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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 14 Nov 2011 13:28:24 -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/2011/Nov/14/t1321295369i1ksdno055a6dgk.htm/, Retrieved Fri, 29 Mar 2024 07:43:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142181, Retrieved Fri, 29 Mar 2024 07:43:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Percentiles] [Percentiles of ti...] [2010-09-25 09:52:29] [b98453cac15ba1066b407e146608df68]
- RM D    [Central Tendency] [] [2011-11-14 18:28:24] [87b6e955a128bfb8d1e350b3ce0d281e] [Current]
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Dataseries X:
11.54
25.47
34.78
29.21
43.9
33.47
55.10
48.13
33.25
25.33
26.98
88.74
36.54
11.78
29.11
32.47
36.99
27.55
18.55
14.33
8.78
40.55
22.63
20.47
60.03
50.14
30.63
36.99
27.55
18.55
14.33
21.63
36.12
23.69
54.12
45.16
69.41
41.96
13.25
26.98
88.74
36.54
11.78
29.11
32.47
55.17
17.66
19.64
44.47
50.17
21.63
36.12
23.69
33.25
25.33
26.98
14.33
8.78
17.66
19.64
13.25
16.17
9.66
20.45
24.21
19.65
21.25
33.64
25.44
60.74
71.33
55.21
66.23
19.65
23.52
25.64
19.33
20.64
18.98
15.67
20.00
11.47
28.65
24.14
19.87
17.65
30.54
28.57
29.65
31.22
32.00
19.64
41.88
45.98
34.12
30.88
25.96
20.33
26.98
27.12
21.66
27.96
28.63
29.10
34.25
39.77
41.23
14.10
19.54
8.78
24.55
34.87
31.47
21.65
19.77
9.23
7.55
22.44
16.89
47.55




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142181&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142181&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean29.73041666666671.4119713774754821.0559627064275
Geometric Mean26.3053484019775
Harmonic Mean23.1917833260392
Quadratic Mean33.4834823831094
Winsorized Mean ( 1 / 40 )29.74066666666671.4106548965503721.082879121885
Winsorized Mean ( 2 / 40 )29.45051.3205933426345322.3009605222206
Winsorized Mean ( 3 / 40 )29.40251.3080278002360922.4784977771061
Winsorized Mean ( 4 / 40 )29.31151.2795638516933122.9074148673477
Winsorized Mean ( 5 / 40 )29.10066666666671.2245597547297723.7641867244678
Winsorized Mean ( 6 / 40 )29.15566666666671.2052646287835824.1902615993071
Winsorized Mean ( 7 / 40 )28.87858333333331.1473004870149225.1708978250942
Winsorized Mean ( 8 / 40 )28.89191666666671.1447652524141925.238289339877
Winsorized Mean ( 9 / 40 )28.88666666666671.1437533323845725.2560284186818
Winsorized Mean ( 10 / 40 )28.92751.1131687946606125.9866249743549
Winsorized Mean ( 11 / 40 )28.56541666666671.0472604644183827.2763248849761
Winsorized Mean ( 12 / 40 )28.64741666666671.0365024852369827.6385412236778
Winsorized Mean ( 13 / 40 )28.45458333333330.99649557445762528.5546509815868
Winsorized Mean ( 14 / 40 )28.38691666666670.98535211607766428.8089061803255
Winsorized Mean ( 15 / 40 )28.19066666666670.95392785765471329.5521998235538
Winsorized Mean ( 16 / 40 )28.260.91563850921191630.8637084566519
Winsorized Mean ( 17 / 40 )28.23308333333330.89246838323141431.6348274782666
Winsorized Mean ( 18 / 40 )28.25558333333330.86736986766696132.5761643176916
Winsorized Mean ( 19 / 40 )28.068750.80874201655084934.7066795412814
Winsorized Mean ( 20 / 40 )28.05708333333330.8066392516451134.7826903738095
Winsorized Mean ( 21 / 40 )27.94333333333330.79041337918247735.3528091367014
Winsorized Mean ( 22 / 40 )27.98183333333330.75540378190485237.0422203378085
Winsorized Mean ( 23 / 40 )27.83233333333330.73474358351745737.8803353410599
Winsorized Mean ( 24 / 40 )27.36233333333330.6529341739263341.9067257098732
Winsorized Mean ( 25 / 40 )27.435250.64515141603723242.5252883555892
Winsorized Mean ( 26 / 40 )27.383250.62832439304244543.5813893320392
Winsorized Mean ( 27 / 40 )27.405750.62597145412514843.7811497942858
Winsorized Mean ( 28 / 40 )27.307750.61405275896401344.4713415929793
Winsorized Mean ( 29 / 40 )27.307750.61405275896401344.4713415929793
Winsorized Mean ( 30 / 40 )26.997750.57700173385818446.7897207508835
Winsorized Mean ( 31 / 40 )26.97450.57434128448547646.9659777708042
Winsorized Mean ( 32 / 40 )26.86516666666670.55493168357559248.4116648261391
Winsorized Mean ( 33 / 40 )26.85691666666670.54799122337317149.0097569471066
Winsorized Mean ( 34 / 40 )26.757750.52903117494966950.5787773330101
Winsorized Mean ( 35 / 40 )26.80441666666670.5133483863498352.214864952162
