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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 19 Oct 2011 07:44:31 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t13190247081s8pzatlcq5rmic.htm/, Retrieved Wed, 15 May 2024 08:20:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132767, Retrieved Wed, 15 May 2024 08:20:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-19 11:44:31] [3065ee55bdba439201dadf7d5b1a020e] [Current]
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Dataseries X:
301,5
285,2
270,9
264,4
253,6
249
235,1
219,8
222,2
225,6
243,3
255,7
246,1
235,5
236,7
226,6
221,5
205,8
203,3
202
187,3
180,9
185,4
183,5
172,5
171
175,7
203,2
212,8
215,5
209,3
198,7
199,4
211,6
211,4
187,5
178,7
171
171,3
168,1
162,6
166,8
162,4
156,6
156,4
157,3
159,5
159,1
163
156
147,9
149,4
153,3
154,2
148,5
155,4
158,8
157,2
163,1
162,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132767&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132767&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132767&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean195.815.0013482363049839.1514429206524
Geometric Mean192.275805757649
Harmonic Mean188.99270554205
Quadratic Mean199.542856716713
Winsorized Mean ( 1 / 20 )195.5483333333334.9089647565619839.8349434210008
Winsorized Mean ( 2 / 20 )195.1016666666674.7659298697673340.9367472870916
Winsorized Mean ( 3 / 20 )194.9716666666674.6503047052020341.9266433119024
Winsorized Mean ( 4 / 20 )194.4516666666674.5008225812312743.2035840465126
Winsorized Mean ( 5 / 20 )194.3766666666674.4458730731204643.7206963558764
Winsorized Mean ( 6 / 20 )193.9766666666674.3355268459571444.7411983730533
Winsorized Mean ( 7 / 20 )193.6854.2568959175797745.4991157289366
Winsorized Mean ( 8 / 20 )193.3383333333334.1761104897949646.2962686944678
Winsorized Mean ( 9 / 20 )192.4383333333333.9685095835213748.4913364282662
Winsorized Mean ( 10 / 20 )192.2553.9284356836919148.9393273760614
Winsorized Mean ( 11 / 20 )192.4566666666673.873764695876749.682074616334
Winsorized Mean ( 12 / 20 )190.8166666666673.5608735095000453.5870387301283
Winsorized Mean ( 13 / 20 )190.6866666666673.5110965874929154.3097183215988
Winsorized Mean ( 14 / 20 )190.573.2790667164718458.1171462729634
Winsorized Mean ( 15 / 20 )190.423.2469227500254458.6462982522476
Winsorized Mean ( 16 / 20 )189.9933333333333.1701225864004159.9324878313509
Winsorized Mean ( 17 / 20 )188.8883333333332.9634955040688963.7383566379598
Winsorized Mean ( 18 / 20 )188.1083333333332.8376208420637466.2908625933712
Winsorized Mean ( 19 / 20 )188.92.6098552896220872.3794919784053
Winsorized Mean ( 20 / 20 )189.2666666666672.5382883447868274.5646833447374
Trimmed Mean ( 1 / 20 )194.8137931034484.7637605617950740.8949590510147
Trimmed Mean ( 2 / 20 )194.0267857142864.5824024571925842.3417164962758
Trimmed Mean ( 3 / 20 )193.429629629634.4531418800640843.4366644583186
Trimmed Mean ( 4 / 20 )192.8365384615384.3459617260891344.3714304486223
Trimmed Mean ( 5 / 20 )192.3524.2682025466924445.0662774073502
Trimmed Mean ( 6 / 20 )191.8458333333334.1845682373146145.8460281810215
Trimmed Mean ( 7 / 20 )191.3826086956524.1085833381883546.5811675077379
Trimmed Mean ( 8 / 20 )190.9340909090914.0292219373629247.3873352913528
Trimmed Mean ( 9 / 20 )190.5047619047623.9440894375087448.3013290958973
Trimmed Mean ( 10 / 20 )190.18253.8845352286094348.9588815154293
Trimmed Mean ( 11 / 20 )189.8552631578953.8091745527577649.8415760497097
Trimmed Mean ( 12 / 20 )189.4611111111113.7143742188614451.0075452680658
Trimmed Mean ( 13 / 20 )189.2617647058823.6662502146564551.6227081144862
Trimmed Mean ( 14 / 20 )189.056253.6024267624240552.4802480294659
Trimmed Mean ( 15 / 20 )188.843.5659939208694952.9557829290846
Trimmed Mean ( 16 / 20 )188.6142857142863.5076059242349253.7729408001916
Trimmed Mean ( 17 / 20 )188.4153846153853.4308496023700754.917995963806
Trimmed Mean ( 18 / 20 )188.3458333333333.370626415605155.8785846041384
Trimmed Mean ( 19 / 20 )188.3818181818183.3015648681363857.0583422424631
Trimmed Mean ( 20 / 20 )188.33.2569601584428757.8146464309299
Median186.35
Midrange224.7
Midmean - Weighted Average at Xnp187.987096774194
Midmean - Weighted Average at X(n+1)p188.84
Midmean - Empirical Distribution Function187.987096774194
Midmean - Empirical Distribution Function - Averaging188.84
Midmean - Empirical Distribution Function - Interpolation188.84
Midmean - Closest Observation187.987096774194
Midmean - True Basic - Statistics Graphics Toolkit188.84
Midmean - MS Excel (old versions)189.05625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 195.81 & 5.00134823630498 & 39.1514429206524 \tabularnewline
Geometric Mean & 192.275805757649 &  &  \tabularnewline
