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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 computationSun, 19 Dec 2010 14:22:14 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t1292768411zesc0aoqb3kqxf7.htm/, Retrieved Sat, 04 May 2024 22:19:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112418, Retrieved Sat, 04 May 2024 22:19:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-12-19 14:22:14] [020d6ac062bd52f65e15713212085515] [Current]
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Dataseries X:
119.880
131.468
155.089
149.581
122.788
143.900
112.115
109.600
117.446
118.456
101.901
89.940
129.143
126.102
143.048
142.258
131.011
146.471
114.073
114.642
118.226
111.338
108.701
80.512
146.865
137.179
166.536
137.070
127.090
139.966
122.243
109.097
116.591
111.964
109.754
77.609
138.445
127.901
156.615
133.264
143.521
152.139
131.523
113.925
86.495
127.877
107.017
78.716
138.278
144.238
143.679
159.932
136.781
148.173
125.673
105.573
122.405
128.045
94.467
85.573




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112418&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112418&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112418&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean124.4984666666672.7032627988387846.0548884555902
Geometric Mean122.630152337588
Harmonic Mean120.60971837857
Quadratic Mean126.218137991996
Winsorized Mean ( 1 / 20 )124.406852.6709516585007746.5777243118772
Winsorized Mean ( 2 / 20 )124.356152.6298487744996547.2864262028375
Winsorized Mean ( 3 / 20 )124.53292.5455305613591848.9221783035699
Winsorized Mean ( 4 / 20 )124.39772.4910489974133649.9378776287304
Winsorized Mean ( 5 / 20 )124.4716166666672.3794796905609252.3104345712338
Winsorized Mean ( 6 / 20 )124.7835166666672.246911635183555.5355692287721
Winsorized Mean ( 7 / 20 )125.4982166666672.034777773522861.6766205625453
Winsorized Mean ( 8 / 20 )125.9352833333331.9334480723927865.1350740325182
Winsorized Mean ( 9 / 20 )125.8169333333331.8366511287806568.5034470410628
Winsorized Mean ( 10 / 20 )126.0412666666671.7795297571049170.8284119236767
Winsorized Mean ( 11 / 20 )126.073351.7607228786121871.6031759065755
Winsorized Mean ( 12 / 20 )126.142351.7390386646944572.5356787982418
Winsorized Mean ( 13 / 20 )126.0732333333331.7163912625939573.4525023990167
Winsorized Mean ( 14 / 20 )126.25851.6270461802293477.5998257051337
Winsorized Mean ( 15 / 20 )125.8421.50941534496583.3713532989939
Winsorized Mean ( 16 / 20 )125.4766666666671.439963778708587.1387659342419
Winsorized Mean ( 17 / 20 )125.9421833333331.353738183403493.032895782481
Winsorized Mean ( 18 / 20 )125.6568833333331.296736249224196.9024220681112
Winsorized Mean ( 19 / 20 )125.802551.2644096995735699.4950845777508
Winsorized Mean ( 20 / 20 )126.3558833333331.1545114722686109.445325030028
Trimmed Mean ( 1 / 20 )124.5821206896552.5739414490677648.4013032754793
Trimmed Mean ( 2 / 20 )124.7699107142862.4539616348619950.8442792836501
Trimmed Mean ( 3 / 20 )124.9997777777782.332570380006753.5888558172546
Trimmed Mean ( 4 / 20 )125.1793461538462.2234102419448856.3006069650684
Trimmed Mean ( 5 / 20 )125.413842.1077361770702359.5016783240521
Trimmed Mean ( 6 / 20 )125.6493958333332.0016774425438862.7720496633309
Trimmed Mean ( 7 / 20 )125.8376304347831.9107955637212865.8561453794218
Trimmed Mean ( 8 / 20 )125.903751.8595724354910967.7057519228878
Trimmed Mean ( 9 / 20 )125.8981190476191.8203587578287169.1611576598163
Trimmed Mean ( 10 / 20 )125.911651.7926750050642370.2367409844532
Trimmed Mean ( 11 / 20 )125.8911842105261.7677253922436771.2164823580094
Trimmed Mean ( 12 / 20 )125.8635833333331.735498868572872.5229993591631
Trimmed Mean ( 13 / 20 )125.8225882352941.6937336853830274.2871145098827
Trimmed Mean ( 14 / 20 )125.78643751.6386717556783276.7612165548868
Trimmed Mean ( 15 / 20 )125.7191.584246080531179.355727336156
Trimmed Mean ( 16 / 20 )125.7014285714291.5393306329148781.6597980210406
Trimmed Mean ( 17 / 20 )125.7338461538461.4906654958748284.347458569206
Trimmed Mean ( 18 / 20 )125.7032083333331.4418230094239187.183522188038
Trimmed Mean ( 19 / 20 )125.7102272727271.3805784579272391.056199342315
Trimmed Mean ( 20 / 20 )125.695651.2865868929171997.6969769332867
Median126.596
Midrange122.0725
Midmean - Weighted Average at Xnp125.255096774194
Midmean - Weighted Average at X(n+1)p125.719
Midmean - Empirical Distribution Function125.255096774194
Midmean - Empirical Distribution Function - Averaging125.719
Midmean - Empirical Distribution Function - Interpolation125.719
Midmean - Closest Observation125.255096774194
Midmean - True Basic - Statistics Graphics Toolkit125.719
Midmean - MS Excel (old versions)125.7864375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 124.498466666667 & 2.70326279883878 & 46.0548884555902 \tabularnewline
