Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 02:47:58 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t1229852923zfe3vgmsp2inou7.htm/, Retrieved Sat, 25 May 2024 17:20:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35473, Retrieved Sat, 25 May 2024 17:20:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact194
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Central Tendency ...] [2008-12-16 22:34:06] [7458e879e85b911182071700fff19fbd]
F         [Central Tendency] [Central Tendency ...] [2008-12-21 09:47:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2009-01-01 21:45:25 [Kenny Simons] [reply
We kunnen hier ook duidelijk bemerken dat de midrange beduidend hoger ligt dan de median en mean. We kunnen hier door het significant verschil tussen de waarden zelfs spreken van de aanwezigheid van enkele outliers. Op de grafiek van de winsorized- en de trimmed mean merken we op dat niet alle waarden binnen het betrouwbaarheidsinterval liggen. Dit kunnen we concluderen omdat, als je vanuit de eerste waarde in de reeks een horizontale rechte tekent, zal je zien dat niet alle punten van de curve binnen de stippelijntjes (welke het betrouwbaarheidsinterval voorstellen)liggen.

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Dataseries X:
29,59
30,7
30,52
32,67
33,19
37,13
35,54
37,75
41,84
42,94
49,14
44,61
40,22
44,23
45,85
53,38
53,26
51,8
55,3
57,81
63,96
63,77
59,15
56,12
57,42
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68
70,3
75,26
71,44
76,36
81,71
92,6
90,6
92,23
94,09
102,79
109,65
124,05
132,69
135,81
116,07
101,42
75,73
55,48




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35473&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35473&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35473&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean65.83253.2166428759256020.4662135460271
Geometric Mean61.5685947895947
Harmonic Mean57.6008273594802
Quadratic Mean70.3162765533936
Winsorized Mean ( 1 / 20 )65.7963.1948975138952120.5940878271810
Winsorized Mean ( 2 / 20 )65.5143.0964453576815021.1578091754392
Winsorized Mean ( 3 / 20 )65.21352.9556270265472422.0641844908903
Winsorized Mean ( 4 / 20 )64.82016666666672.8291152665841622.9118153764479
Winsorized Mean ( 5 / 20 )64.44433333333332.6451950828559624.3627903858623
Winsorized Mean ( 6 / 20 )64.46633333333332.5827592979867724.9602560267943
Winsorized Mean ( 7 / 20 )63.68352.3725504266160826.841789866962
Winsorized Mean ( 8 / 20 )63.81416666666672.2700708604344528.1110901773585
Winsorized Mean ( 9 / 20 )64.00166666666672.2161086953327028.8802019510412
Winsorized Mean ( 10 / 20 )63.91333333333332.1270273236150330.0481957254354
Winsorized Mean ( 11 / 20 )62.521.7605535050284035.5115591894444
Winsorized Mean ( 12 / 20 )61.5261.5611384047047439.4109835582684
Winsorized Mean ( 13 / 20 )61.65816666666671.4903900921060341.3704888359389
Winsorized Mean ( 14 / 20 )62.31616666666671.3393741917469946.5263307674951
Winsorized Mean ( 15 / 20 )62.76866666666671.1971775297192952.4305419275489
Winsorized Mean ( 16 / 20 )63.13666666666671.1346461074172955.6443689833651
Winsorized Mean ( 17 / 20 )62.5191.0236113288462461.076893385371
Winsorized Mean ( 18 / 20 )62.840.92220957947452368.1406931771479
Winsorized Mean ( 19 / 20 )62.56133333333330.85409731866759773.2484834760163
Winsorized Mean ( 20 / 20 )62.4380.81746821496977976.3797281124971
Trimmed Mean ( 1 / 20 )65.25086206896553.0322749988668121.5187811439762
Trimmed Mean ( 2 / 20 )64.66678571428572.8275245254501822.8704597014910
Trimmed Mean ( 3 / 20 )64.19611111111112.6390210636654824.3257289587320
Trimmed Mean ( 4 / 20 )63.80480769230772.4745649325911225.7842527597357
Trimmed Mean ( 5 / 20 )63.50022.3207809468507227.3615655480839
Trimmed Mean ( 6 / 20 )63.26416666666672.1948141618557928.8243842080801
Trimmed Mean ( 7 / 20 )63.00282608695652.0531135696211930.6864788286315
Trimmed Mean ( 8 / 20 )62.87022727272731.9399996591354632.4073393398145
Trimmed Mean ( 9 / 20 )62.70166666666671.8229793967968934.3951592523965
Trimmed Mean ( 10 / 20 )62.4851.6820381790843637.1483838934111
Trimmed Mean ( 11 / 20 )62.25947368421051.5178503528983141.0181896820903
Trimmed Mean ( 12 / 20 )62.221.4186400261551643.858906313697
Trimmed Mean ( 13 / 20 )62.32205882352941.3435639000618246.3856306504378
Trimmed Mean ( 14 / 20 )62.41781251.2596398242232449.5521110873818
Trimmed Mean ( 15 / 20 )62.43233333333331.1903686942928652.4478958768496
Trimmed Mean ( 16 / 20 )62.38428571428571.1363375714732254.8994306624984
Trimmed Mean ( 17 / 20 )62.27576923076921.0741265035190857.9780584751793
Trimmed Mean ( 18 / 20 )62.241.0211757928975860.9493492040136
Trimmed Mean ( 19 / 20 )62.14909090909090.97475025308204563.7589892514342
Trimmed Mean ( 20 / 20 )62.0840.92556054139611867.077189684807
Median62.21
Midrange82.7
Midmean - Weighted Average at Xnp62.0035483870968
Midmean - Weighted Average at X(n+1)p62.4323333333333