Harmonic Mean & 188.99270554205 &  &  \tabularnewline
Quadratic Mean & 199.542856716713 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 195.548333333333 & 4.90896475656198 & 39.8349434210008 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 195.101666666667 & 4.76592986976733 & 40.9367472870916 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 194.971666666667 & 4.65030470520203 & 41.9266433119024 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 194.451666666667 & 4.50082258123127 & 43.2035840465126 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 194.376666666667 & 4.44587307312046 & 43.7206963558764 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 193.976666666667 & 4.33552684595714 & 44.7411983730533 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 193.685 & 4.25689591757977 & 45.4991157289366 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 193.338333333333 & 4.17611048979496 & 46.2962686944678 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 192.438333333333 & 3.96850958352137 & 48.4913364282662 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 192.255 & 3.92843568369191 & 48.9393273760614 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 192.456666666667 & 3.8737646958767 & 49.682074616334 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 190.816666666667 & 3.56087350950004 & 53.5870387301283 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 190.686666666667 & 3.51109658749291 & 54.3097183215988 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 190.57 & 3.27906671647184 & 58.1171462729634 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 190.42 & 3.24692275002544 & 58.6462982522476 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 189.993333333333 & 3.17012258640041 & 59.9324878313509 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 188.888333333333 & 2.96349550406889 & 63.7383566379598 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 188.108333333333 & 2.83762084206374 & 66.2908625933712 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 188.9 & 2.60985528962208 & 72.3794919784053 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 189.266666666667 & 2.53828834478682 & 74.5646833447374 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 194.813793103448 & 4.76376056179507 & 40.8949590510147 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 194.026785714286 & 4.58240245719258 & 42.3417164962758 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 193.42962962963 & 4.45314188006408 & 43.4366644583186 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 192.836538461538 & 4.34596172608913 & 44.3714304486223 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 192.352 & 4.26820254669244 & 45.0662774073502 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 191.845833333333 & 4.18456823731461 & 45.8460281810215 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 191.382608695652 & 4.10858333818835 & 46.5811675077379 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 190.934090909091 & 4.02922193736292 & 47.3873352913528 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 190.504761904762 & 3.94408943750874 & 48.3013290958973 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 190.1825 & 3.88453522860943 & 48.9588815154293 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 189.855263157895 & 3.80917455275776 & 49.8415760497097 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 189.461111111111 & 3.71437421886144 & 51.0075452680658 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 189.261764705882 & 3.66625021465645 & 51.6227081144862 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 189.05625 & 3.60242676242405 & 52.4802480294659 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 188.84 & 3.56599392086949 & 52.9557829290846 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 188.614285714286 & 3.50760592423492 & 53.7729408001916 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 188.415384615385 & 3.43084960237007 & 54.917995963806 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 188.345833333333 & 3.3706264156051 & 55.8785846041384 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 188.381818181818 & 3.30156486813638 & 57.0583422424631 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 188.3 & 3.25696015844287 & 57.8146464309299 \tabularnewline
Median & 186.35 &  &  \tabularnewline
Midrange & 224.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 187.987096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 188.84 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 187.987096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 188.84 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 188.84 &  &  \tabularnewline
