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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 computationTue, 15 Nov 2011 16:09:11 -0500
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/Nov/15/t1321391371152sedxzoqfx91f.htm/, Retrieved Thu, 28 Mar 2024 16:54:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143556, Retrieved Thu, 28 Mar 2024 16:54:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
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]
- RM D  [Central Tendency] [winsorized and tr...] [2011-11-13 14:50:39] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [trimmed and winso...] [2011-11-14 19:40:43] [74be16979710d4c4e7c6647856088456]
-             [Central Tendency] [W6 T6] [2011-11-15 21:09:11] [7c363341293f6644b8647ab9153ed4f7] [Current]
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Dataseries X:
29975
29124
29704
29564
30550
29812
30611
30577
30637
30944
30852
31216
31113
32073
31447
32293
31807
31778
31707
32135
31929
32923
33181
33435
34721
35179
35605
35931
35093
35053
35092
35295
35981
35606
35815
36144
36391
35642
36896
36399
38385
38226
38609
38227
38254
38047
38437
37963
38231
38283
38839
38833
39431
40091
40289
39433
38677
38107
38485
38464




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143556&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143556&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean34892.35432.29707680366680.7138236001695
Geometric Mean34732.0573382968
Harmonic Mean34570.1210555596
Quadratic Mean35049.993630765
Winsorized Mean ( 1 / 20 )34896.3833333333430.01002030872981.1524887449814
Winsorized Mean ( 2 / 20 )34879.1166666667424.79818411444582.1074994455952
Winsorized Mean ( 3 / 20 )34884.4166666667423.67459550538182.3377588289304
Winsorized Mean ( 4 / 20 )34855.8166666667414.68202404823284.0543226986193
Winsorized Mean ( 5 / 20 )34903.2333333333405.45618401537486.0838598826498
Winsorized Mean ( 6 / 20 )34890.3333333333402.43985174800186.6970136823848
Winsorized Mean ( 7 / 20 )34886.3666666667400.46307797014987.1150639991513
Winsorized Mean ( 8 / 20 )34873.3397.25972043516687.7846361111042
Winsorized Mean ( 9 / 20 )34902.4391.02776080160189.258112847156
Winsorized Mean ( 10 / 20 )34913.2333333333387.65719637596290.0621313359377
Winsorized Mean ( 11 / 20 )34934.6833333333380.8672793225691.7240341450988
Winsorized Mean ( 12 / 20 )34934.8833333333374.26786088336193.3419269580847
Winsorized Mean ( 13 / 20 )34978.65364.99368063951495.8335770052596
Winsorized Mean ( 14 / 20 )35033.95354.37170981144898.862152451844
Winsorized Mean ( 15 / 20 )35050.7351.40546084203799.7443235970539
Winsorized Mean ( 16 / 20 )35058.1666666667350.145709916969100.12450723723
Winsorized Mean ( 17 / 20 )35059.0166666667339.575163701943103.243759892402
Winsorized Mean ( 18 / 20 )35084.2166666667330.122502593288106.276356174031
Winsorized Mean ( 19 / 20 )35077.25323.052542144271108.580634491138
Winsorized Mean ( 20 / 20 )34774.25263.315730254451132.062941953359
Trimmed Mean ( 1 / 20 )34898.7586206897425.71523554219181.976766878551
Trimmed Mean ( 2 / 20 )34901.3035714286420.16479522042983.0657493641714
Trimmed Mean ( 3 / 20 )34913.6296296296416.3759994925183.851205814416
Trimmed Mean ( 4 / 20 )34924.8653846154411.80825542652884.8085605968296
Trimmed Mean ( 5 / 20 )34945.58409.03026392696685.4351941210876
Trimmed Mean ( 6 / 20 )34956.1666666667407.95533597021685.6862592164224
Trimmed Mean ( 7 / 20 )34970.4782608696406.72454059457185.9807431578824
Trimmed Mean ( 8 / 20 )34986.8636363636404.89456460546686.4098130594943
Trimmed Mean ( 9 / 20 )35007.1428571429402.51690375254786.9706154717517
Trimmed Mean ( 10 / 20 )35024.6400.13694098203687.5315333646548
Trimmed Mean ( 11 / 20 )35042.1842105263396.87919459194188.2943341148322
Trimmed Mean ( 12 / 20 )35058.4722222222393.23743279268789.1534459810822
Trimmed Mean ( 13 / 20 )35076.6470588235388.86868199972290.2017793730393
Trimmed Mean ( 14 / 20 )35090.78125384.15078297621691.3463744057306
Trimmed Mean ( 15 / 20 )35098.9379.16775576450992.5682615844555
Trimmed Mean ( 16 / 20 )35105.7857142857371.36885483525494.5307751503806
Trimmed Mean ( 17 / 20 )35112.6538461538358.72564593746997.8816380813611
Trimmed Mean ( 18 / 20 )35120.5416666667341.939809407811102.709718787907
Trimmed Mean ( 19 / 20 )35126.0454545455317.897138726828110.495003494604
Trimmed Mean ( 20 / 20 )35133.75279.535412265649125.686222418974
Median35450
Midrange34706.5
Midmean - Weighted Average at Xnp34989.4838709677
Midmean - Weighted Average at X(n+1)p35098.9
Midmean - Empirical Distribution Function34989.4838709677
Midmean - Empirical Distribution Function - Averaging35098.9
Midmean - Empirical Distribution Function - Interpolation35098.9
Midmean - Closest Observation34989.4838709677
Midmean - True Basic - Statistics Graphics Toolkit35098.9