Midmean - Empirical Distribution Function62.0035483870968
Midmean - Empirical Distribution Function - Averaging62.4323333333333
Midmean - Empirical Distribution Function - Interpolation62.4323333333333
Midmean - Closest Observation62.0035483870968
Midmean - True Basic - Statistics Graphics Toolkit62.4323333333333
Midmean - MS Excel (old versions)62.4178125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 65.8325 & 3.21664287592560 & 20.4662135460271 \tabularnewline
Geometric Mean & 61.5685947895947 &  &  \tabularnewline
Harmonic Mean & 57.6008273594802 &  &  \tabularnewline
Quadratic Mean & 70.3162765533936 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 65.796 & 3.19489751389521 & 20.5940878271810 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 65.514 & 3.09644535768150 & 21.1578091754392 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 65.2135 & 2.95562702654724 & 22.0641844908903 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 64.8201666666667 & 2.82911526658416 & 22.9118153764479 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 64.4443333333333 & 2.64519508285596 & 24.3627903858623 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 64.4663333333333 & 2.58275929798677 & 24.9602560267943 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 63.6835 & 2.37255042661608 & 26.841789866962 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 63.8141666666667 & 2.27007086043445 & 28.1110901773585 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 64.0016666666667 & 2.21610869533270 & 28.8802019510412 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 63.9133333333333 & 2.12702732361503 & 30.0481957254354 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 62.52 & 1.76055350502840 & 35.5115591894444 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 61.526 & 1.56113840470474 & 39.4109835582684 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 61.6581666666667 & 1.49039009210603 & 41.3704888359389 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 62.3161666666667 & 1.33937419174699 & 46.5263307674951 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 62.7686666666667 & 1.19717752971929 & 52.4305419275489 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 63.1366666666667 & 1.13464610741729 & 55.6443689833651 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 62.519 & 1.02361132884624 & 61.076893385371 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 62.84 & 0.922209579474523 & 68.1406931771479 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 62.5613333333333 & 0.854097318667597 & 73.2484834760163 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 62.438 & 0.817468214969779 & 76.3797281124971 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 65.2508620689655 & 3.03227499886681 & 21.5187811439762 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 64.6667857142857 & 2.82752452545018 & 22.8704597014910 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 64.1961111111111 & 2.63902106366548 & 24.3257289587320 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 63.8048076923077 & 2.47456493259112 & 25.7842527597357 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 63.5002 & 2.32078094685072 & 27.3615655480839 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 63.2641666666667 & 2.19481416185579 & 28.8243842080801 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 63.0028260869565 & 2.05311356962119 & 30.6864788286315 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 62.8702272727273 & 1.93999965913546 & 32.4073393398145 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 62.7016666666667 & 1.82297939679689 & 34.3951592523965 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 62.485 & 1.68203817908436 & 37.1483838934111 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 62.2594736842105 & 1.51785035289831 & 41.0181896820903 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 62.22 & 1.41864002615516 & 43.858906313697 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 62.3220588235294 & 1.34356390006182 & 46.3856306504378 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 62.4178125 & 1.25963982422324 & 49.5521110873818 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 62.4323333333333 & 1.19036869429286 & 52.4478958768496 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 62.3842857142857 & 1.13633757147322 & 54.8994306624984 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 62.2757692307692 & 1.07412650351908 & 57.9780584751793 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 62.24 & 1.02117579289758 & 60.9493492040136 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 62.1490909090909 & 0.974750253082045 & 63.7589892514342 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 62.084 & 0.925560541396118 & 67.077189684807 \tabularnewline