Midmean - Closest Observation & 187.987096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 188.84 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 189.05625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132767&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]195.81[/C][C]5.00134823630498[/C][C]39.1514429206524[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]192.275805757649[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]188.99270554205[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]199.542856716713[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]195.548333333333[/C][C]4.90896475656198[/C][C]39.8349434210008[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]195.101666666667[/C][C]4.76592986976733[/C][C]40.9367472870916[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]194.971666666667[/C][C]4.65030470520203[/C][C]41.9266433119024[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]194.451666666667[/C][C]4.50082258123127[/C][C]43.2035840465126[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]194.376666666667[/C][C]4.44587307312046[/C][C]43.7206963558764[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]193.976666666667[/C][C]4.33552684595714[/C][C]44.7411983730533[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]193.685[/C][C]4.25689591757977[/C][C]45.4991157289366[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]193.338333333333[/C][C]4.17611048979496[/C][C]46.2962686944678[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]192.438333333333[/C][C]3.96850958352137[/C][C]48.4913364282662[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]192.255[/C][C]3.92843568369191[/C][C]48.9393273760614[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]192.456666666667[/C][C]3.8737646958767[/C][C]49.682074616334[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]190.816666666667[/C][C]3.56087350950004[/C][C]53.5870387301283[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]190.686666666667[/C][C]3.51109658749291[/C][C]54.3097183215988[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]190.57[/C][C]3.27906671647184[/C][C]58.1171462729634[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]190.42[/C][C]3.24692275002544[/C][C]58.6462982522476[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]189.993333333333[/C][C]3.17012258640041[/C][C]59.9324878313509[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]188.888333333333[/C][C]2.96349550406889[/C][C]63.7383566379598[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]188.108333333333[/C][C]2.83762084206374[/C][C]66.2908625933712[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]188.9[/C][C]2.60985528962208[/C][C]72.3794919784053[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]189.266666666667[/C][C]2.53828834478682[/C][C]74.5646833447374[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]194.813793103448[/C][C]4.76376056179507[/C][C]40.8949590510147[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]194.026785714286[/C][C]4.58240245719258[/C][C]42.3417164962758[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]193.42962962963[/C][C]4.45314188006408[/C][C]43.4366644583186[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]192.836538461538[/C][C]4.34596172608913[/C][C]44.3714304486223[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]192.352[/C][C]4.26820254669244[/C][C]45.0662774073502[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]191.845833333333[/C][C]4.18456823731461[/C][C]45.8460281810215[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]191.382608695652[/C][C]4.10858333818835[/C][C]46.5811675077379[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]190.934090909091[/C][C]4.02922193736292[/C][C]47.3873352913528[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]190.504761904762[/C][C]3.94408943750874[/C][C]48.3013290958973[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]190.1825[/C][C]3.88453522860943[/C][C]48.9588815154293[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]189.855263157895[/C][C]3.80917455275776[/C][C]49.8415760497097[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]189.461111111111[/C][C]3.71437421886144[/C][C]51.0075452680658[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]189.261764705882[/C][C]3.66625021465645[/C][C]51.6227081144862[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]189.05625[/C][C]3.60242676242405[/C][C]52.4802480294659[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]188.84[/C][C]3.56599392086949[/C][C]52.9557829290846[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]188.614285714286[/C][C]3.50760592423492[/C][C]53.7729408001916[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]188.415384615385[/C][C]3.43084960237007[/C][C]54.917995963806[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]188.345833333333[/C][C]3.3706264156051[/C][C]55.8785846041384[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]188.381818181818[/C][C]3.30156486813638[/C][C]57.0583422424631[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]188.3[/C][C]3.25696015844287[/C][C]57.8146464309299[/C][/ROW]