Midmean - MS Excel (old versions)35090.78125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 34892.35 & 432.297076803666 & 80.7138236001695 \tabularnewline
Geometric Mean & 34732.0573382968 &  &  \tabularnewline
Harmonic Mean & 34570.1210555596 &  &  \tabularnewline
Quadratic Mean & 35049.993630765 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 34896.3833333333 & 430.010020308729 & 81.1524887449814 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 34879.1166666667 & 424.798184114445 & 82.1074994455952 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 34884.4166666667 & 423.674595505381 & 82.3377588289304 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 34855.8166666667 & 414.682024048232 & 84.0543226986193 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 34903.2333333333 & 405.456184015374 & 86.0838598826498 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 34890.3333333333 & 402.439851748001 & 86.6970136823848 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 34886.3666666667 & 400.463077970149 & 87.1150639991513 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 34873.3 & 397.259720435166 & 87.7846361111042 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 34902.4 & 391.027760801601 & 89.258112847156 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 34913.2333333333 & 387.657196375962 & 90.0621313359377 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 34934.6833333333 & 380.86727932256 & 91.7240341450988 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 34934.8833333333 & 374.267860883361 & 93.3419269580847 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 34978.65 & 364.993680639514 & 95.8335770052596 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 35033.95 & 354.371709811448 & 98.862152451844 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 35050.7 & 351.405460842037 & 99.7443235970539 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 35058.1666666667 & 350.145709916969 & 100.12450723723 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 35059.0166666667 & 339.575163701943 & 103.243759892402 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 35084.2166666667 & 330.122502593288 & 106.276356174031 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 35077.25 & 323.052542144271 & 108.580634491138 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 34774.25 & 263.315730254451 & 132.062941953359 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 34898.7586206897 & 425.715235542191 & 81.976766878551 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 34901.3035714286 & 420.164795220429 & 83.0657493641714 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 34913.6296296296 & 416.37599949251 & 83.851205814416 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 34924.8653846154 & 411.808255426528 & 84.8085605968296 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 34945.58 & 409.030263926966 & 85.4351941210876 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 34956.1666666667 & 407.955335970216 & 85.6862592164224 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 34970.4782608696 & 406.724540594571 & 85.9807431578824 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 34986.8636363636 & 404.894564605466 & 86.4098130594943 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 35007.1428571429 & 402.516903752547 & 86.9706154717517 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 35024.6 & 400.136940982036 & 87.5315333646548 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 35042.1842105263 & 396.879194591941 & 88.2943341148322 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 35058.4722222222 & 393.237432792687 & 89.1534459810822 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 35076.6470588235 & 388.868681999722 & 90.2017793730393 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 35090.78125 & 384.150782976216 & 91.3463744057306 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 35098.9 & 379.167755764509 & 92.5682615844555 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 35105.7857142857 & 371.368854835254 & 94.5307751503806 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 35112.6538461538 & 358.725645937469 & 97.8816380813611 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 35120.5416666667 & 341.939809407811 & 102.709718787907 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 35126.0454545455 & 317.897138726828 & 110.495003494604 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 35133.75 & 279.535412265649 & 125.686222418974 \tabularnewline
Median & 35450 &  &  \tabularnewline
