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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Dec 2008 15:34:06 -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/16/t1229466883ro59nvlt9xad3c7.htm/, Retrieved Wed, 15 May 2024 22:23:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34231, Retrieved Wed, 15 May 2024 22:23:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199
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] [ee28d11f695cd3bc1f8bbd77ba77987a] [Current]
-    D    [Central Tendency] [Central Tendency ...] [2008-12-18 13:42:28] [7458e879e85b911182071700fff19fbd]
F         [Central Tendency] [Central Tendency ...] [2008-12-21 09:47:58] [74be16979710d4c4e7c6647856088456]
- RMPD    [Univariate Data Series] [inschrijvingen pe...] [2009-12-16 15:47:43] [74be16979710d4c4e7c6647856088456]
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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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34231&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34231&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34231&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'Gwilym Jenkins' @ 72.249.127.135







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=34231&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=34231&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34231&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):
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')