Median & 62.21 &  &  \tabularnewline
Midrange & 82.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 62.0035483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 62.4323333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 62.0035483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 62.4323333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 62.4323333333333 &  &  \tabularnewline
Midmean - Closest Observation & 62.0035483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 62.4323333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 62.4178125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35473&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]65.8325[/C][C]3.21664287592560[/C][C]20.4662135460271[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]61.5685947895947[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]57.6008273594802[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]70.3162765533936[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]65.796[/C][C]3.19489751389521[/C][C]20.5940878271810[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]65.514[/C][C]3.09644535768150[/C][C]21.1578091754392[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]65.2135[/C][C]2.95562702654724[/C][C]22.0641844908903[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]64.8201666666667[/C][C]2.82911526658416[/C][C]22.9118153764479[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]64.4443333333333[/C][C]2.64519508285596[/C][C]24.3627903858623[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]64.4663333333333[/C][C]2.58275929798677[/C][C]24.9602560267943[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]63.6835[/C][C]2.37255042661608[/C][C]26.841789866962[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]63.8141666666667[/C][C]2.27007086043445[/C][C]28.1110901773585[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]64.0016666666667[/C][C]2.21610869533270[/C][C]28.8802019510412[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]63.9133333333333[/C][C]2.12702732361503[/C][C]30.0481957254354[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]62.52[/C][C]1.76055350502840[/C][C]35.5115591894444[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]61.526[/C][C]1.56113840470474[/C][C]39.4109835582684[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]61.6581666666667[/C][C]1.49039009210603[/C][C]41.3704888359389[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]62.3161666666667[/C][C]1.33937419174699[/C][C]46.5263307674951[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]62.7686666666667[/C][C]1.19717752971929[/C][C]52.4305419275489[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]63.1366666666667[/C][C]1.13464610741729[/C][C]55.6443689833651[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]62.519[/C][C]1.02361132884624[/C][C]61.076893385371[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]62.84[/C][C]0.922209579474523[/C][C]68.1406931771479[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]62.5613333333333[/C][C]0.854097318667597[/C][C]73.2484834760163[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]62.438[/C][C]0.817468214969779[/C][C]76.3797281124971[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]65.2508620689655[/C][C]3.03227499886681[/C][C]21.5187811439762[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]64.6667857142857[/C][C]2.82752452545018[/C][C]22.8704597014910[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]64.1961111111111[/C][C]2.63902106366548[/C][C]24.3257289587320[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]63.8048076923077[/C][C]2.47456493259112[/C][C]25.7842527597357[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]63.5002[/C][C]2.32078094685072[/C][C]27.3615655480839[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]63.2641666666667[/C][C]2.19481416185579[/C][C]28.8243842080801[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]63.0028260869565[/C][C]2.05311356962119[/C][C]30.6864788286315[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]62.8702272727273[/C][C]1.93999965913546[/C][C]32.4073393398145[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]62.7016666666667[/C][C]1.82297939679689[/C][C]34.3951592523965[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]62.485[/C][C]1.68203817908436[/C][C]37.1483838934111[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]62.2594736842105[/C][C]1.51785035289831[/C][C]41.0181896820903[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]62.22[/C][C]1.41864002615516[/C][C]43.858906313697[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]62.3220588235294[/C][C]1.34356390006182[/C][C]46.3856306504378[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]62.4178125[/C][C]1.25963982422324[/C][C]49.5521110873818[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]62.4323333333333[/C][C]1.19036869429286[/C][C]52.4478958768496[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]62.3842857142857[/C][C]1.13633757147322[/C][C]54.8994306624984[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]62.2757692307692[/C][C]1.07412650351908[/C][C]57.9780584751793[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]62.24[/C][C]1.02117579289758[/C][C]60.9493492040136[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]62.1490909090909[/C][C]0.974750253082045[/C][C]63.7589892514342[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]62.084[/C][C]0.925560541396118[/C][C]67.077189684807[/C][/ROW]