Midrange & 34706.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 34989.4838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 35098.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 34989.4838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 35098.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 35098.9 &  &  \tabularnewline
Midmean - Closest Observation & 34989.4838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 35098.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 35090.78125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143556&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]34892.35[/C][C]432.297076803666[/C][C]80.7138236001695[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]34732.0573382968[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]34570.1210555596[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]35049.993630765[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]34896.3833333333[/C][C]430.010020308729[/C][C]81.1524887449814[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]34879.1166666667[/C][C]424.798184114445[/C][C]82.1074994455952[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]34884.4166666667[/C][C]423.674595505381[/C][C]82.3377588289304[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]34855.8166666667[/C][C]414.682024048232[/C][C]84.0543226986193[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]34903.2333333333[/C][C]405.456184015374[/C][C]86.0838598826498[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]34890.3333333333[/C][C]402.439851748001[/C][C]86.6970136823848[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]34886.3666666667[/C][C]400.463077970149[/C][C]87.1150639991513[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]34873.3[/C][C]397.259720435166[/C][C]87.7846361111042[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]34902.4[/C][C]391.027760801601[/C][C]89.258112847156[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]34913.2333333333[/C][C]387.657196375962[/C][C]90.0621313359377[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]34934.6833333333[/C][C]380.86727932256[/C][C]91.7240341450988[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]34934.8833333333[/C][C]374.267860883361[/C][C]93.3419269580847[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]34978.65[/C][C]364.993680639514[/C][C]95.8335770052596[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]35033.95[/C][C]354.371709811448[/C][C]98.862152451844[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]35050.7[/C][C]351.405460842037[/C][C]99.7443235970539[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]35058.1666666667[/C][C]350.145709916969[/C][C]100.12450723723[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]35059.0166666667[/C][C]339.575163701943[/C][C]103.243759892402[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]35084.2166666667[/C][C]330.122502593288[/C][C]106.276356174031[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]35077.25[/C][C]323.052542144271[/C][C]108.580634491138[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]34774.25[/C][C]263.315730254451[/C][C]132.062941953359[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]34898.7586206897[/C][C]425.715235542191[/C][C]81.976766878551[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]34901.3035714286[/C][C]420.164795220429[/C][C]83.0657493641714[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]34913.6296296296[/C][C]416.37599949251[/C][C]83.851205814416[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]34924.8653846154[/C][C]411.808255426528[/C][C]84.8085605968296[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]34945.58[/C][C]409.030263926966[/C][C]85.4351941210876[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]34956.1666666667[/C][C]407.955335970216[/C][C]85.6862592164224[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]34970.4782608696[/C][C]406.724540594571[/C][C]85.9807431578824[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]34986.8636363636[/C][C]404.894564605466[/C][C]86.4098130594943[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]35007.1428571429[/C][C]402.516903752547[/C][C]86.9706154717517[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]35024.6[/C][C]400.136940982036[/C][C]87.5315333646548[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]35042.1842105263[/C][C]396.879194591941[/C][C]88.2943341148322[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]35058.4722222222[/C][C]393.237432792687[/C][C]89.1534459810822[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]35076.6470588235[/C][C]388.868681999722[/C][C]90.2017793730393[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]35090.78125[/C][C]384.150782976216[/C][C]91.3463744057306[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]35098.9[/C][C]379.167755764509[/C][C]92.5682615844555[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]35105.7857142857[/C][C]371.368854835254[/C][C]94.5307751503806[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]35112.6538461538[/C][C]358.725645937469[/C][C]97.8816380813611[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]35120.5416666667[/C][C]341.939809407811[/C][C]102.709718787907[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]35126.0454545455[/C][C]317.897138726828[/C][C]110.495003494604[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]35133.75[/C][C]279.535412265649[/C][C]125.686222418974[/C][/ROW]
