081690043256
Winsorized Mean ( 13 / 42 )16.6988281250.41266152917505440.4661615983016
Winsorized Mean ( 14 / 42 )16.6474218750.39799766805316841.82793822997
Winsorized Mean ( 15 / 42 )16.639218750.39389344983138142.2429435095277
Winsorized Mean ( 16 / 42 )16.485468750.36571194217282945.0777424769172
Winsorized Mean ( 17 / 42 )16.4602343750.36170028650040545.5079384488725
Winsorized Mean ( 18 / 42 )16.4700781250.35998951647187945.7515493407058
Winsorized Mean ( 19 / 42 )16.456718750.35623504785197446.1962371451960
Winsorized Mean ( 20 / 42 )16.459843750.35438541928007546.4461652610815
Winsorized Mean ( 21 / 42 )16.472968750.35146551237631946.8693745756829
Winsorized Mean ( 22 / 42 )16.42656250.34362485978255547.803766323527
Winsorized Mean ( 23 / 42 )16.3996093750.33726259152042348.6256400422841
Winsorized Mean ( 24 / 42 )16.3696093750.33176752401262249.3406020487323
Winsorized Mean ( 25 / 42 )16.3735156250.32076677077483251.0449245894415
Winsorized Mean ( 26 / 42 )16.2719531250.30286521477269953.7267151568138
Winsorized Mean ( 27 / 42 )16.278281250.30030207702862254.2063558503078
Winsorized Mean ( 28 / 42 )16.256406250.29542110805148955.0279103521833
Winsorized Mean ( 29 / 42 )16.1408593750.27336873071885859.0442781533775
Winsorized Mean ( 30 / 42 )16.0892968750.26586767362146860.5161833172215
Winsorized Mean ( 31 / 42 )15.9924218750.25294504870337963.2248860255565
Winsorized Mean ( 32 / 42 )16.0024218750.24426917619533165.5114252409956
Winsorized Mean ( 33 / 42 )15.9817968750.23900137840162366.8690573329826
Winsorized Mean ( 34 / 42 )15.9472656250.23147176839205768.895078375127
Winsorized Mean ( 35 / 42 )15.857031250.22100486774529171.7496922659426
Winsorized Mean ( 36 / 42 )15.812031250.21169545354439274.6923516082233
Winsorized Mean ( 37 / 42 )15.7571093750.20494787460093876.8834973560047
Winsorized Mean ( 38 / 42 )15.7778906250.20286744429557177.7743845484254
Winsorized Mean ( 39 / 42 )15.7169531250.19231979622007781.7230125754432
Winsorized Mean ( 40 / 42 )15.6982031250.18701964169005383.9387937178094
Winsorized Mean ( 41 / 42 )15.586093750.16713473933390493.2546627476522
Winsorized Mean ( 42 / 42 )15.53031250.153348209783002101.274821023189
Trimmed Mean ( 1 / 42 )18.5941269841270.9187396216096520.2387341818890
Trimmed Mean ( 2 / 42 )18.30491935483870.85142747798914221.4990939663708
Trimmed Mean ( 3 / 42 )18.05008196721310.79573388747168422.6835657641330
Trimmed Mean ( 4 / 42 )17.79283333333330.73746516020193924.1270154761767
Trimmed Mean ( 5 / 42 )17.58983050847460.69715563109579525.2308519416629
Trimmed Mean ( 6 / 42 )17.38086206896550.65137631441662926.6832884221953
Trimmed Mean ( 7 / 42 )17.1650.59899165191884628.6564928659901
Trimmed Mean ( 8 / 42 )16.97339285714290.55199048312590830.7494302456502
Trimmed Mean ( 9 / 42 )16.79245454545450.50564806906337233.2097669759913
Trimmed Mean ( 10 / 42 )16.61833333333330.45791458261402636.2913389620982
Trimmed Mean ( 11 / 42 )16.46679245283020.41564705177260239.6172482942067
Trimmed Mean ( 12 / 42 )16.32903846153850.37504653729735643.5386994350303
Trimmed Mean ( 13 / 42 )16.26901960784310.36224553952093544.9115802208598
Trimmed Mean ( 14 / 42 )16.22670.35403832055900745.8331741444794
Trimmed Mean ( 15 / 42 )16.18744897959180.34688291604247546.6654546273755
Trimmed Mean ( 16 / 42 )16.14729166666670.33931876667865247.587381696335
Trimmed Mean ( 17 / 42 )16.11851063829790.33461235822649448.1706973517921
Trimmed Mean ( 18 / 42 )16.09054347826090.32974922655848748.7963039252403
Trimmed Mean ( 19 / 42 )16.06055555555560.32436583133416949.5137095343733
Trimmed Mean ( 20 / 42 )16.03022727272730.3186552521616750.3058624139492
Trimmed Mean ( 21 / 42 )15.99825581395350.31229288367579051.2283713469508
Trimmed Mean ( 22 / 42 )15.96380952380950.30528294038145852.2918493377401
Trimmed Mean ( 23 / 42 )15.93097560975610.29822472877250353.4193649042056
Trimmed Mean ( 24 / 42 )15.8983750.29087082498513354.6578537081284
Trimmed Mean ( 25 / 42 )15.86615384615380.28304550800070156.0551338836811
Trimmed Mean ( 26 / 42 )15.83197368421050.27533240004961757.501309985158
Trimmed Mean ( 27 / 42 )15.80270270270270.26881528015079658.7864748381787
Trimmed Mean ( 28 / 42 )15.77138888888890.26142757725922160.3279464784644
Trimmed Mean ( 29 / 42 )15.73971428571430.25335839241555562.1243059511454
Trimmed Mean ( 30 / 42 )15.71367647058820.24705658876346263.6035515152073
Trimmed Mean ( 31 / 42 )15.68939393939390.24063376681941565.2003006343168
Trimmed Mean ( 32 / 42 )15.669843750.23489565103334766.7098078702846
Trimmed Mean ( 33 / 42 )15.64838709677420.22917761529457768.280608804923
Trimmed Mean ( 34 / 42 )15.62683333333330.22301319811804870.0713386705549
Trimmed Mean ( 35 / 42 )15.60603448275860.21667549979507272.0249151266228
Trimmed Mean ( 36 / 42 )15.58964285714290.21068425385810873.9952918723684
Trimmed Mean ( 37 / 42 )15.5750.20484040420524676.0348040730976
Trimmed Mean ( 38 / 42 )15.56288461538460.19874916859316778.3041495244758
Trimmed Mean ( 39 / 42 )15.54840.19138813218916581.2401470360359
Trimmed Mean ( 40 / 42 )15.5368750.18417757491121884.3581256159415
Trimmed Mean ( 41 / 42 )15.52565217391300.17602197166705388.2029216402594
Trimmed Mean ( 42 / 42 )15.52136363636360.16989755366994891.3571932090103
Median15.54
Midrange35.8
Midmean - Weighted Average at Xnp15.6252307692308
Midmean - Weighted Average at X(n+1)p15.66984375
Midmean - Empirical Distribution Function15.6252307692308
Midmean - Empirical Distribution Function - Averaging15.66984375
Midmean - Empirical Distribution Function - Interpolation15.66984375
Midmean - Closest Observation15.6252307692308
Midmean - True Basic - Statistics Graphics Toolkit15.66984375
Midmean - MS Excel (old versions)15.6893939393939
Number of observations128



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')