Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Mar 2017 17:21:29 +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/2017/Mar/13/t148942572931rt7qgk356p8em.htm/, Retrieved Tue, 14 May 2024 20:27:30 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 20:27:30 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
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
674
664
653
635
614
595
580
570
608
617
591
565
603
612
599
587
557
528
517
484
514
510
495
458




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean594.9666666666678.8169061623084667.4802085577478
Geometric Mean591.026943780338
Harmonic Mean587.014133686627
Quadratic Mean598.8087062382
Winsorized Mean ( 1 / 20 )595.1833333333338.6586389917935268.7386705806115
Winsorized Mean ( 2 / 20 )595.2166666666678.6363144625060968.9202169803745
Winsorized Mean ( 3 / 20 )594.3166666666678.3517477336876271.1607540861693
Winsorized Mean ( 4 / 20 )593.658.091280966794873.3690997057494
Winsorized Mean ( 5 / 20 )593.48.0471842989484873.7400782628452
Winsorized Mean ( 6 / 20 )593.67.9682349589844574.4957952489461
Winsorized Mean ( 7 / 20 )594.8833333333337.6741584005224277.5177292786707
Winsorized Mean ( 8 / 20 )594.4833333333337.5574070997639878.6623408644876
Winsorized Mean ( 9 / 20 )593.5833333333337.4086638725648780.1201597944591
Winsorized Mean ( 10 / 20 )593.257.2400574723816881.9399572811464
Winsorized Mean ( 11 / 20 )592.157.0107594872146884.4630315845076
Winsorized Mean ( 12 / 20 )590.556.7840967657127187.0491710826827
Winsorized Mean ( 13 / 20 )590.556.5729468234196889.845546581306
Winsorized Mean ( 14 / 20 )592.8833333333336.0652800768427997.750363680147
Winsorized Mean ( 15 / 20 )592.3833333333335.84271682735613101.388335398995
Winsorized Mean ( 16 / 20 )594.255.34608072292639111.156196622993
Winsorized Mean ( 17 / 20 )596.84.90749455678341121.609915832728
Winsorized Mean ( 18 / 20 )598.94.5589484861572131.36801212352
Winsorized Mean ( 19 / 20 )599.2166666666674.41351875879949135.768464894813
Winsorized Mean ( 20 / 20 )601.8833333333333.98798277219663150.924256125061
Trimmed Mean ( 1 / 20 )5958.4882396135027470.0969844269592
Trimmed Mean ( 2 / 20 )594.8035714285718.2766852814764371.8649496990984
Trimmed Mean ( 3 / 20 )594.5740740740748.0281911503120274.0607769473658
Trimmed Mean ( 4 / 20 )594.6730769230777.8551997916092675.7043859735169
Trimmed Mean ( 5 / 20 )594.987.7351300399342976.9191981166815
Trimmed Mean ( 6 / 20 )595.3757.5916752302386178.4247194385431
Trimmed Mean ( 7 / 20 )595.7608695652177.4273411073698480.2118632970915
Trimmed Mean ( 8 / 20 )595.9318181818187.296020935249881.6790170245605
Trimmed Mean ( 9 / 20 )596.1904761904767.1491687174825883.3929789253053
Trimmed Mean ( 10 / 20 )596.6256.9866803220898185.394632714717
Trimmed Mean ( 11 / 20 )597.1578947368426.8060434942203987.7393591804021
Trimmed Mean ( 12 / 20 )597.9166666666676.6113628736909590.4377324448485
Trimmed Mean ( 13 / 20 )5996.3873761416597893.7787264622165
Trimmed Mean ( 14 / 20 )600.218756.120057975788898.0740300785532
Trimmed Mean ( 15 / 20 )601.2666666666675.89602112734509101.978377227663
Trimmed Mean ( 16 / 20 )602.5357142857145.61589819594703107.291067833203
Trimmed Mean ( 17 / 20 )603.7307692307695.36586295083098112.513266694087
Trimmed Mean ( 18 / 20 )604.755.14403059133961117.563453261368
Trimmed Mean ( 19 / 20 )605.6363636363644.92345981126928123.010319338877
Trimmed Mean ( 20 / 20 )606.654.59076590330496132.14570570093
Median610
Midrange594
Midmean - Weighted Average at Xnp598.903225806452
Midmean - Weighted Average at X(n+1)p601.266666666667
Midmean - Empirical Distribution Function598.903225806452
Midmean - Empirical Distribution Function - Averaging601.266666666667
Midmean - Empirical Distribution Function - Interpolation601.266666666667
Midmean - Closest Observation598.903225806452
Midmean - True Basic - Statistics Graphics Toolkit601.266666666667
Midmean - MS Excel (old versions)600.21875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 594.966666666667 & 8.81690616230846 & 67.4802085577478 \tabularnewline
Geometric Mean & 591.026943780338 &  &  \tabularnewline
Harmonic Mean & 587.014133686627 &  &  \tabularnewline