[ROW][C]Median[/C][C]35450[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]34706.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]34989.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]35098.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]34989.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]35098.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]35098.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]34989.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]35098.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]35090.78125[/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=143556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143556&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 Mean34892.35432.29707680366680.7138236001695
Geometric Mean34732.0573382968
Harmonic Mean34570.1210555596
Quadratic Mean35049.993630765
Winsorized Mean ( 1 / 20 )34896.3833333333430.01002030872981.1524887449814
Winsorized Mean ( 2 / 20 )34879.1166666667424.79818411444582.1074994455952
Winsorized Mean ( 3 / 20 )34884.4166666667423.67459550538182.3377588289304
Winsorized Mean ( 4 / 20 )34855.8166666667414.68202404823284.0543226986193
Winsorized Mean ( 5 / 20 )34903.2333333333405.45618401537486.0838598826498
Winsorized Mean ( 6 / 20 )34890.3333333333402.43985174800186.6970136823848
Winsorized Mean ( 7 / 20 )34886.3666666667400.46307797014987.1150639991513
Winsorized Mean ( 8 / 20 )34873.3397.25972043516687.7846361111042
Winsorized Mean ( 9 / 20 )34902.4391.02776080160189.258112847156
Winsorized Mean ( 10 / 20 )34913.2333333333387.65719637596290.0621313359377
Winsorized Mean ( 11 / 20 )34934.6833333333380.8672793225691.7240341450988
Winsorized Mean ( 12 / 20 )34934.8833333333374.26786088336193.3419269580847
Winsorized Mean ( 13 / 20 )34978.65364.99368063951495.8335770052596
Winsorized Mean ( 14 / 20 )35033.95354.37170981144898.862152451844
Winsorized Mean ( 15 / 20 )35050.7351.40546084203799.7443235970539
Winsorized Mean ( 16 / 20 )35058.1666666667350.145709916969100.12450723723
Winsorized Mean ( 17 / 20 )35059.0166666667339.575163701943103.243759892402
Winsorized Mean ( 18 / 20 )35084.2166666667330.122502593288106.276356174031
Winsorized Mean ( 19 / 20 )35077.25323.052542144271108.580634491138
Winsorized Mean ( 20 / 20 )34774.25263.315730254451132.062941953359
Trimmed Mean ( 1 / 20 )34898.7586206897425.71523554219181.976766878551
Trimmed Mean ( 2 / 20 )34901.3035714286420.16479522042983.0657493641714
Trimmed Mean ( 3 / 20 )34913.6296296296416.3759994925183.851205814416
Trimmed Mean ( 4 / 20 )34924.8653846154411.80825542652884.8085605968296
Trimmed Mean ( 5 / 20 )34945.58409.03026392696685.4351941210876
Trimmed Mean ( 6 / 20 )34956.1666666667407.95533597021685.6862592164224
Trimmed Mean ( 7 / 20 )34970.4782608696406.72454059457185.9807431578824
Trimmed Mean ( 8 / 20 )34986.8636363636404.89456460546686.4098130594943
Trimmed Mean ( 9 / 20 )35007.1428571429402.51690375254786.9706154717517
Trimmed Mean ( 10 / 20 )35024.6400.13694098203687.5315333646548
Trimmed Mean ( 11 / 20 )35042.1842105263396.87919459194188.2943341148322
Trimmed Mean ( 12 / 20 )35058.4722222222393.23743279268789.1534459810822
Trimmed Mean ( 13 / 20 )35076.6470588235388.86868199972290.2017793730393
Trimmed Mean ( 14 / 20 )35090.78125384.15078297621691.3463744057306
Trimmed Mean ( 15 / 20 )35098.9379.16775576450992.5682615844555
Trimmed Mean ( 16 / 20 )35105.7857142857371.36885483525494.5307751503806
Trimmed Mean ( 17 / 20 )35112.6538461538358.72564593746997.8816380813611
Trimmed Mean ( 18 / 20 )35120.5416666667341.939809407811102.709718787907
Trimmed Mean ( 19 / 20 )35126.0454545455317.897138726828110.495003494604
Trimmed Mean ( 20 / 20 )35133.75279.535412265649125.686222418974
Median35450
Midrange34706.5
Midmean - Weighted Average at Xnp34989.4838709677
Midmean - Weighted Average at X(n+1)p35098.9
Midmean - Empirical Distribution Function34989.4838709677
Midmean - Empirical Distribution Function - Averaging35098.9
Midmean - Empirical Distribution Function - Interpolation35098.9
Midmean - Closest Observation34989.4838709677
Midmean - True Basic - Statistics Graphics Toolkit35098.9
Midmean - MS Excel (old versions)35090.78125
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')