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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 10 Oct 2015 19:19:36 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/10/t144450134065186cm6v2o80dl.htm/, Retrieved Tue, 14 May 2024 16:17:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282279, Retrieved Tue, 14 May 2024 16:17:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
467
475
470
442
433
427
410
406
429
425
431
408
454
459
441
420
416
400
401
398
442
458
476
447
511
514
513
511
498
490
495
486
530
539
555
548
615
634
645
634
630
635
642
637
675
679
676
660
716
730
717
694
670
641
626
604
630
634
635
619




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282279&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282279&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282279&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean538.38333333333313.306663121440140.4596801181411
Geometric Mean528.786585388393
Harmonic Mean519.457363529452
Quadratic Mean547.999619829552
Winsorized Mean ( 1 / 20 )538.213.249513369168540.6203597826006
Winsorized Mean ( 2 / 20 )538.213.236031972342840.6617331481662
Winsorized Mean ( 3 / 20 )537.3512.954501540757641.4797897325021
Winsorized Mean ( 4 / 20 )536.48333333333312.734256740262942.1291437950276
Winsorized Mean ( 5 / 20 )536.412.658826000313642.3735976769657
Winsorized Mean ( 6 / 20 )536.912.540346186843342.8138100815181
Winsorized Mean ( 7 / 20 )536.78333333333312.357094800238143.4392826154405
Winsorized Mean ( 8 / 20 )536.11666666666712.01301299290144.6279935752572
Winsorized Mean ( 9 / 20 )534.16666666666711.586695240289146.1017275063274
Winsorized Mean ( 10 / 20 )53411.45418286412246.6205233786385
Winsorized Mean ( 11 / 20 )534.18333333333311.368245288593146.989075250631
Winsorized Mean ( 12 / 20 )533.78333333333311.180620129417847.7418360658612
Winsorized Mean ( 13 / 20 )535.08333333333310.853083908279349.3024229661714
Winsorized Mean ( 14 / 20 )535.31666666666710.818886281713549.4798311700051
Winsorized Mean ( 15 / 20 )535.06666666666710.779921350893549.635488910345
Winsorized Mean ( 16 / 20 )536.410.586933637357350.6662286147941
Winsorized Mean ( 17 / 20 )538.38333333333310.307341787625552.2329951238924
Winsorized Mean ( 18 / 20 )538.3833333333339.9539928015360854.087173264808
Winsorized Mean ( 19 / 20 )538.79.9107400511557154.3551740051119
Winsorized Mean ( 20 / 20 )540.0333333333339.3441714715453657.7936026728351
Trimmed Mean ( 1 / 20 )537.513.134656733295840.9222723451509
Trimmed Mean ( 2 / 20 )536.7512.983387237383241.3412917743477
Trimmed Mean ( 3 / 20 )535.94444444444412.795723884646941.8846521913079
Trimmed Mean ( 4 / 20 )535.40384615384612.684751109915442.2084628633612
Trimmed Mean ( 5 / 20 )535.0812.61449894658842.4178560135938
Trimmed Mean ( 6 / 20 )534.7512.532740809518942.6682405810103
Trimmed Mean ( 7 / 20 )534.28260869565212.44441411051942.933528565562
Trimmed Mean ( 8 / 20 )533.79545454545512.360792698562843.1845649031488
Trimmed Mean ( 9 / 20 )533.38095238095212.318505968364343.2991593096395
Trimmed Mean ( 10 / 20 )533.2512.339469194418443.2149869332475
Trimmed Mean ( 11 / 20 )533.13157894736812.361159001200543.1295786176353
Trimmed Mean ( 12 / 20 )532.97222222222212.368898920026343.0897063407395
Trimmed Mean ( 13 / 20 )532.85294117647112.379553923822843.0429839762697
Trimmed Mean ( 14 / 20 )532.5312512.42217583070542.869402048206
Trimmed Mean ( 15 / 20 )532.13333333333312.42797487070942.817380858043
Trimmed Mean ( 16 / 20 )531.71428571428612.380097650594142.9491188778118
Trimmed Mean ( 17 / 20 )531.03846153846212.292521900511643.2001232811603
Trimmed Mean ( 18 / 20 )529.95833333333312.162468875791243.5732529920952
Trimmed Mean ( 19 / 20 )528.68181818181811.991408606250744.0883832368315
Trimmed Mean ( 20 / 20 )527.111.61462326914745.3824448529627
Median512
Midrange564
Midmean - Weighted Average at Xnp529.225806451613
Midmean - Weighted Average at X(n+1)p529.225806451613
Midmean - Empirical Distribution Function529.225806451613
Midmean - Empirical Distribution Function - Averaging529.225806451613
Midmean - Empirical Distribution Function - Interpolation529.225806451613
Midmean - Closest Observation529.225806451613
Midmean - True Basic - Statistics Graphics Toolkit529.225806451613
Midmean - MS Excel (old versions)535.636363636364
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 538.383333333333 & 13.3066631214401 & 40.4596801181411 \tabularnewline
Geometric Mean & 528.786585388393 &  &  \tabularnewline
Harmonic Mean & 519.457363529452 &  &  \tabularnewline