[ROW][C]Median[/C][C]186.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]224.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]187.987096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]188.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]187.987096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]188.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]188.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]187.987096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]188.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]189.05625[/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=132767&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132767&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 Mean195.815.0013482363049839.1514429206524
Geometric Mean192.275805757649
Harmonic Mean188.99270554205
Quadratic Mean199.542856716713
Winsorized Mean ( 1 / 20 )195.5483333333334.9089647565619839.8349434210008
Winsorized Mean ( 2 / 20 )195.1016666666674.7659298697673340.9367472870916
Winsorized Mean ( 3 / 20 )194.9716666666674.6503047052020341.9266433119024
Winsorized Mean ( 4 / 20 )194.4516666666674.5008225812312743.2035840465126
Winsorized Mean ( 5 / 20 )194.3766666666674.4458730731204643.7206963558764
Winsorized Mean ( 6 / 20 )193.9766666666674.3355268459571444.7411983730533
Winsorized Mean ( 7 / 20 )193.6854.2568959175797745.4991157289366
Winsorized Mean ( 8 / 20 )193.3383333333334.1761104897949646.2962686944678
Winsorized Mean ( 9 / 20 )192.4383333333333.9685095835213748.4913364282662
Winsorized Mean ( 10 / 20 )192.2553.9284356836919148.9393273760614
Winsorized Mean ( 11 / 20 )192.4566666666673.873764695876749.682074616334
Winsorized Mean ( 12 / 20 )190.8166666666673.5608735095000453.5870387301283
Winsorized Mean ( 13 / 20 )190.6866666666673.5110965874929154.3097183215988
Winsorized Mean ( 14 / 20 )190.573.2790667164718458.1171462729634
Winsorized Mean ( 15 / 20 )190.423.2469227500254458.6462982522476
Winsorized Mean ( 16 / 20 )189.9933333333333.1701225864004159.9324878313509
Winsorized Mean ( 17 / 20 )188.8883333333332.9634955040688963.7383566379598
Winsorized Mean ( 18 / 20 )188.1083333333332.8376208420637466.2908625933712
Winsorized Mean ( 19 / 20 )188.92.6098552896220872.3794919784053
Winsorized Mean ( 20 / 20 )189.2666666666672.5382883447868274.5646833447374
Trimmed Mean ( 1 / 20 )194.8137931034484.7637605617950740.8949590510147
Trimmed Mean ( 2 / 20 )194.0267857142864.5824024571925842.3417164962758
Trimmed Mean ( 3 / 20 )193.429629629634.4531418800640843.4366644583186
Trimmed Mean ( 4 / 20 )192.8365384615384.3459617260891344.3714304486223
Trimmed Mean ( 5 / 20 )192.3524.2682025466924445.0662774073502
Trimmed Mean ( 6 / 20 )191.8458333333334.1845682373146145.8460281810215
Trimmed Mean ( 7 / 20 )191.3826086956524.1085833381883546.5811675077379
Trimmed Mean ( 8 / 20 )190.9340909090914.0292219373629247.3873352913528
Trimmed Mean ( 9 / 20 )190.5047619047623.9440894375087448.3013290958973
Trimmed Mean ( 10 / 20 )190.18253.8845352286094348.9588815154293
Trimmed Mean ( 11 / 20 )189.8552631578953.8091745527577649.8415760497097
Trimmed Mean ( 12 / 20 )189.4611111111113.7143742188614451.0075452680658
Trimmed Mean ( 13 / 20 )189.2617647058823.6662502146564551.6227081144862
Trimmed Mean ( 14 / 20 )189.056253.6024267624240552.4802480294659
Trimmed Mean ( 15 / 20 )188.843.5659939208694952.9557829290846
Trimmed Mean ( 16 / 20 )188.6142857142863.5076059242349253.7729408001916
Trimmed Mean ( 17 / 20 )188.4153846153853.4308496023700754.917995963806
Trimmed Mean ( 18 / 20 )188.3458333333333.370626415605155.8785846041384
Trimmed Mean ( 19 / 20 )188.3818181818183.3015648681363857.0583422424631
Trimmed Mean ( 20 / 20 )188.33.2569601584428757.8146464309299
Median186.35
Midrange224.7
Midmean - Weighted Average at Xnp187.987096774194
Midmean - Weighted Average at X(n+1)p188.84
Midmean - Empirical Distribution Function187.987096774194
Midmean - Empirical Distribution Function - Averaging188.84
Midmean - Empirical Distribution Function - Interpolation188.84
Midmean - Closest Observation187.987096774194
Midmean - True Basic - Statistics Graphics Toolkit188.84
Midmean - MS Excel (old versions)189.05625
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')