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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Nov 2010 21:29:42 +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/Nov/15/t1289856468kj2gmjob795vvag.htm/, Retrieved Sun, 28 Apr 2024 12:04:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95094, Retrieved Sun, 28 Apr 2024 12:04:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [] [2010-11-15 21:29:42] [6fde1c772c7be11768d9b6a0344566b2] [Current]
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Dataseries X:
145
621
262
208
362
424
339
736
291
58
498
643
390
332
750
368
659
234
396
300
343
536
543
217
298
1103
406
254
862
204
206
250
21
298
350
800
726
370
536
291
808
543
149
350
242
198
213
296
317
482
155
802
200
282
573
388
250
396
572




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=95094&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=95094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95094&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 Mean404.16949152542428.711020662905214.0771551200063
Geometric Mean341.644582164393
Harmonic Mean248.603334151871
Quadratic Mean459.525510625095
Winsorized Mean ( 1 / 19 )400.7118644067827.106658295184314.7827836261900
Winsorized Mean ( 2 / 19 )401.83050847457626.017462019743315.4446466826644
Winsorized Mean ( 3 / 19 )401.72881355932225.901341731880915.5099615192850
Winsorized Mean ( 4 / 19 )40225.797450931754315.5829349598714
Winsorized Mean ( 5 / 19 )401.40677966101724.138482685805316.6293293943064
Winsorized Mean ( 6 / 19 )400.18644067796623.758175246512416.8441572858889
Winsorized Mean ( 7 / 19 )399.47457627118623.402237749758117.0699306853814
Winsorized Mean ( 8 / 19 )390.66101694915321.277021327454718.3607005387105
Winsorized Mean ( 9 / 19 )388.52542372881420.707254506728618.7627685554629
Winsorized Mean ( 10 / 19 )385.6440677966119.802498863973319.4745153349415
Winsorized Mean ( 11 / 19 )377.44067796610217.926733661489621.0546262968655
Winsorized Mean ( 12 / 19 )380.69491525423717.369556495000521.9173653261563
Winsorized Mean ( 13 / 19 )376.06779661016915.928020889260923.6104535035941
Winsorized Mean ( 14 / 19 )377.96610169491515.656488677166524.1411793850138
Winsorized Mean ( 15 / 19 )376.18644067796615.334864845263124.5314480742992
Winsorized Mean ( 16 / 19 )377.27118644067815.181982586964024.8499288073628
Winsorized Mean ( 17 / 19 )368.62711864406812.921624513702128.527923733829
Winsorized Mean ( 18 / 19 )369.84745762711911.233086865919832.9248284146366
Winsorized Mean ( 19 / 19 )354.0677966101697.7461879317041245.7086504654782
Trimmed Mean ( 1 / 19 )398.63157894736826.156826904675315.2400587578961
Trimmed Mean ( 2 / 19 )396.424.977344616827115.8703819833973
Trimmed Mean ( 3 / 19 )393.37735849056624.243162614184716.2263218191013
Trimmed Mean ( 4 / 19 )390.15686274509823.368864362802816.6955850608696
Trimmed Mean ( 5 / 19 )386.59183673469422.29090137984517.3430329329007
Trimmed Mean ( 6 / 19 )382.87234042553221.510804828016217.7990709081637
Trimmed Mean ( 7 / 19 )379.08888888888920.616797658196418.3873798042626
Trimmed Mean ( 8 / 19 )375.09302325581419.545126645413619.1911277967509
Trimmed Mean ( 9 / 19 )372.29268292682918.812237970055519.7899199191201
Trimmed Mean ( 10 / 19 )369.56410256410317.993693409804420.5385350382115
Trimmed Mean ( 11 / 19 )36717.151856639623221.397100483698
Trimmed Mean ( 12 / 19 )365.416.572489099648922.0485889477966
Trimmed Mean ( 13 / 19 )363.12121212121215.892319803665122.8488487903112
Trimmed Mean ( 14 / 19 )361.22580645161315.365490567552623.5089016431676
Trimmed Mean ( 15 / 19 )358.79310344827614.637944089534524.5111677742230
Trimmed Mean ( 16 / 19 )356.25925925925913.638348041490726.1218776772263
Trimmed Mean ( 17 / 19 )353.1612.081070592735829.2325086000532
Trimmed Mean ( 18 / 19 )350.82608695652210.720792138951932.7238959966273
Trimmed Mean ( 19 / 19 )347.8571428571439.2618741583531637.5579647174773
Median350
Midrange562
Midmean - Weighted Average at Xnp355.166666666667
Midmean - Weighted Average at X(n+1)p366.90625
Midmean - Empirical Distribution Function366.90625
Midmean - Empirical Distribution Function - Averaging366.90625
Midmean - Empirical Distribution Function - Interpolation355.166666666667
Midmean - Closest Observation355.166666666667
Midmean - True Basic - Statistics Graphics Toolkit366.90625
Midmean - MS Excel (old versions)366.90625
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 404.169491525424 & 28.7110206629052 & 14.0771551200063 \tabularnewline
Geometric Mean & 341.644582164393 &  &  \tabularnewline