Winsorized Mean ( 36 / 40 )26.77441666666670.5023606987517353.2971960847971
Winsorized Mean ( 37 / 40 )26.78058333333330.50170859744314353.3787610374133
Winsorized Mean ( 38 / 40 )26.58741666666670.46960413771615256.6166575873256
Winsorized Mean ( 39 / 40 )26.78566666666670.44877345655997959.6863880319239
Winsorized Mean ( 40 / 40 )26.75566666666670.4191199552412463.8377303014991
Trimmed Mean ( 1 / 40 )29.41830508474581.3317002564439822.0907857773498
Trimmed Mean ( 2 / 40 )29.08482758620691.2404359844528923.4472620520075
Trimmed Mean ( 3 / 40 )28.89236842105261.1926926198704524.2244883046153
Trimmed Mean ( 4 / 40 )28.71017857142861.1441665458554625.0926568998422
Trimmed Mean ( 5 / 40 )28.54618181818181.0991228133513225.9717853832385
Trimmed Mean ( 6 / 40 )28.4229629629631.0643049388010526.705657304364
Trimmed Mean ( 7 / 40 )28.28471698113211.0297273970643927.4681600798114
Trimmed Mean ( 8 / 40 )28.18682692307691.0038766648277328.0779780132791
Trimmed Mean ( 9 / 40 )28.0831372549020.97517439146842528.7980667874329
Trimmed Mean ( 10 / 40 )27.9760.94280858089116929.6730434650439
Trimmed Mean ( 11 / 40 )27.85948979591840.91152342261616530.5636576139303
Trimmed Mean ( 12 / 40 )27.77927083333330.88768891299003631.2939256386152
Trimmed Mean ( 13 / 40 )27.6869148936170.86219016665280532.1123065009001
Trimmed Mean ( 14 / 40 )27.60989130434780.83960183119109932.8845058200732
Trimmed Mean ( 15 / 40 )27.53588888888890.81551956271119333.7648416395382
Trimmed Mean ( 16 / 40 )27.47636363636360.79282435589173634.6563061946544
Trimmed Mean ( 17 / 40 )27.4080232558140.77228254116369235.4896320904975
Trimmed Mean ( 18 / 40 )27.33869047619050.7519361655915736.357727859362
Trimmed Mean ( 19 / 40 )27.26414634146340.73191502722842937.2504257013353
Trimmed Mean ( 20 / 40 )27.2006250.71703879332385437.9346630241729
Trimmed Mean ( 21 / 40 )27.13474358974360.69995337184406538.7665017146151
Trimmed Mean ( 22 / 40 )27.07394736842110.68233603078720239.678319987274
Trimmed Mean ( 23 / 40 )27.0070270270270.66643588677264640.5245689241229
Trimmed Mean ( 24 / 40 )26.94722222222220.65071205798191641.411899305808
Trimmed Mean ( 25 / 40 )26.91757142857140.64351504430347141.8289699158573
Trimmed Mean ( 26 / 40 )26.88102941176470.63568232370295542.2868914384441
Trimmed Mean ( 27 / 40 )26.84590909090910.62834659185826342.7246832222252
Trimmed Mean ( 28 / 40 )26.807031250.61957529455217943.2667853055306
Trimmed Mean ( 29 / 40 )26.77241935483870.61050345867630543.8530183152225
Trimmed Mean ( 30 / 40 )26.73550.59926406962310344.6138878588447
Trimmed Mean ( 31 / 40 )26.71741379310340.59104077101610945.2040114714442
Trimmed Mean ( 32 / 40 )26.69964285714290.58106233679299245.9497048191145
Trimmed Mean ( 33 / 40 )26.68814814814810.57153416168993946.6956307025207
Trimmed Mean ( 34 / 40 )26.67634615384620.56049872944087847.5939458069013
Trimmed Mean ( 35 / 40 )26.67060.54961265841109848.5261749194484
Trimmed Mean ( 36 / 40 )26.66104166666670.53827033200583549.5309514223379
Trimmed Mean ( 37 / 40 )26.65282608695650.52550759110918650.7182513400055
Trimmed Mean ( 38 / 40 )26.64340909090910.50885062449902452.3599811185064
Trimmed Mean ( 39 / 40 )26.6476190476190.49380762540557153.9635632919459
Trimmed Mean ( 40 / 40 )26.6370.47828743637573455.6924518064791
Median26.98
Midrange48.145
Midmean - Weighted Average at Xnp26.3976190476191
Midmean - Weighted Average at X(n+1)p26.7355
Midmean - Empirical Distribution Function26.3976190476191
Midmean - Empirical Distribution Function - Averaging26.7355
Midmean - Empirical Distribution Function - Interpolation26.7355
Midmean - Closest Observation26.3976190476191
Midmean - True Basic - Statistics Graphics Toolkit26.7355
Midmean - MS Excel (old versions)26.6967692307692
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 29.7304166666667 & 1.41197137747548 & 21.0559627064275 \tabularnewline
Geometric Mean & 26.3053484019775 &  &  \tabularnewline
Harmonic Mean & 23.1917833260392 &  &  \tabularnewline