Geometric Mean & 122.630152337588 &  &  \tabularnewline
Harmonic Mean & 120.60971837857 &  &  \tabularnewline
Quadratic Mean & 126.218137991996 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 124.40685 & 2.67095165850077 & 46.5777243118772 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 124.35615 & 2.62984877449965 & 47.2864262028375 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 124.5329 & 2.54553056135918 & 48.9221783035699 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 124.3977 & 2.49104899741336 & 49.9378776287304 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 124.471616666667 & 2.37947969056092 & 52.3104345712338 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 124.783516666667 & 2.2469116351835 & 55.5355692287721 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 125.498216666667 & 2.0347777735228 & 61.6766205625453 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 125.935283333333 & 1.93344807239278 & 65.1350740325182 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 125.816933333333 & 1.83665112878065 & 68.5034470410628 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 126.041266666667 & 1.77952975710491 & 70.8284119236767 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 126.07335 & 1.76072287861218 & 71.6031759065755 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 126.14235 & 1.73903866469445 & 72.5356787982418 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 126.073233333333 & 1.71639126259395 & 73.4525023990167 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 126.2585 & 1.62704618022934 & 77.5998257051337 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 125.842 & 1.509415344965 & 83.3713532989939 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 125.476666666667 & 1.4399637787085 & 87.1387659342419 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 125.942183333333 & 1.3537381834034 & 93.032895782481 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 125.656883333333 & 1.2967362492241 & 96.9024220681112 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 125.80255 & 1.26440969957356 & 99.4950845777508 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 126.355883333333 & 1.1545114722686 & 109.445325030028 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 124.582120689655 & 2.57394144906776 & 48.4013032754793 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 124.769910714286 & 2.45396163486199 & 50.8442792836501 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 124.999777777778 & 2.3325703800067 & 53.5888558172546 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 125.179346153846 & 2.22341024194488 & 56.3006069650684 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 125.41384 & 2.10773617707023 & 59.5016783240521 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 125.649395833333 & 2.00167744254388 & 62.7720496633309 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 125.837630434783 & 1.91079556372128 & 65.8561453794218 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 125.90375 & 1.85957243549109 & 67.7057519228878 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 125.898119047619 & 1.82035875782871 & 69.1611576598163 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 125.91165 & 1.79267500506423 & 70.2367409844532 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 125.891184210526 & 1.76772539224367 & 71.2164823580094 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 125.863583333333 & 1.7354988685728 & 72.5229993591631 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 125.822588235294 & 1.69373368538302 & 74.2871145098827 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 125.7864375 & 1.63867175567832 & 76.7612165548868 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 125.719 & 1.5842460805311 & 79.355727336156 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 125.701428571429 & 1.53933063291487 & 81.6597980210406 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 125.733846153846 & 1.49066549587482 & 84.347458569206 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 125.703208333333 & 1.44182300942391 & 87.183522188038 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 125.710227272727 & 1.38057845792723 & 91.056199342315 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 125.69565 & 1.28658689291719 & 97.6969769332867 \tabularnewline
Median & 126.596 &  &  \tabularnewline
Midrange & 122.0725 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 125.255096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 125.719 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 125.255096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 125.719 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 125.719 &  &  \tabularnewline