[ROW][C]Median[/C][C]62.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]82.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]62.0035483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]62.4323333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]62.0035483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]62.4323333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]62.4323333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]62.0035483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]62.4323333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]62.4178125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35473&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35473&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 Mean65.83253.2166428759256020.4662135460271
Geometric Mean61.5685947895947
Harmonic Mean57.6008273594802
Quadratic Mean70.3162765533936
Winsorized Mean ( 1 / 20 )65.7963.1948975138952120.5940878271810
Winsorized Mean ( 2 / 20 )65.5143.0964453576815021.1578091754392
Winsorized Mean ( 3 / 20 )65.21352.9556270265472422.0641844908903
Winsorized Mean ( 4 / 20 )64.82016666666672.8291152665841622.9118153764479
Winsorized Mean ( 5 / 20 )64.44433333333332.6451950828559624.3627903858623
Winsorized Mean ( 6 / 20 )64.46633333333332.5827592979867724.9602560267943
Winsorized Mean ( 7 / 20 )63.68352.3725504266160826.841789866962
Winsorized Mean ( 8 / 20 )63.81416666666672.2700708604344528.1110901773585
Winsorized Mean ( 9 / 20 )64.00166666666672.2161086953327028.8802019510412
Winsorized Mean ( 10 / 20 )63.91333333333332.1270273236150330.0481957254354
Winsorized Mean ( 11 / 20 )62.521.7605535050284035.5115591894444
Winsorized Mean ( 12 / 20 )61.5261.5611384047047439.4109835582684
Winsorized Mean ( 13 / 20 )61.65816666666671.4903900921060341.3704888359389
Winsorized Mean ( 14 / 20 )62.31616666666671.3393741917469946.5263307674951
Winsorized Mean ( 15 / 20 )62.76866666666671.1971775297192952.4305419275489
Winsorized Mean ( 16 / 20 )63.13666666666671.1346461074172955.6443689833651
Winsorized Mean ( 17 / 20 )62.5191.0236113288462461.076893385371
Winsorized Mean ( 18 / 20 )62.840.92220957947452368.1406931771479
Winsorized Mean ( 19 / 20 )62.56133333333330.85409731866759773.2484834760163
Winsorized Mean ( 20 / 20 )62.4380.81746821496977976.3797281124971
Trimmed Mean ( 1 / 20 )65.25086206896553.0322749988668121.5187811439762
Trimmed Mean ( 2 / 20 )64.66678571428572.8275245254501822.8704597014910
Trimmed Mean ( 3 / 20 )64.19611111111112.6390210636654824.3257289587320
Trimmed Mean ( 4 / 20 )63.80480769230772.4745649325911225.7842527597357
Trimmed Mean ( 5 / 20 )63.50022.3207809468507227.3615655480839
Trimmed Mean ( 6 / 20 )63.26416666666672.1948141618557928.8243842080801
Trimmed Mean ( 7 / 20 )63.00282608695652.0531135696211930.6864788286315
Trimmed Mean ( 8 / 20 )62.87022727272731.9399996591354632.4073393398145
Trimmed Mean ( 9 / 20 )62.70166666666671.8229793967968934.3951592523965
Trimmed Mean ( 10 / 20 )62.4851.6820381790843637.1483838934111
Trimmed Mean ( 11 / 20 )62.25947368421051.5178503528983141.0181896820903
Trimmed Mean ( 12 / 20 )62.221.4186400261551643.858906313697
Trimmed Mean ( 13 / 20 )62.32205882352941.3435639000618246.3856306504378
Trimmed Mean ( 14 / 20 )62.41781251.2596398242232449.5521110873818
Trimmed Mean ( 15 / 20 )62.43233333333331.1903686942928652.4478958768496
Trimmed Mean ( 16 / 20 )62.38428571428571.1363375714732254.8994306624984
Trimmed Mean ( 17 / 20 )62.27576923076921.0741265035190857.9780584751793
Trimmed Mean ( 18 / 20 )62.241.0211757928975860.9493492040136
Trimmed Mean ( 19 / 20 )62.14909090909090.97475025308204563.7589892514342
Trimmed Mean ( 20 / 20 )62.0840.92556054139611867.077189684807
Median62.21
Midrange82.7
Midmean - Weighted Average at Xnp62.0035483870968
Midmean - Weighted Average at X(n+1)p62.4323333333333
Midmean - Empirical Distribution Function62.0035483870968
Midmean - Empirical Distribution Function - Averaging62.4323333333333
Midmean - Empirical Distribution Function - Interpolation62.4323333333333
Midmean - Closest Observation62.0035483870968
Midmean - True Basic - Statistics Graphics Toolkit62.4323333333333
Midmean - MS Excel (old versions)62.4178125
Number of observations60



Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')