Quadratic Mean & 598.8087062382 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 595.183333333333 & 8.65863899179352 & 68.7386705806115 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 595.216666666667 & 8.63631446250609 & 68.9202169803745 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 594.316666666667 & 8.35174773368762 & 71.1607540861693 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 593.65 & 8.0912809667948 & 73.3690997057494 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 593.4 & 8.04718429894848 & 73.7400782628452 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 593.6 & 7.96823495898445 & 74.4957952489461 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 594.883333333333 & 7.67415840052242 & 77.5177292786707 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 594.483333333333 & 7.55740709976398 & 78.6623408644876 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 593.583333333333 & 7.40866387256487 & 80.1201597944591 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 593.25 & 7.24005747238168 & 81.9399572811464 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 592.15 & 7.01075948721468 & 84.4630315845076 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 590.55 & 6.78409676571271 & 87.0491710826827 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 590.55 & 6.57294682341968 & 89.845546581306 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 592.883333333333 & 6.06528007684279 & 97.750363680147 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 592.383333333333 & 5.84271682735613 & 101.388335398995 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 594.25 & 5.34608072292639 & 111.156196622993 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 596.8 & 4.90749455678341 & 121.609915832728 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 598.9 & 4.5589484861572 & 131.36801212352 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 599.216666666667 & 4.41351875879949 & 135.768464894813 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 601.883333333333 & 3.98798277219663 & 150.924256125061 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 595 & 8.48823961350274 & 70.0969844269592 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 594.803571428571 & 8.27668528147643 & 71.8649496990984 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 594.574074074074 & 8.02819115031202 & 74.0607769473658 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 594.673076923077 & 7.85519979160926 & 75.7043859735169 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 594.98 & 7.73513003993429 & 76.9191981166815 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 595.375 & 7.59167523023861 & 78.4247194385431 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 595.760869565217 & 7.42734110736984 & 80.2118632970915 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 595.931818181818 & 7.2960209352498 & 81.6790170245605 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 596.190476190476 & 7.14916871748258 & 83.3929789253053 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 596.625 & 6.98668032208981 & 85.394632714717 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 597.157894736842 & 6.80604349422039 & 87.7393591804021 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 597.916666666667 & 6.61136287369095 & 90.4377324448485 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 599 & 6.38737614165978 & 93.7787264622165 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 600.21875 & 6.1200579757888 & 98.0740300785532 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 601.266666666667 & 5.89602112734509 & 101.978377227663 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 602.535714285714 & 5.61589819594703 & 107.291067833203 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 603.730769230769 & 5.36586295083098 & 112.513266694087 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 604.75 & 5.14403059133961 & 117.563453261368 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 605.636363636364 & 4.92345981126928 & 123.010319338877 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 606.65 & 4.59076590330496 & 132.14570570093 \tabularnewline
Median & 610 &  &  \tabularnewline
Midrange & 594 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 598.903225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 601.266666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 598.903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 601.266666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 601.266666666667 &  &  \tabularnewline