Midmean - Closest Observation & 125.255096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 125.719 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 125.7864375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112418&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]124.498466666667[/C][C]2.70326279883878[/C][C]46.0548884555902[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]122.630152337588[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]120.60971837857[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]126.218137991996[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]124.40685[/C][C]2.67095165850077[/C][C]46.5777243118772[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]124.35615[/C][C]2.62984877449965[/C][C]47.2864262028375[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]124.5329[/C][C]2.54553056135918[/C][C]48.9221783035699[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]124.3977[/C][C]2.49104899741336[/C][C]49.9378776287304[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]124.471616666667[/C][C]2.37947969056092[/C][C]52.3104345712338[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]124.783516666667[/C][C]2.2469116351835[/C][C]55.5355692287721[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]125.498216666667[/C][C]2.0347777735228[/C][C]61.6766205625453[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]125.935283333333[/C][C]1.93344807239278[/C][C]65.1350740325182[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]125.816933333333[/C][C]1.83665112878065[/C][C]68.5034470410628[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]126.041266666667[/C][C]1.77952975710491[/C][C]70.8284119236767[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]126.07335[/C][C]1.76072287861218[/C][C]71.6031759065755[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]126.14235[/C][C]1.73903866469445[/C][C]72.5356787982418[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]126.073233333333[/C][C]1.71639126259395[/C][C]73.4525023990167[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]126.2585[/C][C]1.62704618022934[/C][C]77.5998257051337[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]125.842[/C][C]1.509415344965[/C][C]83.3713532989939[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]125.476666666667[/C][C]1.4399637787085[/C][C]87.1387659342419[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]125.942183333333[/C][C]1.3537381834034[/C][C]93.032895782481[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]125.656883333333[/C][C]1.2967362492241[/C][C]96.9024220681112[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]125.80255[/C][C]1.26440969957356[/C][C]99.4950845777508[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]126.355883333333[/C][C]1.1545114722686[/C][C]109.445325030028[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]124.582120689655[/C][C]2.57394144906776[/C][C]48.4013032754793[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]124.769910714286[/C][C]2.45396163486199[/C][C]50.8442792836501[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]124.999777777778[/C][C]2.3325703800067[/C][C]53.5888558172546[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]125.179346153846[/C][C]2.22341024194488[/C][C]56.3006069650684[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]125.41384[/C][C]2.10773617707023[/C][C]59.5016783240521[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]125.649395833333[/C][C]2.00167744254388[/C][C]62.7720496633309[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]125.837630434783[/C][C]1.91079556372128[/C][C]65.8561453794218[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]125.90375[/C][C]1.85957243549109[/C][C]67.7057519228878[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]125.898119047619[/C][C]1.82035875782871[/C][C]69.1611576598163[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]125.91165[/C][C]1.79267500506423[/C][C]70.2367409844532[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]125.891184210526[/C][C]1.76772539224367[/C][C]71.2164823580094[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]125.863583333333[/C][C]1.7354988685728[/C][C]72.5229993591631[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]125.822588235294[/C][C]1.69373368538302[/C][C]74.2871145098827[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]125.7864375[/C][C]1.63867175567832[/C][C]76.7612165548868[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]125.719[/C][C]1.5842460805311[/C][C]79.355727336156[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]125.701428571429[/C][C]1.53933063291487[/C][C]81.6597980210406[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]125.733846153846[/C][C]1.49066549587482[/C][C]84.347458569206[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]125.703208333333[/C][C]1.44182300942391[/C][C]87.183522188038[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]125.710227272727[/C][C]1.38057845792723[/C][C]91.056199342315[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]125.69565[/C][C]1.28658689291719[/C][C]97.6969769332867[/C][/ROW]