Harmonic Mean & 248.603334151871 &  &  \tabularnewline
Quadratic Mean & 459.525510625095 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 400.71186440678 & 27.1066582951843 & 14.7827836261900 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 401.830508474576 & 26.0174620197433 & 15.4446466826644 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 401.728813559322 & 25.9013417318809 & 15.5099615192850 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 402 & 25.7974509317543 & 15.5829349598714 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 401.406779661017 & 24.1384826858053 & 16.6293293943064 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 400.186440677966 & 23.7581752465124 & 16.8441572858889 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 399.474576271186 & 23.4022377497581 & 17.0699306853814 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 390.661016949153 & 21.2770213274547 & 18.3607005387105 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 388.525423728814 & 20.7072545067286 & 18.7627685554629 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 385.64406779661 & 19.8024988639733 & 19.4745153349415 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 377.440677966102 & 17.9267336614896 & 21.0546262968655 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 380.694915254237 & 17.3695564950005 & 21.9173653261563 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 376.067796610169 & 15.9280208892609 & 23.6104535035941 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 377.966101694915 & 15.6564886771665 & 24.1411793850138 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 376.186440677966 & 15.3348648452631 & 24.5314480742992 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 377.271186440678 & 15.1819825869640 & 24.8499288073628 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 368.627118644068 & 12.9216245137021 & 28.527923733829 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 369.847457627119 & 11.2330868659198 & 32.9248284146366 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 354.067796610169 & 7.74618793170412 & 45.7086504654782 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 398.631578947368 & 26.1568269046753 & 15.2400587578961 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 396.4 & 24.9773446168271 & 15.8703819833973 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 393.377358490566 & 24.2431626141847 & 16.2263218191013 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 390.156862745098 & 23.3688643628028 & 16.6955850608696 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 386.591836734694 & 22.290901379845 & 17.3430329329007 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 382.872340425532 & 21.5108048280162 & 17.7990709081637 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 379.088888888889 & 20.6167976581964 & 18.3873798042626 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 375.093023255814 & 19.5451266454136 & 19.1911277967509 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 372.292682926829 & 18.8122379700555 & 19.7899199191201 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 369.564102564103 & 17.9936934098044 & 20.5385350382115 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 367 & 17.1518566396232 & 21.397100483698 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 365.4 & 16.5724890996489 & 22.0485889477966 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 363.121212121212 & 15.8923198036651 & 22.8488487903112 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 361.225806451613 & 15.3654905675526 & 23.5089016431676 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 358.793103448276 & 14.6379440895345 & 24.5111677742230 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 356.259259259259 & 13.6383480414907 & 26.1218776772263 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 353.16 & 12.0810705927358 & 29.2325086000532 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 350.826086956522 & 10.7207921389519 & 32.7238959966273 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 347.857142857143 & 9.26187415835316 & 37.5579647174773 \tabularnewline
Median & 350 &  &  \tabularnewline
Midrange & 562 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 355.166666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 366.90625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 366.90625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 366.90625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 355.166666666667 &  &  \tabularnewline