Quadratic Mean & 547.999619829552 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 538.2 & 13.2495133691685 & 40.6203597826006 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 538.2 & 13.2360319723428 & 40.6617331481662 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 537.35 & 12.9545015407576 & 41.4797897325021 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 536.483333333333 & 12.7342567402629 & 42.1291437950276 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 536.4 & 12.6588260003136 & 42.3735976769657 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 536.9 & 12.5403461868433 & 42.8138100815181 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 536.783333333333 & 12.3570948002381 & 43.4392826154405 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 536.116666666667 & 12.013012992901 & 44.6279935752572 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 534.166666666667 & 11.5866952402891 & 46.1017275063274 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 534 & 11.454182864122 & 46.6205233786385 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 534.183333333333 & 11.3682452885931 & 46.989075250631 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 533.783333333333 & 11.1806201294178 & 47.7418360658612 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 535.083333333333 & 10.8530839082793 & 49.3024229661714 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 535.316666666667 & 10.8188862817135 & 49.4798311700051 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 535.066666666667 & 10.7799213508935 & 49.635488910345 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 536.4 & 10.5869336373573 & 50.6662286147941 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 538.383333333333 & 10.3073417876255 & 52.2329951238924 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 538.383333333333 & 9.95399280153608 & 54.087173264808 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 538.7 & 9.91074005115571 & 54.3551740051119 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 540.033333333333 & 9.34417147154536 & 57.7936026728351 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 537.5 & 13.1346567332958 & 40.9222723451509 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 536.75 & 12.9833872373832 & 41.3412917743477 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 535.944444444444 & 12.7957238846469 & 41.8846521913079 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 535.403846153846 & 12.6847511099154 & 42.2084628633612 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 535.08 & 12.614498946588 & 42.4178560135938 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 534.75 & 12.5327408095189 & 42.6682405810103 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 534.282608695652 & 12.444414110519 & 42.933528565562 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 533.795454545455 & 12.3607926985628 & 43.1845649031488 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 533.380952380952 & 12.3185059683643 & 43.2991593096395 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 533.25 & 12.3394691944184 & 43.2149869332475 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 533.131578947368 & 12.3611590012005 & 43.1295786176353 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 532.972222222222 & 12.3688989200263 & 43.0897063407395 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 532.852941176471 & 12.3795539238228 & 43.0429839762697 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 532.53125 & 12.422175830705 & 42.869402048206 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 532.133333333333 & 12.427974870709 & 42.817380858043 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 531.714285714286 & 12.3800976505941 & 42.9491188778118 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 531.038461538462 & 12.2925219005116 & 43.2001232811603 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 529.958333333333 & 12.1624688757912 & 43.5732529920952 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 528.681818181818 & 11.9914086062507 & 44.0883832368315 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 527.1 & 11.614623269147 & 45.3824448529627 \tabularnewline
Median & 512 &  &  \tabularnewline
Midrange & 564 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 529.225806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 529.225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 529.225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 529.225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 529.225806451613 &  &  \tabularnewline