Quadratic Mean & 33.4834823831094 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 29.7406666666667 & 1.41065489655037 & 21.082879121885 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 29.4505 & 1.32059334263453 & 22.3009605222206 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 29.4025 & 1.30802780023609 & 22.4784977771061 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 29.3115 & 1.27956385169331 & 22.9074148673477 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 29.1006666666667 & 1.22455975472977 & 23.7641867244678 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 29.1556666666667 & 1.20526462878358 & 24.1902615993071 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 28.8785833333333 & 1.14730048701492 & 25.1708978250942 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 28.8919166666667 & 1.14476525241419 & 25.238289339877 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 28.8866666666667 & 1.14375333238457 & 25.2560284186818 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 28.9275 & 1.11316879466061 & 25.9866249743549 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 28.5654166666667 & 1.04726046441838 & 27.2763248849761 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 28.6474166666667 & 1.03650248523698 & 27.6385412236778 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 28.4545833333333 & 0.996495574457625 & 28.5546509815868 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 28.3869166666667 & 0.985352116077664 & 28.8089061803255 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 28.1906666666667 & 0.953927857654713 & 29.5521998235538 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 28.26 & 0.915638509211916 & 30.8637084566519 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 28.2330833333333 & 0.892468383231414 & 31.6348274782666 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 28.2555833333333 & 0.867369867666961 & 32.5761643176916 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 28.06875 & 0.808742016550849 & 34.7066795412814 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 28.0570833333333 & 0.80663925164511 & 34.7826903738095 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 27.9433333333333 & 0.790413379182477 & 35.3528091367014 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 27.9818333333333 & 0.755403781904852 & 37.0422203378085 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 27.8323333333333 & 0.734743583517457 & 37.8803353410599 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 27.3623333333333 & 0.65293417392633 & 41.9067257098732 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 27.43525 & 0.645151416037232 & 42.5252883555892 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 27.38325 & 0.628324393042445 & 43.5813893320392 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 27.40575 & 0.625971454125148 & 43.7811497942858 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 27.30775 & 0.614052758964013 & 44.4713415929793 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 27.30775 & 0.614052758964013 & 44.4713415929793 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 26.99775 & 0.577001733858184 & 46.7897207508835 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 26.9745 & 0.574341284485476 & 46.9659777708042 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 26.8651666666667 & 0.554931683575592 & 48.4116648261391 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 26.8569166666667 & 0.547991223373171 & 49.0097569471066 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 26.75775 & 0.529031174949669 & 50.5787773330101 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 26.8044166666667 & 0.51334838634983 & 52.214864952162 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 26.7744166666667 & 0.50236069875173 & 53.2971960847971 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 26.7805833333333 & 0.501708597443143 & 53.3787610374133 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 26.5874166666667 & 0.469604137716152 & 56.6166575873256 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 26.7856666666667 & 0.448773456559979 & 59.6863880319239 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 26.7556666666667 & 0.41911995524124 & 63.8377303014991 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 29.4183050847458 & 1.33170025644398 & 22.0907857773498 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 29.0848275862069 & 1.24043598445289 & 23.4472620520075 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 28.8923684210526 & 1.19269261987045 & 24.2244883046153 