Midmean - Closest Observation & 598.903225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 601.266666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 600.21875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]594.966666666667[/C][C]8.81690616230846[/C][C]67.4802085577478[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]591.026943780338[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]587.014133686627[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]598.8087062382[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]595.183333333333[/C][C]8.65863899179352[/C][C]68.7386705806115[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]595.216666666667[/C][C]8.63631446250609[/C][C]68.9202169803745[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]594.316666666667[/C][C]8.35174773368762[/C][C]71.1607540861693[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]593.65[/C][C]8.0912809667948[/C][C]73.3690997057494[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]593.4[/C][C]8.04718429894848[/C][C]73.7400782628452[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]593.6[/C][C]7.96823495898445[/C][C]74.4957952489461[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]594.883333333333[/C][C]7.67415840052242[/C][C]77.5177292786707[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]594.483333333333[/C][C]7.55740709976398[/C][C]78.6623408644876[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]593.583333333333[/C][C]7.40866387256487[/C][C]80.1201597944591[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]593.25[/C][C]7.24005747238168[/C][C]81.9399572811464[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]592.15[/C][C]7.01075948721468[/C][C]84.4630315845076[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]590.55[/C][C]6.78409676571271[/C][C]87.0491710826827[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]590.55[/C][C]6.57294682341968[/C][C]89.845546581306[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]592.883333333333[/C][C]6.06528007684279[/C][C]97.750363680147[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]592.383333333333[/C][C]5.84271682735613[/C][C]101.388335398995[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]594.25[/C][C]5.34608072292639[/C][C]111.156196622993[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]596.8[/C][C]4.90749455678341[/C][C]121.609915832728[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]598.9[/C][C]4.5589484861572[/C][C]131.36801212352[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]599.216666666667[/C][C]4.41351875879949[/C][C]135.768464894813[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]601.883333333333[/C][C]3.98798277219663[/C][C]150.924256125061[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]595[/C][C]8.48823961350274[/C][C]70.0969844269592[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]594.803571428571[/C][C]8.27668528147643[/C][C]71.8649496990984[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]594.574074074074[/C][C]8.02819115031202[/C][C]74.0607769473658[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]594.673076923077[/C][C]7.85519979160926[/C][C]75.7043859735169[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]594.98[/C][C]7.73513003993429[/C][C]76.9191981166815[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]595.375[/C][C]7.59167523023861[/C][C]78.4247194385431[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]595.760869565217[/C][C]7.42734110736984[/C][C]80.2118632970915[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]595.931818181818[/C][C]7.2960209352498[/C][C]81.6790170245605[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]596.190476190476[/C][C]7.14916871748258[/C][C]83.3929789253053[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]596.625[/C][C]6.98668032208981[/C][C]85.394632714717[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]597.157894736842[/C][C]6.80604349422039[/C][C]87.7393591804021[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]597.916666666667[/C][C]6.61136287369095[/C][C]90.4377324448485[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]599[/C][C]6.38737614165978[/C][C]93.7787264622165[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]600.21875[/C][C]6.1200579757888[/C][C]98.0740300785532[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]601.266666666667[/C][C]5.89602112734509[/C][C]101.978377227663[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]602.535714285714[/C][C]5.61589819594703[/C][C]107.291067833203[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]603.730769230769[/C][C]5.36586295083098[/C][C]112.513266694087[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]604.75[/C][C]5.14403059133961[/C][C]117.563453261368[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]605.636363636364[/C][C]4.92345981126928[/C][C]123.010319338877[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]606.65[/C][C]4.59076590330496[/C][C]132.14570570093[/C][/ROW]