Midmean - Closest Observation & 529.225806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 529.225806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 535.636363636364 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282279&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]538.383333333333[/C][C]13.3066631214401[/C][C]40.4596801181411[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]528.786585388393[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]519.457363529452[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]547.999619829552[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]538.2[/C][C]13.2495133691685[/C][C]40.6203597826006[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]538.2[/C][C]13.2360319723428[/C][C]40.6617331481662[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]537.35[/C][C]12.9545015407576[/C][C]41.4797897325021[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]536.483333333333[/C][C]12.7342567402629[/C][C]42.1291437950276[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]536.4[/C][C]12.6588260003136[/C][C]42.3735976769657[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]536.9[/C][C]12.5403461868433[/C][C]42.8138100815181[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]536.783333333333[/C][C]12.3570948002381[/C][C]43.4392826154405[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]536.116666666667[/C][C]12.013012992901[/C][C]44.6279935752572[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]534.166666666667[/C][C]11.5866952402891[/C][C]46.1017275063274[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]534[/C][C]11.454182864122[/C][C]46.6205233786385[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]534.183333333333[/C][C]11.3682452885931[/C][C]46.989075250631[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]533.783333333333[/C][C]11.1806201294178[/C][C]47.7418360658612[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]535.083333333333[/C][C]10.8530839082793[/C][C]49.3024229661714[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]535.316666666667[/C][C]10.8188862817135[/C][C]49.4798311700051[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]535.066666666667[/C][C]10.7799213508935[/C][C]49.635488910345[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]536.4[/C][C]10.5869336373573[/C][C]50.6662286147941[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]538.383333333333[/C][C]10.3073417876255[/C][C]52.2329951238924[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]538.383333333333[/C][C]9.95399280153608[/C][C]54.087173264808[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]538.7[/C][C]9.91074005115571[/C][C]54.3551740051119[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]540.033333333333[/C][C]9.34417147154536[/C][C]57.7936026728351[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]537.5[/C][C]13.1346567332958[/C][C]40.9222723451509[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]536.75[/C][C]12.9833872373832[/C][C]41.3412917743477[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]535.944444444444[/C][C]12.7957238846469[/C][C]41.8846521913079[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]535.403846153846[/C][C]12.6847511099154[/C][C]42.2084628633612[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]535.08[/C][C]12.614498946588[/C][C]42.4178560135938[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]534.75[/C][C]12.5327408095189[/C][C]42.6682405810103[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]534.282608695652[/C][C]12.444414110519[/C][C]42.933528565562[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]533.795454545455[/C][C]12.3607926985628[/C][C]43.1845649031488[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]533.380952380952[/C][C]12.3185059683643[/C][C]43.2991593096395[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]533.25[/C][C]12.3394691944184[/C][C]43.2149869332475[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]533.131578947368[/C][C]12.3611590012005[/C][C]43.1295786176353[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]532.972222222222[/C][C]12.3688989200263[/C][C]43.0897063407395[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]532.852941176471[/C][C]12.3795539238228[/C][C]43.0429839762697[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]532.53125[/C][C]12.422175830705[/C][C]42.869402048206[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]532.133333333333[/C][C]12.427974870709[/C][C]42.817380858043[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]531.714285714286[/C][C]12.3800976505941[/C][C]42.9491188778118[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]531.038461538462[/C][C]12.2925219005116[/C][C]43.2001232811603[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]529.958333333333[/C][C]12.1624688757912[/C][C]43.5732529920952[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]528.681818181818[/C][C]11.9914086062507[/C][C]44.0883832368315[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]527.1[/C][C]11.614623269147[/C][C]45.3824448529627[/C][/ROW]