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 28.7101785714286 & 1.14416654585546 & 25.0926568998422 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 28.5461818181818 & 1.09912281335132 & 25.9717853832385 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 28.422962962963 & 1.06430493880105 & 26.705657304364 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 28.2847169811321 & 1.02972739706439 & 27.4681600798114 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 28.1868269230769 & 1.00387666482773 & 28.0779780132791 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 28.083137254902 & 0.975174391468425 & 28.7980667874329 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 27.976 & 0.942808580891169 & 29.6730434650439 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 27.8594897959184 & 0.911523422616165 & 30.5636576139303 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 27.7792708333333 & 0.887688912990036 & 31.2939256386152 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 27.686914893617 & 0.862190166652805 & 32.1123065009001 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 27.6098913043478 & 0.839601831191099 & 32.8845058200732 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 27.5358888888889 & 0.815519562711193 & 33.7648416395382 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 27.4763636363636 & 0.792824355891736 & 34.6563061946544 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 27.408023255814 & 0.772282541163692 & 35.4896320904975 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 27.3386904761905 & 0.75193616559157 & 36.357727859362 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 27.2641463414634 & 0.731915027228429 & 37.2504257013353 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 27.200625 & 0.717038793323854 & 37.9346630241729 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 27.1347435897436 & 0.699953371844065 & 38.7665017146151 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 27.0739473684211 & 0.682336030787202 & 39.678319987274 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 27.007027027027 & 0.666435886772646 & 40.5245689241229 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 26.9472222222222 & 0.650712057981916 & 41.411899305808 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 26.9175714285714 & 0.643515044303471 & 41.8289699158573 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 26.8810294117647 & 0.635682323702955 & 42.2868914384441 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 26.8459090909091 & 0.628346591858263 & 42.7246832222252 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 26.80703125 & 0.619575294552179 & 43.2667853055306 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 26.7724193548387 & 0.610503458676305 & 43.8530183152225 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 26.7355 & 0.599264069623103 & 44.6138878588447 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 26.7174137931034 & 0.591040771016109 & 45.2040114714442 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 26.6996428571429 & 0.581062336792992 & 45.9497048191145 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 26.6881481481481 & 0.571534161689939 & 46.6956307025207 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 26.6763461538462 & 0.560498729440878 & 47.5939458069013 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 26.6706 & 0.549612658411098 & 48.5261749194484 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 26.6610416666667 & 0.538270332005835 & 49.5309514223379 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 26.6528260869565 & 0.525507591109186 & 50.7182513400055 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 26.6434090909091 & 0.508850624499024 & 52.3599811185064 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 26.647619047619 & 0.493807625405571 & 53.9635632919459 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 26.637 & 0.478287436375734 & 55.6924518064791 \tabularnewline
Median & 26.98 &  &  \tabularnewline
Midrange & 48.145 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.3976190476191 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26.7355 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26.3976190476191 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26.7355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26.7355 &  &  \tabularnewline