[ROW][C]Median[/C][C]610[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]594[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]598.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]601.266666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]598.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]601.266666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]601.266666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]598.903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]601.266666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]600.21875[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean594.9666666666678.8169061623084667.4802085577478
Geometric Mean591.026943780338
Harmonic Mean587.014133686627
Quadratic Mean598.8087062382
Winsorized Mean ( 1 / 20 )595.1833333333338.6586389917935268.7386705806115
Winsorized Mean ( 2 / 20 )595.2166666666678.6363144625060968.9202169803745
Winsorized Mean ( 3 / 20 )594.3166666666678.3517477336876271.1607540861693
Winsorized Mean ( 4 / 20 )593.658.091280966794873.3690997057494
Winsorized Mean ( 5 / 20 )593.48.0471842989484873.7400782628452
Winsorized Mean ( 6 / 20 )593.67.9682349589844574.4957952489461
Winsorized Mean ( 7 / 20 )594.8833333333337.6741584005224277.5177292786707
Winsorized Mean ( 8 / 20 )594.4833333333337.5574070997639878.6623408644876
Winsorized Mean ( 9 / 20 )593.5833333333337.4086638725648780.1201597944591
Winsorized Mean ( 10 / 20 )593.257.2400574723816881.9399572811464
Winsorized Mean ( 11 / 20 )592.157.0107594872146884.4630315845076
Winsorized Mean ( 12 / 20 )590.556.7840967657127187.0491710826827
Winsorized Mean ( 13 / 20 )590.556.5729468234196889.845546581306
Winsorized Mean ( 14 / 20 )592.8833333333336.0652800768427997.750363680147
Winsorized Mean ( 15 / 20 )592.3833333333335.84271682735613101.388335398995
Winsorized Mean ( 16 / 20 )594.255.34608072292639111.156196622993
Winsorized Mean ( 17 / 20 )596.84.90749455678341121.609915832728
Winsorized Mean ( 18 / 20 )598.94.5589484861572131.36801212352
Winsorized Mean ( 19 / 20 )599.2166666666674.41351875879949135.768464894813
Winsorized Mean ( 20 / 20 )601.8833333333333.98798277219663150.924256125061
Trimmed Mean ( 1 / 20 )5958.4882396135027470.0969844269592
Trimmed Mean ( 2 / 20 )594.8035714285718.2766852814764371.8649496990984
Trimmed Mean ( 3 / 20 )594.5740740740748.0281911503120274.0607769473658
Trimmed Mean ( 4 / 20 )594.6730769230777.8551997916092675.7043859735169
Trimmed Mean ( 5 / 20 )594.987.7351300399342976.9191981166815
Trimmed Mean ( 6 / 20 )595.3757.5916752302386178.4247194385431
Trimmed Mean ( 7 / 20 )595.7608695652177.4273411073698480.2118632970915
Trimmed Mean ( 8 / 20 )595.9318181818187.296020935249881.6790170245605
Trimmed Mean ( 9 / 20 )596.1904761904767.1491687174825883.3929789253053
Trimmed Mean ( 10 / 20 )596.6256.9866803220898185.394632714717
Trimmed Mean ( 11 / 20 )597.1578947368426.8060434942203987.7393591804021
Trimmed Mean ( 12 / 20 )597.9166666666676.6113628736909590.4377324448485
Trimmed Mean ( 13 / 20 )5996.3873761416597893.7787264622165
Trimmed Mean ( 14 / 20 )600.218756.120057975788898.0740300785532
Trimmed Mean ( 15 / 20 )601.2666666666675.89602112734509101.978377227663
Trimmed Mean ( 16 / 20 )602.5357142857145.61589819594703107.291067833203
Trimmed Mean ( 17 / 20 )603.7307692307695.36586295083098112.513266694087
Trimmed Mean ( 18 / 20 )604.755.14403059133961117.563453261368
Trimmed Mean ( 19 / 20 )605.6363636363644.92345981126928123.010319338877
Trimmed Mean ( 20 / 20 )606.654.59076590330496132.14570570093
Median610
Midrange594
Midmean - Weighted Average at Xnp598.903225806452
Midmean - Weighted Average at X(n+1)p601.266666666667
Midmean - Empirical Distribution Function598.903225806452
Midmean - Empirical Distribution Function - Averaging601.266666666667
Midmean - Empirical Distribution Function - Interpolation601.266666666667
Midmean - Closest Observation598.903225806452
Midmean - True Basic - Statistics Graphics Toolkit601.266666666667
Midmean - MS Excel (old versions)600.21875
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')