[ROW][C]Median[/C][C]512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]529.225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]529.225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]529.225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]529.225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]529.225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]529.225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]529.225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]535.636363636364[/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=282279&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282279&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 Mean538.38333333333313.306663121440140.4596801181411
Geometric Mean528.786585388393
Harmonic Mean519.457363529452
Quadratic Mean547.999619829552
Winsorized Mean ( 1 / 20 )538.213.249513369168540.6203597826006
Winsorized Mean ( 2 / 20 )538.213.236031972342840.6617331481662
Winsorized Mean ( 3 / 20 )537.3512.954501540757641.4797897325021
Winsorized Mean ( 4 / 20 )536.48333333333312.734256740262942.1291437950276
Winsorized Mean ( 5 / 20 )536.412.658826000313642.3735976769657
Winsorized Mean ( 6 / 20 )536.912.540346186843342.8138100815181
Winsorized Mean ( 7 / 20 )536.78333333333312.357094800238143.4392826154405
Winsorized Mean ( 8 / 20 )536.11666666666712.01301299290144.6279935752572
Winsorized Mean ( 9 / 20 )534.16666666666711.586695240289146.1017275063274
Winsorized Mean ( 10 / 20 )53411.45418286412246.6205233786385
Winsorized Mean ( 11 / 20 )534.18333333333311.368245288593146.989075250631
Winsorized Mean ( 12 / 20 )533.78333333333311.180620129417847.7418360658612
Winsorized Mean ( 13 / 20 )535.08333333333310.853083908279349.3024229661714
Winsorized Mean ( 14 / 20 )535.31666666666710.818886281713549.4798311700051
Winsorized Mean ( 15 / 20 )535.06666666666710.779921350893549.635488910345
Winsorized Mean ( 16 / 20 )536.410.586933637357350.6662286147941
Winsorized Mean ( 17 / 20 )538.38333333333310.307341787625552.2329951238924
Winsorized Mean ( 18 / 20 )538.3833333333339.9539928015360854.087173264808
Winsorized Mean ( 19 / 20 )538.79.9107400511557154.3551740051119
Winsorized Mean ( 20 / 20 )540.0333333333339.3441714715453657.7936026728351
Trimmed Mean ( 1 / 20 )537.513.134656733295840.9222723451509
Trimmed Mean ( 2 / 20 )536.7512.983387237383241.3412917743477
Trimmed Mean ( 3 / 20 )535.94444444444412.795723884646941.8846521913079
Trimmed Mean ( 4 / 20 )535.40384615384612.684751109915442.2084628633612
Trimmed Mean ( 5 / 20 )535.0812.61449894658842.4178560135938
Trimmed Mean ( 6 / 20 )534.7512.532740809518942.6682405810103
Trimmed Mean ( 7 / 20 )534.28260869565212.44441411051942.933528565562
Trimmed Mean ( 8 / 20 )533.79545454545512.360792698562843.1845649031488
Trimmed Mean ( 9 / 20 )533.38095238095212.318505968364343.2991593096395
Trimmed Mean ( 10 / 20 )533.2512.339469194418443.2149869332475
Trimmed Mean ( 11 / 20 )533.13157894736812.361159001200543.1295786176353
Trimmed Mean ( 12 / 20 )532.97222222222212.368898920026343.0897063407395
Trimmed Mean ( 13 / 20 )532.85294117647112.379553923822843.0429839762697
Trimmed Mean ( 14 / 20 )532.5312512.42217583070542.869402048206
Trimmed Mean ( 15 / 20 )532.13333333333312.42797487070942.817380858043
Trimmed Mean ( 16 / 20 )531.71428571428612.380097650594142.9491188778118
Trimmed Mean ( 17 / 20 )531.03846153846212.292521900511643.2001232811603
Trimmed Mean ( 18 / 20 )529.95833333333312.162468875791243.5732529920952
Trimmed Mean ( 19 / 20 )528.68181818181811.991408606250744.0883832368315
Trimmed Mean ( 20 / 20 )527.111.61462326914745.3824448529627
Median512
Midrange564
Midmean - Weighted Average at Xnp529.225806451613
Midmean - Weighted Average at X(n+1)p529.225806451613
Midmean - Empirical Distribution Function529.225806451613
Midmean - Empirical Distribution Function - Averaging529.225806451613
Midmean - Empirical Distribution Function - Interpolation529.225806451613
Midmean - Closest Observation529.225806451613
Midmean - True Basic - Statistics Graphics Toolkit529.225806451613
Midmean - MS Excel (old versions)535.636363636364
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')