Midmean - Closest Observation & 26.3976190476191 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26.7355 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26.6967692307692 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142181&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]29.7304166666667[/C][C]1.41197137747548[/C][C]21.0559627064275[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26.3053484019775[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]23.1917833260392[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]33.4834823831094[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]29.7406666666667[/C][C]1.41065489655037[/C][C]21.082879121885[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]29.4505[/C][C]1.32059334263453[/C][C]22.3009605222206[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]29.4025[/C][C]1.30802780023609[/C][C]22.4784977771061[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]29.3115[/C][C]1.27956385169331[/C][C]22.9074148673477[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]29.1006666666667[/C][C]1.22455975472977[/C][C]23.7641867244678[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]29.1556666666667[/C][C]1.20526462878358[/C][C]24.1902615993071[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]28.8785833333333[/C][C]1.14730048701492[/C][C]25.1708978250942[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]28.8919166666667[/C][C]1.14476525241419[/C][C]25.238289339877[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]28.8866666666667[/C][C]1.14375333238457[/C][C]25.2560284186818[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]28.9275[/C][C]1.11316879466061[/C][C]25.9866249743549[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]28.5654166666667[/C][C]1.04726046441838[/C][C]27.2763248849761[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]28.6474166666667[/C][C]1.03650248523698[/C][C]27.6385412236778[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]28.4545833333333[/C][C]0.996495574457625[/C][C]28.5546509815868[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]28.3869166666667[/C][C]0.985352116077664[/C][C]28.8089061803255[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]28.1906666666667[/C][C]0.953927857654713[/C][C]29.5521998235538[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]28.26[/C][C]0.915638509211916[/C][C]30.8637084566519[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]28.2330833333333[/C][C]0.892468383231414[/C][C]31.6348274782666[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]28.2555833333333[/C][C]0.867369867666961[/C][C]32.5761643176916[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]28.06875[/C][C]0.808742016550849[/C][C]34.7066795412814[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]28.0570833333333[/C][C]0.80663925164511[/C][C]34.7826903738095[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]27.9433333333333[/C][C]0.790413379182477[/C][C]35.3528091367014[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]27.9818333333333[/C][C]0.755403781904852[/C][C]37.0422203378085[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]27.8323333333333[/C][C]0.734743583517457[/C][C]37.8803353410599[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]27.3623333333333[/C][C]0.65293417392633[/C][C]41.9067257098732[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]27.43525[/C][C]0.645151416037232[/C][C]42.5252883555892[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]27.38325[/C][C]0.628324393042445[/C][C]43.5813893320392[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]27.40575[/C][C]0.625971454125148[/C][C]43.7811497942858[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]27.30775[/C][C]0.614052758964013[/C][C]44.4713415929793[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]27.30775[/C][C]0.614052758964013[/C][C]44.4713415929793[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]26.99775[/C][C]0.577001733858184[/C][C]46.7897207508835[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]26.9745[/C][C]0.574341284485476[/C][C]46.9659777708042[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]26.8651666666667[/