[ROW][C]Median[/C][C]126.596[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]122.0725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]125.255096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]125.719[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]125.255096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]125.719[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]125.719[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]125.255096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]125.719[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]125.7864375[/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=112418&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112418&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 Mean124.4984666666672.7032627988387846.0548884555902
Geometric Mean122.630152337588
Harmonic Mean120.60971837857
Quadratic Mean126.218137991996
Winsorized Mean ( 1 / 20 )124.406852.6709516585007746.5777243118772
Winsorized Mean ( 2 / 20 )124.356152.6298487744996547.2864262028375
Winsorized Mean ( 3 / 20 )124.53292.5455305613591848.9221783035699
Winsorized Mean ( 4 / 20 )124.39772.4910489974133649.9378776287304
Winsorized Mean ( 5 / 20 )124.4716166666672.3794796905609252.3104345712338
Winsorized Mean ( 6 / 20 )124.7835166666672.246911635183555.5355692287721
Winsorized Mean ( 7 / 20 )125.4982166666672.034777773522861.6766205625453
Winsorized Mean ( 8 / 20 )125.9352833333331.9334480723927865.1350740325182
Winsorized Mean ( 9 / 20 )125.8169333333331.8366511287806568.5034470410628
Winsorized Mean ( 10 / 20 )126.0412666666671.7795297571049170.8284119236767
Winsorized Mean ( 11 / 20 )126.073351.7607228786121871.6031759065755
Winsorized Mean ( 12 / 20 )126.142351.7390386646944572.5356787982418
Winsorized Mean ( 13 / 20 )126.0732333333331.7163912625939573.4525023990167
Winsorized Mean ( 14 / 20 )126.25851.6270461802293477.5998257051337
Winsorized Mean ( 15 / 20 )125.8421.50941534496583.3713532989939
Winsorized Mean ( 16 / 20 )125.4766666666671.439963778708587.1387659342419
Winsorized Mean ( 17 / 20 )125.9421833333331.353738183403493.032895782481
Winsorized Mean ( 18 / 20 )125.6568833333331.296736249224196.9024220681112
Winsorized Mean ( 19 / 20 )125.802551.2644096995735699.4950845777508
Winsorized Mean ( 20 / 20 )126.3558833333331.1545114722686109.445325030028
Trimmed Mean ( 1 / 20 )124.5821206896552.5739414490677648.4013032754793
Trimmed Mean ( 2 / 20 )124.7699107142862.4539616348619950.8442792836501
Trimmed Mean ( 3 / 20 )124.9997777777782.332570380006753.5888558172546
Trimmed Mean ( 4 / 20 )125.1793461538462.2234102419448856.3006069650684
Trimmed Mean ( 5 / 20 )125.413842.1077361770702359.5016783240521
Trimmed Mean ( 6 / 20 )125.6493958333332.0016774425438862.7720496633309
Trimmed Mean ( 7 / 20 )125.8376304347831.9107955637212865.8561453794218
Trimmed Mean ( 8 / 20 )125.903751.8595724354910967.7057519228878
Trimmed Mean ( 9 / 20 )125.8981190476191.8203587578287169.1611576598163
Trimmed Mean ( 10 / 20 )125.911651.7926750050642370.2367409844532
Trimmed Mean ( 11 / 20 )125.8911842105261.7677253922436771.2164823580094
Trimmed Mean ( 12 / 20 )125.8635833333331.735498868572872.5229993591631
Trimmed Mean ( 13 / 20 )125.8225882352941.6937336853830274.2871145098827
Trimmed Mean ( 14 / 20 )125.78643751.6386717556783276.7612165548868
Trimmed Mean ( 15 / 20 )125.7191.584246080531179.355727336156
Trimmed Mean ( 16 / 20 )125.7014285714291.5393306329148781.6597980210406
Trimmed Mean ( 17 / 20 )125.7338461538461.4906654958748284.347458569206
Trimmed Mean ( 18 / 20 )125.7032083333331.4418230094239187.183522188038
Trimmed Mean ( 19 / 20 )125.7102272727271.3805784579272391.056199342315
Trimmed Mean ( 20 / 20 )125.695651.2865868929171997.6969769332867
Median126.596
Midrange122.0725
Midmean - Weighted Average at Xnp125.255096774194
Midmean - Weighted Average at X(n+1)p125.719
Midmean - Empirical Distribution Function125.255096774194
Midmean - Empirical Distribution Function - Averaging125.719
Midmean - Empirical Distribution Function - Interpolation125.719
Midmean - Closest Observation125.255096774194
Midmean - True Basic - Statistics Graphics Toolkit125.719
Midmean - MS Excel (old versions)125.7864375
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')