Midmean - Closest Observation & 355.166666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 366.90625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 366.90625 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95094&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]404.169491525424[/C][C]28.7110206629052[/C][C]14.0771551200063[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]341.644582164393[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]248.603334151871[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]459.525510625095[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]400.71186440678[/C][C]27.1066582951843[/C][C]14.7827836261900[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]401.830508474576[/C][C]26.0174620197433[/C][C]15.4446466826644[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]401.728813559322[/C][C]25.9013417318809[/C][C]15.5099615192850[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]402[/C][C]25.7974509317543[/C][C]15.5829349598714[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]401.406779661017[/C][C]24.1384826858053[/C][C]16.6293293943064[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]400.186440677966[/C][C]23.7581752465124[/C][C]16.8441572858889[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]399.474576271186[/C][C]23.4022377497581[/C][C]17.0699306853814[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]390.661016949153[/C][C]21.2770213274547[/C][C]18.3607005387105[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]388.525423728814[/C][C]20.7072545067286[/C][C]18.7627685554629[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]385.64406779661[/C][C]19.8024988639733[/C][C]19.4745153349415[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]377.440677966102[/C][C]17.9267336614896[/C][C]21.0546262968655[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]380.694915254237[/C][C]17.3695564950005[/C][C]21.9173653261563[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]376.067796610169[/C][C]15.9280208892609[/C][C]23.6104535035941[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]377.966101694915[/C][C]15.6564886771665[/C][C]24.1411793850138[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]376.186440677966[/C][C]15.3348648452631[/C][C]24.5314480742992[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]377.271186440678[/C][C]15.1819825869640[/C][C]24.8499288073628[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]368.627118644068[/C][C]12.9216245137021[/C][C]28.527923733829[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]369.847457627119[/C][C]11.2330868659198[/C][C]32.9248284146366[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]354.067796610169[/C][C]7.74618793170412[/C][C]45.7086504654782[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]398.631578947368[/C][C]26.1568269046753[/C][C]15.2400587578961[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]396.4[/C][C]24.9773446168271[/C][C]15.8703819833973[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]393.377358490566[/C][C]24.2431626141847[/C][C]16.2263218191013[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]390.156862745098[/C][C]23.3688643628028[/C][C]16.6955850608696[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]386.591836734694[/C][C]22.290901379845[/C][C]17.3430329329007[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]382.872340425532[/C][C]21.5108048280162[/C][C]17.7990709081637[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]379.088888888889[/C][C]20.6167976581964[/C][C]18.3873798042626[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]375.093023255814[/C][C]19.5451266454136[/C][C]19.1911277967509[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]372.292682926829[/C][C]18.8122379700555[/C][C]19.7899199191201[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]369.564102564103[/C][C]17.9936934098044[/C][C]20.5385350382115[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]367[/C][C]17.1518566396232[/C][C]21.397100483698[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]365.4[/C][C]16.5724890996489[/C][C]22.0485889477966[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]363.121212121212[/C][C]15.8923198036651[/C][C]22.8488487903112[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]361.225806451613[/C][C]15.3654905675526[/C][C]23.5089016431676[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]358.793103448276[/C][C]14.6379440895345[/C][C]24.5111677742230[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]356.259259259259[/C][C]13.6383480414907[/C][C]26.1218776772263[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]353.16[/C][C]12.0810705927358[/C][C]29.2325086000532[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]350.826086956522[/C][C]10.7207921389519[/C][C]32.7238959966273[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]347.857142857143[/C][C]9.26187415835316[/C][C]37.5579647174773[/C][/ROW]