C][C]0.554931683575592[/C][C]48.4116648261391[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]26.8569166666667[/C][C]0.547991223373171[/C][C]49.0097569471066[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]26.75775[/C][C]0.529031174949669[/C][C]50.5787773330101[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]26.8044166666667[/C][C]0.51334838634983[/C][C]52.214864952162[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]26.7744166666667[/C][C]0.50236069875173[/C][C]53.2971960847971[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]26.7805833333333[/C][C]0.501708597443143[/C][C]53.3787610374133[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]26.5874166666667[/C][C]0.469604137716152[/C][C]56.6166575873256[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]26.7856666666667[/C][C]0.448773456559979[/C][C]59.6863880319239[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]26.7556666666667[/C][C]0.41911995524124[/C][C]63.8377303014991[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]29.4183050847458[/C][C]1.33170025644398[/C][C]22.0907857773498[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]29.0848275862069[/C][C]1.24043598445289[/C][C]23.4472620520075[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]28.8923684210526[/C][C]1.19269261987045[/C][C]24.2244883046153[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]28.7101785714286[/C][C]1.14416654585546[/C][C]25.0926568998422[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]28.5461818181818[/C][C]1.09912281335132[/C][C]25.9717853832385[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]28.422962962963[/C][C]1.06430493880105[/C][C]26.705657304364[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]28.2847169811321[/C][C]1.02972739706439[/C][C]27.4681600798114[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]28.1868269230769[/C][C]1.00387666482773[/C][C]28.0779780132791[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]28.083137254902[/C][C]0.975174391468425[/C][C]28.7980667874329[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]27.976[/C][C]0.942808580891169[/C][C]29.6730434650439[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]27.8594897959184[/C][C]0.911523422616165[/C][C]30.5636576139303[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]27.7792708333333[/C][C]0.887688912990036[/C][C]31.2939256386152[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]27.686914893617[/C][C]0.862190166652805[/C][C]32.1123065009001[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]27.6098913043478[/C][C]0.839601831191099[/C][C]32.8845058200732[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]27.5358888888889[/C][C]0.815519562711193[/C][C]33.7648416395382[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]27.4763636363636[/C][C]0.792824355891736[/C][C]34.6563061946544[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]27.408023255814[/C][C]0.772282541163692[/C][C]35.4896320904975[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]27.3386904761905[/C][C]0.75193616559157[/C][C]36.357727859362[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]27.2641463414634[/C][C]0.731915027228429[/C][C]37.2504257013353[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]27.200625[/C][C]0.717038793323854[/C][C]37.9346630241729[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]27.1347435897436[/C][C]0.699953371844065[/C][C]38.7665017146151[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]27.0739473684211[/C][C]0.682336030787202[/C][C]39.678319987274[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]27.007027027027[/C][C]0.666435886772646[/C][C]40.5245689241229[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]26.9472222222222[/C][C]0.650712057981916[/C][C]41.411899305808[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]26.9175714285714[/C][C]0.643515044303471[/C][C]41.8289699158573[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]26.8810294117647[/C][C]0.635682323702955[/C][C]42.2868914384441[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]26.8459090909091[/C][C]0.628346591858263[/C][C]42.7246832222252[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]26.80703125[/C][C]0.619575294552179[/C][C]43.2667853055306[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]26.7724193548387[/C][C]0.610503458676305[/C][C]43.8530183152225[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]26.7355[/C][C]0.599264069623103[/C][C]44.6138878588447[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]26.7174137931034[/C][C]0.591040771016109[/C][C]45.2040114714442[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]26.6996428571429[/C][C]0.581062336792992[/C][C]45.9497048191145[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]26.6881481481481[/C][C]0.571534161689939[/C][C]46.6956307025207[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]26.6763461538462[/C][C]0.560498729440878[/C][C]47.5939458069013[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]26.6706[/C][C]0.549612658411098[/C][C]48.5261749194484[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]26.6610416666667[/C][C]0.538270332005835[/C][C]49.5309514223379[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]26.6528260869565[/C][C]0.525507591109186[/C][C]50.7182513400055[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]26.6434090909091[/C][C]0.508850624499024[/C][C]52.3599811185064[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]26.647619047619[/C][C]0.493807625405571[/C][C]53.9635632919459[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]26.637[/C][C]0.478287436375734[/C][C]55.6924518064791[/C][/ROW]
[ROW][C]Median[/C][C]26.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]48.145[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.3976190476191[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26.7355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26.3976190476191[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26.7355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26.7355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26.3976190476191[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26.7355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26.6967692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142181&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 Mean29.73041666666671.4119713774754821.0559627064275
Geometric Mean26.3053484019775
Harmonic Mean23.1917833260392
Quadratic Mean33.4834823831094
Winsorized Mean ( 1 / 40 )29.74066666666671.4106548965503721.082879121885
Winsorized Mean ( 2 / 40 )29.45051.3205933426345322.3009605222206
Winsorized Mean ( 3 / 40 )29.40251.3080278002360922.4784977771061
Winsorized Mean ( 4 / 40 )29.31151.2795638516933122.9074148673477
Winsorized Mean ( 5 / 40 )29.10066666666671.2245597547297723.7641867244678
Winsorized Mean ( 6 / 40 )29.15566666666671.2052646287835824.1902615993071
Winsorized Mean ( 7 / 40 )28.87858333333331.1473004870149225.1708978250942
Winsorized Mean ( 8 / 40 )28.89191666666671.1447652524141925.238289339877
Winsorized Mean ( 9 / 40 )28.88666666666671.1437533323845725.2560284186818
Winsorized Mean ( 10 / 40 )28.92751.1131687946606125.9866249743549
Winsorized Mean ( 11 / 40 )28.56541666666671.0472604644183827.2763248849761
Winsorized Mean ( 12 / 40 )28.64741666666671.0365024852369827.6385412236778
Winsorized Mean ( 13 / 40 )28.45458333333330.99649557445762528.5546509815868
Winsorized Mean ( 14 / 40 )28.38691666666670.98535211607766428.8089061803255
Winsorized Mean ( 15 / 40 )28.19066666666670.95392785765471329.5521998235538
Winsorized Mean ( 16 / 40 )28.260.91563850921191630.8637084566519
Winsorized Mean ( 17 / 40 )28.23308333333330.89246838323141431.6348274782666
Winsorized Mean ( 18 / 40 )28.25558333333330.86736986766696132.5761643176916
Winsorized Mean ( 19 / 40 )28.068750.80874201655084934.7066795412814
Winsorized Mean ( 20 / 40 )28.05708333333330.8066392516451134.7826903738095
Winsorized Mean ( 21 / 40 )27.94333333333330.79041337918247735.3528091367014
Winsorized Mean ( 22 / 40 )27.98183333333330.75540378190485237.0422203378085
Winsorized Mean ( 23 / 40 )27.83233333333330.73474358351745737.8803353410599
Winsorized Mean ( 24 / 40 )27.36233333333330.6529341739263341.9067257098732
Winsorized Mean ( 25 / 40 )27.435250.64515141603723242.5252883555892
Winsorized Mean ( 26 / 40 )27.383250.62832439304244543.5813893320392
Winsorized Mean ( 27 / 40 )27.405750.62597145412514843.7811497942858
Winsorized Mean ( 28 / 40 )27.307750.61405275896401344.4713415929793