[ROW][C]Median[/C][C]350[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]562[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]355.166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]366.90625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]366.90625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]366.90625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]355.166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]355.166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]366.90625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]366.90625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95094&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 Mean404.16949152542428.711020662905214.0771551200063
Geometric Mean341.644582164393
Harmonic Mean248.603334151871
Quadratic Mean459.525510625095
Winsorized Mean ( 1 / 19 )400.7118644067827.106658295184314.7827836261900
Winsorized Mean ( 2 / 19 )401.83050847457626.017462019743315.4446466826644
Winsorized Mean ( 3 / 19 )401.72881355932225.901341731880915.5099615192850
Winsorized Mean ( 4 / 19 )40225.797450931754315.5829349598714
Winsorized Mean ( 5 / 19 )401.40677966101724.138482685805316.6293293943064
Winsorized Mean ( 6 / 19 )400.18644067796623.758175246512416.8441572858889
Winsorized Mean ( 7 / 19 )399.47457627118623.402237749758117.0699306853814
Winsorized Mean ( 8 / 19 )390.66101694915321.277021327454718.3607005387105
Winsorized Mean ( 9 / 19 )388.52542372881420.707254506728618.7627685554629
Winsorized Mean ( 10 / 19 )385.6440677966119.802498863973319.4745153349415
Winsorized Mean ( 11 / 19 )377.44067796610217.926733661489621.0546262968655
Winsorized Mean ( 12 / 19 )380.69491525423717.369556495000521.9173653261563
Winsorized Mean ( 13 / 19 )376.06779661016915.928020889260923.6104535035941
Winsorized Mean ( 14 / 19 )377.96610169491515.656488677166524.1411793850138
Winsorized Mean ( 15 / 19 )376.18644067796615.334864845263124.5314480742992
Winsorized Mean ( 16 / 19 )377.27118644067815.181982586964024.8499288073628
Winsorized Mean ( 17 / 19 )368.62711864406812.921624513702128.527923733829
Winsorized Mean ( 18 / 19 )369.84745762711911.233086865919832.9248284146366
Winsorized Mean ( 19 / 19 )354.0677966101697.7461879317041245.7086504654782
Trimmed Mean ( 1 / 19 )398.63157894736826.156826904675315.2400587578961
Trimmed Mean ( 2 / 19 )396.424.977344616827115.8703819833973
Trimmed Mean ( 3 / 19 )393.37735849056624.243162614184716.2263218191013
Trimmed Mean ( 4 / 19 )390.15686274509823.368864362802816.6955850608696
Trimmed Mean ( 5 / 19 )386.59183673469422.29090137984517.3430329329007
Trimmed Mean ( 6 / 19 )382.87234042553221.510804828016217.7990709081637
Trimmed Mean ( 7 / 19 )379.08888888888920.616797658196418.3873798042626
Trimmed Mean ( 8 / 19 )375.09302325581419.545126645413619.1911277967509
Trimmed Mean ( 9 / 19 )372.29268292682918.812237970055519.7899199191201
Trimmed Mean ( 10 / 19 )369.56410256410317.993693409804420.5385350382115
Trimmed Mean ( 11 / 19 )36717.151856639623221.397100483698
Trimmed Mean ( 12 / 19 )365.416.572489099648922.0485889477966
Trimmed Mean ( 13 / 19 )363.12121212121215.892319803665122.8488487903112
Trimmed Mean ( 14 / 19 )361.22580645161315.365490567552623.5089016431676
Trimmed Mean ( 15 / 19 )358.79310344827614.637944089534524.5111677742230
Trimmed Mean ( 16 / 19 )356.25925925925913.638348041490726.1218776772263
Trimmed Mean ( 17 / 19 )353.1612.081070592735829.2325086000532
Trimmed Mean ( 18 / 19 )350.82608695652210.720792138951932.7238959966273
Trimmed Mean ( 19 / 19 )347.8571428571439.2618741583531637.5579647174773
Median350
Midrange562
Midmean - Weighted Average at Xnp355.166666666667
Midmean - Weighted Average at X(n+1)p366.90625
Midmean - Empirical Distribution Function366.90625
Midmean - Empirical Distribution Function - Averaging366.90625
Midmean - Empirical Distribution Function - Interpolation355.166666666667
Midmean - Closest Observation355.166666666667
Midmean - True Basic - Statistics Graphics Toolkit366.90625
Midmean - MS Excel (old versions)366.90625
Number of observations59



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')