Winsorized Mean ( 29 / 40 )27.307750.61405275896401344.4713415929793
Winsorized Mean ( 30 / 40 )26.997750.57700173385818446.7897207508835
Winsorized Mean ( 31 / 40 )26.97450.57434128448547646.9659777708042
Winsorized Mean ( 32 / 40 )26.86516666666670.55493168357559248.4116648261391
Winsorized Mean ( 33 / 40 )26.85691666666670.54799122337317149.0097569471066
Winsorized Mean ( 34 / 40 )26.757750.52903117494966950.5787773330101
Winsorized Mean ( 35 / 40 )26.80441666666670.5133483863498352.214864952162
Winsorized Mean ( 36 / 40 )26.77441666666670.5023606987517353.2971960847971
Winsorized Mean ( 37 / 40 )26.78058333333330.50170859744314353.3787610374133
Winsorized Mean ( 38 / 40 )26.58741666666670.46960413771615256.6166575873256
Winsorized Mean ( 39 / 40 )26.78566666666670.44877345655997959.6863880319239
Winsorized Mean ( 40 / 40 )26.75566666666670.4191199552412463.8377303014991
Trimmed Mean ( 1 / 40 )29.41830508474581.3317002564439822.0907857773498
Trimmed Mean ( 2 / 40 )29.08482758620691.2404359844528923.4472620520075
Trimmed Mean ( 3 / 40 )28.89236842105261.1926926198704524.2244883046153
Trimmed Mean ( 4 / 40 )28.71017857142861.1441665458554625.0926568998422
Trimmed Mean ( 5 / 40 )28.54618181818181.0991228133513225.9717853832385
Trimmed Mean ( 6 / 40 )28.4229629629631.0643049388010526.705657304364
Trimmed Mean ( 7 / 40 )28.28471698113211.0297273970643927.4681600798114
Trimmed Mean ( 8 / 40 )28.18682692307691.0038766648277328.0779780132791
Trimmed Mean ( 9 / 40 )28.0831372549020.97517439146842528.7980667874329
Trimmed Mean ( 10 / 40 )27.9760.94280858089116929.6730434650439
Trimmed Mean ( 11 / 40 )27.85948979591840.91152342261616530.5636576139303
Trimmed Mean ( 12 / 40 )27.77927083333330.88768891299003631.2939256386152
Trimmed Mean ( 13 / 40 )27.6869148936170.86219016665280532.1123065009001
Trimmed Mean ( 14 / 40 )27.60989130434780.83960183119109932.8845058200732
Trimmed Mean ( 15 / 40 )27.53588888888890.81551956271119333.7648416395382
Trimmed Mean ( 16 / 40 )27.47636363636360.79282435589173634.6563061946544
Trimmed Mean ( 17 / 40 )27.4080232558140.77228254116369235.4896320904975
Trimmed Mean ( 18 / 40 )27.33869047619050.7519361655915736.357727859362
Trimmed Mean ( 19 / 40 )27.26414634146340.73191502722842937.2504257013353
Trimmed Mean ( 20 / 40 )27.2006250.71703879332385437.9346630241729
Trimmed Mean ( 21 / 40 )27.13474358974360.69995337184406538.7665017146151
Trimmed Mean ( 22 / 40 )27.07394736842110.68233603078720239.678319987274
Trimmed Mean ( 23 / 40 )27.0070270270270.66643588677264640.5245689241229
Trimmed Mean ( 24 / 40 )26.94722222222220.65071205798191641.411899305808
Trimmed Mean ( 25 / 40 )26.91757142857140.64351504430347141.8289699158573
Trimmed Mean ( 26 / 40 )26.88102941176470.63568232370295542.2868914384441
Trimmed Mean ( 27 / 40 )26.84590909090910.62834659185826342.7246832222252
Trimmed Mean ( 28 / 40 )26.807031250.61957529455217943.2667853055306
Trimmed Mean ( 29 / 40 )26.77241935483870.61050345867630543.8530183152225
Trimmed Mean ( 30 / 40 )26.73550.59926406962310344.6138878588447
Trimmed Mean ( 31 / 40 )26.71741379310340.59104077101610945.2040114714442
Trimmed Mean ( 32 / 40 )26.69964285714290.58106233679299245.9497048191145
Trimmed Mean ( 33 / 40 )26.68814814814810.57153416168993946.6956307025207
Trimmed Mean ( 34 / 40 )26.67634615384620.56049872944087847.5939458069013
Trimmed Mean ( 35 / 40 )26.67060.54961265841109848.5261749194484
Trimmed Mean ( 36 / 40 )26.66104166666670.53827033200583549.5309514223379
Trimmed Mean ( 37 / 40 )26.65282608695650.52550759110918650.7182513400055
Trimmed Mean ( 38 / 40 )26.64340909090910.50885062449902452.3599811185064
Trimmed Mean ( 39 / 40 )26.6476190476190.49380762540557153.9635632919459
Trimmed Mean ( 40 / 40 )26.6370.47828743637573455.6924518064791
Median26.98
Midrange48.145
Midmean - Weighted Average at Xnp26.3976190476191
Midmean - Weighted Average at X(n+1)p26.7355
Midmean - Empirical Distribution Function26.3976190476191
Midmean - Empirical Distribution Function - Averaging26.7355
Midmean - Empirical Distribution Function - Interpolation26.7355
Midmean - Closest Observation26.3976190476191
Midmean - True Basic - Statistics Graphics Toolkit26.7355
Midmean - MS Excel (old versions)26.6967692307692
Number of observations120



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')